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SInE---0.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM473+1 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n121.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 15:21:28 EST 2018

% Result   : Theorem 1.61s
% Output   : CNFRefutation 1.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  248 (  35 unt;   0 def)
%            Number of atoms       : 1070 ( 244 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives : 1381 ( 559   ~; 705   |;  92   &)
%                                         (   4 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :  312 (   1 sgn 143   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X2,X3) )
       => doDivides0(X1,X3) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mDivTrans) ).

fof(7,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & equal(X2,sdtasdt0(X1,X3)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mDefDiv) ).

fof(9,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( ~ equal(X2,X1)
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mLETotal) ).

fof(10,axiom,
    ~ equal(xl,sz00),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__1347) ).

fof(12,axiom,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__1409) ).

fof(16,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( ~ equal(X1,sz00)
          & ~ equal(X2,X3)
          & sdtlseqdt0(X2,X3) )
       => ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
          & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mMonMul) ).

fof(17,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & equal(sdtpldt0(X1,X3),X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mDefLE) ).

fof(19,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => equal(X1,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mLEAsym) ).

fof(20,axiom,
    equal(xp,sdtsldt0(xm,xl)),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__1360) ).

fof(21,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( ~ equal(X1,sz00)
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( equal(X3,sdtsldt0(X2,X1))
          <=> ( aNaturalNumber0(X3)
              & equal(X2,sdtasdt0(X1,X3)) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mDefQuot) ).

fof(22,axiom,
    ( doDivides0(xl,xm)
    & doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__1324_04) ).

fof(24,axiom,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__1324) ).

fof(26,axiom,
    ( aNaturalNumber0(sz10)
    & ~ equal(sz10,sz00) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mSortsC_01) ).

fof(27,axiom,
    equal(xq,sdtsldt0(sdtpldt0(xm,xn),xl)),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__1379) ).

fof(28,conjecture,
    sdtlseqdt0(xp,xq),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m__) ).

fof(29,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mMulAsso) ).

fof(31,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => sdtlseqdt0(X1,X1) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mLERefl) ).

fof(32,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/tmp168nTy/sel_theBenchmark.p_1',mDefDiff) ).

fof(33,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mSortsB_02) ).

fof(34,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mSortsC) ).

fof(35,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',mSortsB) ).

fof(36,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/tmp168nTy/sel_theBenchmark.p_1',mAddCanc) ).

fof(39,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m_AddZero) ).

fof(40,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1',m_MulUnit) ).

fof(41,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(assume_negation,[status(cth)],[28]) ).

fof(42,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(fof_simplification,[status(thm)],[41,theory(equality)]) ).

fof(48,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X2,X3)
      | doDivides0(X1,X3) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(49,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ~ doDivides0(X4,X5)
      | ~ doDivides0(X5,X6)
      | doDivides0(X4,X6) ),
    inference(variable_rename,[status(thm)],[48]) ).

cnf(50,plain,
    ( doDivides0(X1,X2)
    | ~ doDivides0(X3,X2)
    | ~ doDivides0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[49]) ).

fof(68,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ( ( ~ doDivides0(X1,X2)
          | ? [X3] :
              ( aNaturalNumber0(X3)
              & equal(X2,sdtasdt0(X1,X3)) ) )
        & ( ! [X3] :
              ( ~ aNaturalNumber0(X3)
              | ~ equal(X2,sdtasdt0(X1,X3)) )
          | doDivides0(X1,X2) ) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(69,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ doDivides0(X4,X5)
          | ? [X6] :
              ( aNaturalNumber0(X6)
              & equal(X5,sdtasdt0(X4,X6)) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(X5,sdtasdt0(X4,X7)) )
          | doDivides0(X4,X5) ) ) ),
    inference(variable_rename,[status(thm)],[68]) ).

fof(70,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ doDivides0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(X5,sdtasdt0(X4,X7)) )
          | doDivides0(X4,X5) ) ) ),
    inference(skolemize,[status(esa)],[69]) ).

fof(71,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ aNaturalNumber0(X7)
          | ~ equal(X5,sdtasdt0(X4,X7))
          | doDivides0(X4,X5) )
        & ( ~ doDivides0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) ) )
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[70]) ).

fof(72,plain,
    ! [X4,X5,X7] :
      ( ( ~ aNaturalNumber0(X7)
        | ~ equal(X5,sdtasdt0(X4,X7))
        | doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( aNaturalNumber0(esk1_2(X4,X5))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( equal(X5,sdtasdt0(X4,esk1_2(X4,X5)))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[71]) ).

cnf(75,plain,
    ( doDivides0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 != sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[72]) ).

fof(79,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | sdtlseqdt0(X1,X2)
      | ( ~ equal(X2,X1)
        & sdtlseqdt0(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(80,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtlseqdt0(X3,X4)
      | ( ~ equal(X4,X3)
        & sdtlseqdt0(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[79]) ).

fof(81,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)],[80]) ).

cnf(82,plain,
    ( sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[81]) ).

cnf(84,plain,
    xl != sz00,
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(88,plain,
    sdtlseqdt0(xm,sdtpldt0(xm,xn)),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(103,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | equal(X1,sz00)
      | equal(X2,X3)
      | ~ sdtlseqdt0(X2,X3)
      | ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1))
        & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(104,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | equal(X4,sz00)
      | equal(X5,X6)
      | ~ sdtlseqdt0(X5,X6)
      | ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        & sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        & ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
        & sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) ) ),
    inference(variable_rename,[status(thm)],[103]) ).

fof(105,plain,
    ! [X4,X5,X6] :
      ( ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        | equal(X4,sz00)
        | equal(X5,X6)
        | ~ sdtlseqdt0(X5,X6)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( sdtlseqdt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        | equal(X4,sz00)
        | equal(X5,X6)
        | ~ sdtlseqdt0(X5,X6)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
        | equal(X4,sz00)
        | equal(X5,X6)
        | ~ sdtlseqdt0(X5,X6)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( sdtlseqdt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
        | equal(X4,sz00)
        | equal(X5,X6)
        | ~ sdtlseqdt0(X5,X6)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) ) ),
    inference(distribute,[status(thm)],[104]) ).

cnf(108,plain,
    ( X2 = X1
    | X3 = sz00
    | sdtlseqdt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

fof(110,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)],[17]) ).

fof(111,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)],[110]) ).

fof(112,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)],[111]) ).

fof(113,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)],[112]) ).

fof(114,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)],[113]) ).

cnf(117,plain,
    ( sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[114]) ).

fof(121,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X2,X1)
      | equal(X1,X2) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(122,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | ~ sdtlseqdt0(X3,X4)
      | ~ sdtlseqdt0(X4,X3)
      | equal(X3,X4) ),
    inference(variable_rename,[status(thm)],[121]) ).

cnf(123,plain,
    ( X1 = X2
    | ~ sdtlseqdt0(X2,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(124,plain,
    xp = sdtsldt0(xm,xl),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(125,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(X1,sz00)
      | ~ doDivides0(X1,X2)
      | ! [X3] :
          ( ( ~ equal(X3,sdtsldt0(X2,X1))
            | ( aNaturalNumber0(X3)
              & equal(X2,sdtasdt0(X1,X3)) ) )
          & ( ~ aNaturalNumber0(X3)
            | ~ equal(X2,sdtasdt0(X1,X3))
            | equal(X3,sdtsldt0(X2,X1)) ) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(126,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | equal(X4,sz00)
      | ~ doDivides0(X4,X5)
      | ! [X6] :
          ( ( ~ equal(X6,sdtsldt0(X5,X4))
            | ( aNaturalNumber0(X6)
              & equal(X5,sdtasdt0(X4,X6)) ) )
          & ( ~ aNaturalNumber0(X6)
            | ~ equal(X5,sdtasdt0(X4,X6))
            | equal(X6,sdtsldt0(X5,X4)) ) ) ),
    inference(variable_rename,[status(thm)],[125]) ).

fof(127,plain,
    ! [X4,X5,X6] :
      ( ( ( ~ equal(X6,sdtsldt0(X5,X4))
          | ( aNaturalNumber0(X6)
            & equal(X5,sdtasdt0(X4,X6)) ) )
        & ( ~ aNaturalNumber0(X6)
          | ~ equal(X5,sdtasdt0(X4,X6))
          | equal(X6,sdtsldt0(X5,X4)) ) )
      | equal(X4,sz00)
      | ~ doDivides0(X4,X5)
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[126]) ).

fof(128,plain,
    ! [X4,X5,X6] :
      ( ( aNaturalNumber0(X6)
        | ~ equal(X6,sdtsldt0(X5,X4))
        | equal(X4,sz00)
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( equal(X5,sdtasdt0(X4,X6))
        | ~ equal(X6,sdtsldt0(X5,X4))
        | equal(X4,sz00)
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( ~ aNaturalNumber0(X6)
        | ~ equal(X5,sdtasdt0(X4,X6))
        | equal(X6,sdtsldt0(X5,X4))
        | equal(X4,sz00)
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[127]) ).

cnf(129,plain,
    ( X2 = sz00
    | X3 = sdtsldt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1)
    | X1 != sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[128]) ).

cnf(130,plain,
    ( X2 = sz00
    | X1 = sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1)
    | X3 != sdtsldt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[128]) ).

cnf(131,plain,
    ( X2 = sz00
    | aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1)
    | X3 != sdtsldt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[128]) ).

cnf(132,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(133,plain,
    doDivides0(xl,xm),
    inference(split_conjunct,[status(thm)],[22]) ).

cnf(139,plain,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[24]) ).

cnf(140,plain,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[24]) ).

cnf(141,plain,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[24]) ).

cnf(145,plain,
    sz10 != sz00,
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(146,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(147,plain,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    inference(split_conjunct,[status(thm)],[27]) ).

cnf(148,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(149,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | equal(sdtasdt0(sdtasdt0(X1,X2),X3),sdtasdt0(X1,sdtasdt0(X2,X3))) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(150,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | equal(sdtasdt0(sdtasdt0(X4,X5),X6),sdtasdt0(X4,sdtasdt0(X5,X6))) ),
    inference(variable_rename,[status(thm)],[149]) ).

cnf(151,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[150]) ).

fof(157,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | sdtlseqdt0(X1,X1) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(158,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | sdtlseqdt0(X2,X2) ),
    inference(variable_rename,[status(thm)],[157]) ).

cnf(159,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[158]) ).

fof(160,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)],[32]) ).

fof(161,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)],[160]) ).

fof(162,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)],[161]) ).

fof(163,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)],[162]) ).

cnf(164,plain,
    ( X3 = sdtmndt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[163]) ).

cnf(165,plain,
    ( sdtpldt0(X2,X3) = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[163]) ).

fof(167,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[33]) ).

fof(168,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[167]) ).

cnf(169,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[168]) ).

cnf(170,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(171,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(172,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[171]) ).

cnf(173,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[172]) ).

fof(174,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)],[36]) ).

fof(175,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)],[174]) ).

fof(176,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)],[175]) ).

cnf(178,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
    inference(split_conjunct,[status(thm)],[176]) ).

fof(185,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(186,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtpldt0(X2,sz00),X2)
        & equal(X2,sdtpldt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[185]) ).

fof(187,plain,
    ! [X2] :
      ( ( equal(sdtpldt0(X2,sz00),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtpldt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[186]) ).

cnf(189,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[187]) ).

fof(190,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    inference(fof_nnf,[status(thm)],[40]) ).

fof(191,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz10),X2)
        & equal(X2,sdtasdt0(sz10,X2)) ) ),
    inference(variable_rename,[status(thm)],[190]) ).

fof(192,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz10),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtasdt0(sz10,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[191]) ).

cnf(193,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[192]) ).

cnf(252,plain,
    ( sdtpldt0(xm,xn) = xm
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(spm,[status(thm)],[123,88,theory(equality)]) ).

cnf(254,plain,
    ( sdtpldt0(xm,xn) = xm
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | $false
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[252,140,theory(equality)]) ).

cnf(255,plain,
    ( sdtpldt0(xm,xn) = xm
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(cn,[status(thm)],[254,theory(equality)]) ).

cnf(306,plain,
    ( doDivides0(sz10,X1)
    | X2 != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[75,193,theory(equality)]) ).

cnf(316,plain,
    ( doDivides0(sz10,X1)
    | X2 != X1
    | ~ aNaturalNumber0(X2)
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[306,146,theory(equality)]) ).

cnf(317,plain,
    ( doDivides0(sz10,X1)
    | X2 != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[316,theory(equality)]) ).

cnf(318,plain,
    ( doDivides0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[317,theory(equality)]) ).

cnf(360,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[178,189,theory(equality)]) ).

cnf(370,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[360,170,theory(equality)]) ).

cnf(371,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[370,theory(equality)]) ).

cnf(378,plain,
    ( doDivides0(X1,xm)
    | ~ doDivides0(X1,xl)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[50,133,theory(equality)]) ).

cnf(380,plain,
    ( doDivides0(X1,xm)
    | ~ doDivides0(X1,xl)
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[378,141,theory(equality)]) ).

cnf(381,plain,
    ( doDivides0(X1,xm)
    | ~ doDivides0(X1,xl)
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[380,140,theory(equality)]) ).

cnf(382,plain,
    ( doDivides0(X1,xm)
    | ~ doDivides0(X1,xl)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[381,theory(equality)]) ).

cnf(385,plain,
    ( sz00 = X1
    | aNaturalNumber0(sdtsldt0(X2,X1))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[131,theory(equality)]) ).

cnf(386,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xp != X1
    | ~ doDivides0(xl,xm)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[131,124,theory(equality)]) ).

cnf(387,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xq != X1
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(spm,[status(thm)],[131,147,theory(equality)]) ).

cnf(388,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xp != X1
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[386,133,theory(equality)]) ).

cnf(389,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xp != X1
    | $false
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[388,141,theory(equality)]) ).

cnf(390,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xp != X1
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[389,140,theory(equality)]) ).

cnf(391,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xp != X1 ),
    inference(cn,[status(thm)],[390,theory(equality)]) ).

cnf(392,plain,
    ( aNaturalNumber0(X1)
    | xp != X1 ),
    inference(sr,[status(thm)],[391,84,theory(equality)]) ).

cnf(393,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xq != X1
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[387,132,theory(equality)]) ).

cnf(394,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xq != X1
    | $false
    | $false
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[393,141,theory(equality)]) ).

cnf(395,plain,
    ( sz00 = xl
    | aNaturalNumber0(X1)
    | xq != X1
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(cn,[status(thm)],[394,theory(equality)]) ).

cnf(396,plain,
    ( aNaturalNumber0(X1)
    | xq != X1
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(sr,[status(thm)],[395,84,theory(equality)]) ).

cnf(416,plain,
    ( sdtmndt0(X1,X2) = X3
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[164,117]) ).

cnf(418,plain,
    ( sdtmndt0(X1,X2) = sz00
    | X2 != X1
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[416,189,theory(equality)]) ).

cnf(423,plain,
    ( sdtmndt0(X1,X2) = sz00
    | X2 != X1
    | $false
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[418,170,theory(equality)]) ).

cnf(424,plain,
    ( sdtmndt0(X1,X2) = sz00
    | X2 != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[423,theory(equality)]) ).

cnf(425,plain,
    ( sdtmndt0(X1,X1) = sz00
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[424,theory(equality)]) ).

cnf(511,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[151,193,theory(equality)]) ).

cnf(538,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[511,146,theory(equality)]) ).

cnf(539,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[538,theory(equality)]) ).

cnf(540,plain,
    ( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
    | sz00 = X1
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[130,theory(equality)]) ).

cnf(541,plain,
    ( sdtasdt0(xl,X1) = xm
    | sz00 = xl
    | xp != X1
    | ~ doDivides0(xl,xm)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[130,124,theory(equality)]) ).

cnf(542,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | sz00 = xl
    | xq != X1
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(spm,[status(thm)],[130,147,theory(equality)]) ).

cnf(543,plain,
    ( sdtasdt0(xl,X1) = xm
    | sz00 = xl
    | xp != X1
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[541,133,theory(equality)]) ).

cnf(544,plain,
    ( sdtasdt0(xl,X1) = xm
    | sz00 = xl
    | xp != X1
    | $false
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[543,141,theory(equality)]) ).

cnf(545,plain,
    ( sdtasdt0(xl,X1) = xm
    | sz00 = xl
    | xp != X1
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[544,140,theory(equality)]) ).

cnf(546,plain,
    ( sdtasdt0(xl,X1) = xm
    | sz00 = xl
    | xp != X1 ),
    inference(cn,[status(thm)],[545,theory(equality)]) ).

cnf(547,plain,
    ( sdtasdt0(xl,X1) = xm
    | xp != X1 ),
    inference(sr,[status(thm)],[546,84,theory(equality)]) ).

cnf(548,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | sz00 = xl
    | xq != X1
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[542,132,theory(equality)]) ).

cnf(549,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | sz00 = xl
    | xq != X1
    | $false
    | $false
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[548,141,theory(equality)]) ).

cnf(550,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | sz00 = xl
    | xq != X1
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(cn,[status(thm)],[549,theory(equality)]) ).

cnf(551,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | xq != X1
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(sr,[status(thm)],[550,84,theory(equality)]) ).

cnf(724,plain,
    ( sdtsldt0(X1,X2) = X3
    | sz00 = X2
    | sdtasdt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[129,75]) ).

cnf(725,plain,
    ( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
    | sz00 = X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(er,[status(thm)],[724,theory(equality)]) ).

cnf(793,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | xp != X2 ),
    inference(spm,[status(thm)],[82,392,theory(equality)]) ).

cnf(809,plain,
    ( sz00 = xl
    | X1 = X2
    | sdtlseqdt0(sdtasdt0(xl,X2),xm)
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xp != X1 ),
    inference(spm,[status(thm)],[108,547,theory(equality)]) ).

cnf(814,plain,
    ( sdtsldt0(X1,xl) = X2
    | sz00 = xl
    | xm != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(X1)
    | xp != X2 ),
    inference(spm,[status(thm)],[724,547,theory(equality)]) ).

cnf(852,plain,
    ( sz00 = xl
    | X1 = X2
    | sdtlseqdt0(sdtasdt0(xl,X2),xm)
    | ~ sdtlseqdt0(X2,X1)
    | $false
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xp != X1 ),
    inference(rw,[status(thm)],[809,141,theory(equality)]) ).

cnf(853,plain,
    ( sz00 = xl
    | X1 = X2
    | sdtlseqdt0(sdtasdt0(xl,X2),xm)
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xp != X1 ),
    inference(cn,[status(thm)],[852,theory(equality)]) ).

cnf(854,plain,
    ( X1 = X2
    | sdtlseqdt0(sdtasdt0(xl,X2),xm)
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xp != X1 ),
    inference(sr,[status(thm)],[853,84,theory(equality)]) ).

cnf(863,plain,
    ( sdtsldt0(X1,xl) = X2
    | sz00 = xl
    | xm != X1
    | ~ aNaturalNumber0(X2)
    | $false
    | ~ aNaturalNumber0(X1)
    | xp != X2 ),
    inference(rw,[status(thm)],[814,141,theory(equality)]) ).

cnf(864,plain,
    ( sdtsldt0(X1,xl) = X2
    | sz00 = xl
    | xm != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xp != X2 ),
    inference(cn,[status(thm)],[863,theory(equality)]) ).

cnf(865,plain,
    ( sdtsldt0(X1,xl) = X2
    | xm != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | xp != X2 ),
    inference(sr,[status(thm)],[864,84,theory(equality)]) ).

cnf(907,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | xp != X1
    | xp != X2 ),
    inference(spm,[status(thm)],[793,392,theory(equality)]) ).

cnf(940,plain,
    ( sdtlseqdt0(X1,xp)
    | sdtlseqdt0(xp,X1)
    | xp != X1 ),
    inference(er,[status(thm)],[907,theory(equality)]) ).

cnf(941,plain,
    sdtlseqdt0(xp,xp),
    inference(er,[status(thm)],[940,theory(equality)]) ).

cnf(1450,plain,
    ( sdtpldt0(X1,X2) = X1
    | sz00 != X2
    | ~ sdtlseqdt0(X1,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[165,425,theory(equality)]) ).

cnf(1558,plain,
    ( doDivides0(sz10,xm)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xl) ),
    inference(spm,[status(thm)],[382,318,theory(equality)]) ).

cnf(1562,plain,
    ( doDivides0(sz10,xm)
    | $false
    | ~ aNaturalNumber0(xl) ),
    inference(rw,[status(thm)],[1558,146,theory(equality)]) ).

cnf(1563,plain,
    ( doDivides0(sz10,xm)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1562,141,theory(equality)]) ).

cnf(1564,plain,
    doDivides0(sz10,xm),
    inference(cn,[status(thm)],[1563,theory(equality)]) ).

cnf(1671,plain,
    ( aNaturalNumber0(X1)
    | xq != X1
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[396,173,theory(equality)]) ).

cnf(1673,plain,
    ( aNaturalNumber0(X1)
    | xq != X1
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[1671,139,theory(equality)]) ).

cnf(1674,plain,
    ( aNaturalNumber0(X1)
    | xq != X1
    | $false
    | $false ),
    inference(rw,[status(thm)],[1673,140,theory(equality)]) ).

cnf(1675,plain,
    ( aNaturalNumber0(X1)
    | xq != X1 ),
    inference(cn,[status(thm)],[1674,theory(equality)]) ).

cnf(1677,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | xp != X1
    | xq != X2 ),
    inference(spm,[status(thm)],[793,1675,theory(equality)]) ).

cnf(1685,plain,
    ( sdtlseqdt0(X1,xp)
    | sdtlseqdt0(xp,X1)
    | xq != X1 ),
    inference(er,[status(thm)],[1677,theory(equality)]) ).

cnf(1687,plain,
    ( sdtlseqdt0(xp,xq)
    | sdtlseqdt0(xq,xp) ),
    inference(er,[status(thm)],[1685,theory(equality)]) ).

cnf(1688,plain,
    sdtlseqdt0(xq,xp),
    inference(sr,[status(thm)],[1687,148,theory(equality)]) ).

cnf(3587,plain,
    ( sz00 = xl
    | aNaturalNumber0(xp)
    | ~ doDivides0(xl,xm)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[385,124,theory(equality)]) ).

cnf(3588,plain,
    ( sz00 = xl
    | aNaturalNumber0(xq)
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(spm,[status(thm)],[385,147,theory(equality)]) ).

cnf(3600,plain,
    ( sz00 = xl
    | aNaturalNumber0(xp)
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[3587,133,theory(equality)]) ).

cnf(3601,plain,
    ( sz00 = xl
    | aNaturalNumber0(xp)
    | $false
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[3600,141,theory(equality)]) ).

cnf(3602,plain,
    ( sz00 = xl
    | aNaturalNumber0(xp)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[3601,140,theory(equality)]) ).

cnf(3603,plain,
    ( sz00 = xl
    | aNaturalNumber0(xp) ),
    inference(cn,[status(thm)],[3602,theory(equality)]) ).

cnf(3604,plain,
    aNaturalNumber0(xp),
    inference(sr,[status(thm)],[3603,84,theory(equality)]) ).

cnf(3605,plain,
    ( sz00 = xl
    | aNaturalNumber0(xq)
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[3588,132,theory(equality)]) ).

cnf(3606,plain,
    ( sz00 = xl
    | aNaturalNumber0(xq)
    | $false
    | $false
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(rw,[status(thm)],[3605,141,theory(equality)]) ).

cnf(3607,plain,
    ( sz00 = xl
    | aNaturalNumber0(xq)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(cn,[status(thm)],[3606,theory(equality)]) ).

cnf(3608,plain,
    ( aNaturalNumber0(xq)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(sr,[status(thm)],[3607,84,theory(equality)]) ).

cnf(3918,plain,
    ( aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[3608,173,theory(equality)]) ).

cnf(3921,plain,
    ( aNaturalNumber0(xq)
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[3918,139,theory(equality)]) ).

cnf(3922,plain,
    ( aNaturalNumber0(xq)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3921,140,theory(equality)]) ).

cnf(3923,plain,
    aNaturalNumber0(xq),
    inference(cn,[status(thm)],[3922,theory(equality)]) ).

cnf(10249,plain,
    ( sdtasdt0(xl,xp) = xm
    | sz00 = xl
    | ~ doDivides0(xl,xm)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[540,124,theory(equality)]) ).

cnf(10311,plain,
    ( sdtasdt0(xl,xp) = xm
    | sz00 = xl
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[10249,133,theory(equality)]) ).

cnf(10312,plain,
    ( sdtasdt0(xl,xp) = xm
    | sz00 = xl
    | $false
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[10311,141,theory(equality)]) ).

cnf(10313,plain,
    ( sdtasdt0(xl,xp) = xm
    | sz00 = xl
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[10312,140,theory(equality)]) ).

cnf(10314,plain,
    ( sdtasdt0(xl,xp) = xm
    | sz00 = xl ),
    inference(cn,[status(thm)],[10313,theory(equality)]) ).

cnf(10315,plain,
    sdtasdt0(xl,xp) = xm,
    inference(sr,[status(thm)],[10314,84,theory(equality)]) ).

cnf(10381,plain,
    ( sdtasdt0(sz10,xm) = xm
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xl) ),
    inference(spm,[status(thm)],[539,10315,theory(equality)]) ).

cnf(10498,plain,
    ( sdtasdt0(sz10,xm) = xm
    | $false
    | ~ aNaturalNumber0(xl) ),
    inference(rw,[status(thm)],[10381,3604,theory(equality)]) ).

cnf(10499,plain,
    ( sdtasdt0(sz10,xm) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[10498,141,theory(equality)]) ).

cnf(10500,plain,
    sdtasdt0(sz10,xm) = xm,
    inference(cn,[status(thm)],[10499,theory(equality)]) ).

cnf(10750,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | xq != X1
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[551,173,theory(equality)]) ).

cnf(10754,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | xq != X1
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[10750,139,theory(equality)]) ).

cnf(10755,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | xq != X1
    | $false
    | $false ),
    inference(rw,[status(thm)],[10754,140,theory(equality)]) ).

cnf(10756,plain,
    ( sdtasdt0(xl,X1) = sdtpldt0(xm,xn)
    | xq != X1 ),
    inference(cn,[status(thm)],[10755,theory(equality)]) ).

cnf(13050,plain,
    ( sdtpldt0(xm,xn) = xm
    | xq != xp ),
    inference(spm,[status(thm)],[10315,10756,theory(equality)]) ).

cnf(13053,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xl)
    | xq != X1 ),
    inference(spm,[status(thm)],[169,10756,theory(equality)]) ).

cnf(13134,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(X1)
    | $false
    | xq != X1 ),
    inference(rw,[status(thm)],[13053,141,theory(equality)]) ).

cnf(13135,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(X1)
    | xq != X1 ),
    inference(cn,[status(thm)],[13134,theory(equality)]) ).

cnf(30395,plain,
    ( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
    | sz00 = X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[725,169]) ).

cnf(30398,plain,
    ( sdtsldt0(xm,sz10) = xm
    | sz00 = sz10
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[30395,10500,theory(equality)]) ).

cnf(30446,plain,
    ( sdtsldt0(xm,sz10) = xm
    | sz00 = sz10
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[30398,140,theory(equality)]) ).

cnf(30447,plain,
    ( sdtsldt0(xm,sz10) = xm
    | sz00 = sz10
    | $false
    | $false ),
    inference(rw,[status(thm)],[30446,146,theory(equality)]) ).

cnf(30448,plain,
    ( sdtsldt0(xm,sz10) = xm
    | sz00 = sz10 ),
    inference(cn,[status(thm)],[30447,theory(equality)]) ).

cnf(30449,plain,
    sdtsldt0(xm,sz10) = xm,
    inference(sr,[status(thm)],[30448,145,theory(equality)]) ).

cnf(30523,plain,
    ( sz00 = sz10
    | aNaturalNumber0(X1)
    | xm != X1
    | ~ doDivides0(sz10,xm)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[131,30449,theory(equality)]) ).

cnf(30527,plain,
    ( sz00 = sz10
    | aNaturalNumber0(X1)
    | xm != X1
    | $false
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[30523,1564,theory(equality)]) ).

cnf(30528,plain,
    ( sz00 = sz10
    | aNaturalNumber0(X1)
    | xm != X1
    | $false
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[30527,146,theory(equality)]) ).

cnf(30529,plain,
    ( sz00 = sz10
    | aNaturalNumber0(X1)
    | xm != X1
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[30528,140,theory(equality)]) ).

cnf(30530,plain,
    ( sz00 = sz10
    | aNaturalNumber0(X1)
    | xm != X1 ),
    inference(cn,[status(thm)],[30529,theory(equality)]) ).

cnf(30531,plain,
    ( aNaturalNumber0(X1)
    | xm != X1 ),
    inference(sr,[status(thm)],[30530,145,theory(equality)]) ).

cnf(44641,plain,
    ( X1 = X2
    | sdtlseqdt0(sdtasdt0(xl,X2),xm)
    | xp != X1
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[854,392]) ).

cnf(44646,plain,
    ( xp = xq
    | sdtlseqdt0(sdtasdt0(xl,xq),xm)
    | ~ aNaturalNumber0(xq) ),
    inference(spm,[status(thm)],[44641,1688,theory(equality)]) ).

cnf(44807,plain,
    ( xp = xq
    | sdtlseqdt0(sdtasdt0(xl,xq),xm)
    | $false ),
    inference(rw,[status(thm)],[44646,3923,theory(equality)]) ).

cnf(44808,plain,
    ( xp = xq
    | sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
    inference(cn,[status(thm)],[44807,theory(equality)]) ).

cnf(45016,plain,
    ( xq = xp
    | sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
    inference(spm,[status(thm)],[44808,10756,theory(equality)]) ).

cnf(46389,plain,
    ( sdtsldt0(X1,xl) = X2
    | xp != X2
    | xm != X1
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[865,30531]) ).

cnf(46390,plain,
    ( sdtsldt0(X1,xl) = X2
    | xp != X2
    | xm != X1 ),
    inference(csr,[status(thm)],[46389,392]) ).

cnf(46391,plain,
    ( sdtsldt0(X1,xl) = xp
    | xm != X1 ),
    inference(er,[status(thm)],[46390,theory(equality)]) ).

cnf(46396,plain,
    ( xp = xq
    | xm != sdtpldt0(xm,xn) ),
    inference(spm,[status(thm)],[147,46391,theory(equality)]) ).

cnf(58681,plain,
    ( sdtpldt0(X1,X2) = X1
    | sz00 != X2
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[1450,159]) ).

cnf(58876,plain,
    ( xq = xp
    | sz00 != xn
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[46396,58681,theory(equality)]) ).

cnf(58949,plain,
    ( xq = xp
    | sz00 != xn
    | $false ),
    inference(rw,[status(thm)],[58876,140,theory(equality)]) ).

cnf(58950,plain,
    ( xq = xp
    | sz00 != xn ),
    inference(cn,[status(thm)],[58949,theory(equality)]) ).

cnf(58968,plain,
    ( ~ sdtlseqdt0(xp,xp)
    | xn != sz00 ),
    inference(spm,[status(thm)],[148,58950,theory(equality)]) ).

cnf(59043,plain,
    ( $false
    | xn != sz00 ),
    inference(rw,[status(thm)],[58968,941,theory(equality)]) ).

cnf(59044,plain,
    xn != sz00,
    inference(cn,[status(thm)],[59043,theory(equality)]) ).

cnf(75728,plain,
    ( aNaturalNumber0(sdtpldt0(xm,xn))
    | xq != X1 ),
    inference(csr,[status(thm)],[13135,1675]) ).

cnf(75729,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(er,[status(thm)],[75728,theory(equality)]) ).

cnf(75808,plain,
    ( sdtpldt0(xm,xn) = xm
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | $false ),
    inference(rw,[status(thm)],[255,75729,theory(equality)]) ).

cnf(75809,plain,
    ( sdtpldt0(xm,xn) = xm
    | ~ sdtlseqdt0(sdtpldt0(xm,xn),xm) ),
    inference(cn,[status(thm)],[75808,theory(equality)]) ).

cnf(76341,plain,
    ( sdtpldt0(xm,xn) = xm
    | xq = xp ),
    inference(spm,[status(thm)],[75809,45016,theory(equality)]) ).

cnf(76398,plain,
    sdtpldt0(xm,xn) = xm,
    inference(csr,[status(thm)],[76341,13050]) ).

cnf(76416,plain,
    ( sz00 = xn
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[371,76398,theory(equality)]) ).

cnf(76588,plain,
    ( sz00 = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[76416,140,theory(equality)]) ).

cnf(76589,plain,
    ( sz00 = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[76588,139,theory(equality)]) ).

cnf(76590,plain,
    sz00 = xn,
    inference(cn,[status(thm)],[76589,theory(equality)]) ).

cnf(76591,plain,
    $false,
    inference(sr,[status(thm)],[76590,59044,theory(equality)]) ).

cnf(76592,plain,
    $false,
    76591,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM473+1 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.03/0.23  % Computer : n121.star.cs.uiowa.edu
% 0.03/0.23  % Model    : x86_64 x86_64
% 0.03/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23  % Memory   : 32218.625MB
% 0.03/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23  % CPULimit : 300
% 0.03/0.23  % DateTime : Fri Jan  5 05:01:00 CST 2018
% 0.03/0.23  % CPUTime  : 
% 0.03/0.27  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.28  --creating new selector for []
% 1.61/1.85  -running prover on /export/starexec/sandbox/tmp/tmp168nTy/sel_theBenchmark.p_1 with time limit 29
% 1.61/1.85  -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/tmp168nTy/sel_theBenchmark.p_1']
% 1.61/1.85  -prover status Theorem
% 1.61/1.85  Problem theBenchmark.p solved in phase 0.
% 1.61/1.85  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.61/1.85  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.61/1.85  Solved 1 out of 1.
% 1.61/1.85  # Problem is unsatisfiable (or provable), constructing proof object
% 1.61/1.85  # SZS status Theorem
% 1.61/1.85  # SZS output start CNFRefutation.
% See solution above
% 1.61/1.86  # SZS output end CNFRefutation
%------------------------------------------------------------------------------