%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM459+2 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n112.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 15:21:24 EST 2018

% Result   : Theorem 2.39s
% Output   : CNFRefutation 2.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :  100
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  459 (  79 unt;   0 def)
%            Number of atoms       : 1469 ( 362 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives : 1723 ( 713   ~; 891   |;  93   &)
%                                         (   2 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :  394 (   0 sgn 136   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',m_MulZero) ).

fof(2,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mAddComm) ).

fof(4,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( ~ equal(X1,sz00)
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
                | equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) )
             => equal(X2,X3) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mMulCanc) ).

fof(5,axiom,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',m__745) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( equal(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
        & equal(sdtasdt0(sdtpldt0(X2,X3),X1),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mAMDistr) ).

fof(8,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & equal(sdtpldt0(X1,X3),X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mDefLE) ).

fof(9,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/tmp2ID3DG/sel_theBenchmark.p_1',mAddAsso) ).

fof(10,axiom,
    ( aNaturalNumber0(sz10)
    & ~ equal(sz10,sz00) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mSortsC_01) ).

fof(11,conjecture,
    ( ( ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(xm,X1),xn) )
      & sdtlseqdt0(xm,xn)
      & ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(xn,X1),xm) )
      & sdtlseqdt0(xn,xm) )
   => equal(xm,xn) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',m__) ).

fof(12,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/tmp2ID3DG/sel_theBenchmark.p_1',mMulAsso) ).

fof(13,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( equal(sdtpldt0(X1,X2),sz00)
       => ( equal(X1,sz00)
          & equal(X2,sz00) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mZeroAdd) ).

fof(14,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => sdtlseqdt0(X1,X1) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mLERefl) ).

fof(15,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/tmp2ID3DG/sel_theBenchmark.p_1',mDefDiff) ).

fof(16,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mSortsB_02) ).

fof(17,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mSortsC) ).

fof(18,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mSortsB) ).

fof(19,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/tmp2ID3DG/sel_theBenchmark.p_1',mAddCanc) ).

fof(20,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',mMulComm) ).

fof(21,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',m_AddZero) ).

fof(22,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1',m_MulUnit) ).

fof(23,negated_conjecture,
    ~ ( ( ? [X1] :
            ( aNaturalNumber0(X1)
            & equal(sdtpldt0(xm,X1),xn) )
        & sdtlseqdt0(xm,xn)
        & ? [X1] :
            ( aNaturalNumber0(X1)
            & equal(sdtpldt0(xn,X1),xm) )
        & sdtlseqdt0(xn,xm) )
     => equal(xm,xn) ),
    inference(assume_negation,[status(cth)],[11]) ).

fof(24,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(25,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[24]) ).

fof(26,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz00),sz00)
        | ~ aNaturalNumber0(X2) )
      & ( equal(sz00,sdtasdt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[25]) ).

cnf(27,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(29,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(sdtpldt0(X1,X2),sdtpldt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(30,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(sdtpldt0(X3,X4),sdtpldt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[29]) ).

cnf(31,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(35,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | equal(X1,sz00)
      | ! [X2,X3] :
          ( ~ aNaturalNumber0(X2)
          | ~ aNaturalNumber0(X3)
          | ( ~ equal(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
            & ~ equal(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) )
          | equal(X2,X3) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(36,plain,
    ! [X4] :
      ( ~ aNaturalNumber0(X4)
      | equal(X4,sz00)
      | ! [X5,X6] :
          ( ~ aNaturalNumber0(X5)
          | ~ aNaturalNumber0(X6)
          | ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
            & ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) )
          | equal(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[35]) ).

fof(37,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        & ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4)) )
      | equal(X5,X6)
      | equal(X4,sz00)
      | ~ aNaturalNumber0(X4) ),
    inference(shift_quantors,[status(thm)],[36]) ).

fof(38,plain,
    ! [X4,X5,X6] :
      ( ( ~ equal(sdtasdt0(X4,X5),sdtasdt0(X4,X6))
        | equal(X5,X6)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6)
        | equal(X4,sz00)
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(sdtasdt0(X5,X4),sdtasdt0(X6,X4))
        | equal(X5,X6)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6)
        | equal(X4,sz00)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[37]) ).

cnf(39,plain,
    ( X1 = sz00
    | X3 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[38]) ).

cnf(41,plain,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[5]) ).

cnf(42,plain,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[5]) ).

fof(43,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | ( equal(sdtasdt0(X1,sdtpldt0(X2,X3)),sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)))
        & equal(sdtasdt0(sdtpldt0(X2,X3),X1),sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1))) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(44,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ( equal(sdtasdt0(X4,sdtpldt0(X5,X6)),sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6)))
        & equal(sdtasdt0(sdtpldt0(X5,X6),X4),sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4))) ) ),
    inference(variable_rename,[status(thm)],[43]) ).

fof(45,plain,
    ! [X4,X5,X6] :
      ( ( equal(sdtasdt0(X4,sdtpldt0(X5,X6)),sdtpldt0(sdtasdt0(X4,X5),sdtasdt0(X4,X6)))
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( equal(sdtasdt0(sdtpldt0(X5,X6),X4),sdtpldt0(sdtasdt0(X5,X4),sdtasdt0(X6,X4)))
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) ) ),
    inference(distribute,[status(thm)],[44]) ).

cnf(46,plain,
    ( sdtasdt0(sdtpldt0(X2,X1),X3) = sdtpldt0(sdtasdt0(X2,X3),sdtasdt0(X1,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[45]) ).

cnf(47,plain,
    ( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(51,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)],[8]) ).

fof(52,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)],[51]) ).

fof(53,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ sdtlseqdt0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(sdtpldt0(X4,esk1_2(X4,X5)),X5) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(sdtpldt0(X4,X7),X5) )
          | sdtlseqdt0(X4,X5) ) ) ),
    inference(skolemize,[status(esa)],[52]) ).

fof(54,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ aNaturalNumber0(X7)
          | ~ equal(sdtpldt0(X4,X7),X5)
          | sdtlseqdt0(X4,X5) )
        & ( ~ sdtlseqdt0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(sdtpldt0(X4,esk1_2(X4,X5)),X5) ) ) )
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[53]) ).

fof(55,plain,
    ! [X4,X5,X7] :
      ( ( ~ aNaturalNumber0(X7)
        | ~ equal(sdtpldt0(X4,X7),X5)
        | sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( aNaturalNumber0(esk1_2(X4,X5))
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( equal(sdtpldt0(X4,esk1_2(X4,X5)),X5)
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[54]) ).

cnf(56,plain,
    ( sdtpldt0(X2,esk1_2(X2,X1)) = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(57,plain,
    ( aNaturalNumber0(esk1_2(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[55]) ).

cnf(58,plain,
    ( sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[55]) ).

fof(59,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)],[9]) ).

fof(60,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)],[59]) ).

cnf(61,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[60]) ).

cnf(62,plain,
    sz10 != sz00,
    inference(split_conjunct,[status(thm)],[10]) ).

cnf(63,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[10]) ).

fof(64,negated_conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(sdtpldt0(xm,X1),xn) )
    & sdtlseqdt0(xm,xn)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(sdtpldt0(xn,X1),xm) )
    & sdtlseqdt0(xn,xm)
    & ~ equal(xm,xn) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(65,negated_conjecture,
    ( ? [X2] :
        ( aNaturalNumber0(X2)
        & equal(sdtpldt0(xm,X2),xn) )
    & sdtlseqdt0(xm,xn)
    & ? [X3] :
        ( aNaturalNumber0(X3)
        & equal(sdtpldt0(xn,X3),xm) )
    & sdtlseqdt0(xn,xm)
    & ~ equal(xm,xn) ),
    inference(variable_rename,[status(thm)],[64]) ).

fof(66,negated_conjecture,
    ( aNaturalNumber0(esk2_0)
    & equal(sdtpldt0(xm,esk2_0),xn)
    & sdtlseqdt0(xm,xn)
    & aNaturalNumber0(esk3_0)
    & equal(sdtpldt0(xn,esk3_0),xm)
    & sdtlseqdt0(xn,xm)
    & ~ equal(xm,xn) ),
    inference(skolemize,[status(esa)],[65]) ).

cnf(67,negated_conjecture,
    xm != xn,
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(68,negated_conjecture,
    sdtlseqdt0(xn,xm),
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(69,negated_conjecture,
    sdtpldt0(xn,esk3_0) = xm,
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(70,negated_conjecture,
    aNaturalNumber0(esk3_0),
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(71,negated_conjecture,
    sdtlseqdt0(xm,xn),
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(72,negated_conjecture,
    sdtpldt0(xm,esk2_0) = xn,
    inference(split_conjunct,[status(thm)],[66]) ).

cnf(73,negated_conjecture,
    aNaturalNumber0(esk2_0),
    inference(split_conjunct,[status(thm)],[66]) ).

fof(74,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)],[12]) ).

fof(75,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)],[74]) ).

cnf(76,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[75]) ).

fof(77,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ equal(sdtpldt0(X1,X2),sz00)
      | ( equal(X1,sz00)
        & equal(X2,sz00) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(78,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | ~ equal(sdtpldt0(X3,X4),sz00)
      | ( equal(X3,sz00)
        & equal(X4,sz00) ) ),
    inference(variable_rename,[status(thm)],[77]) ).

fof(79,plain,
    ! [X3,X4] :
      ( ( equal(X3,sz00)
        | ~ equal(sdtpldt0(X3,X4),sz00)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) )
      & ( equal(X4,sz00)
        | ~ equal(sdtpldt0(X3,X4),sz00)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[78]) ).

cnf(81,plain,
    ( X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X1) != sz00 ),
    inference(split_conjunct,[status(thm)],[79]) ).

fof(82,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | sdtlseqdt0(X1,X1) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(83,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | sdtlseqdt0(X2,X2) ),
    inference(variable_rename,[status(thm)],[82]) ).

cnf(84,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[83]) ).

fof(85,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)],[15]) ).

fof(86,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)],[85]) ).

fof(87,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)],[86]) ).

fof(88,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)],[87]) ).

cnf(89,plain,
    ( X3 = sdtmndt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[88]) ).

cnf(90,plain,
    ( sdtpldt0(X2,X3) = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[88]) ).

cnf(91,plain,
    ( aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[88]) ).

fof(92,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(93,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[92]) ).

cnf(94,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(95,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(96,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(97,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[96]) ).

cnf(98,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[97]) ).

fof(99,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)],[19]) ).

fof(100,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)],[99]) ).

fof(101,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)],[100]) ).

cnf(102,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
    inference(split_conjunct,[status(thm)],[101]) ).

cnf(103,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
    inference(split_conjunct,[status(thm)],[101]) ).

fof(104,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(105,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[104]) ).

cnf(106,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[105]) ).

fof(107,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(108,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtpldt0(X2,sz00),X2)
        & equal(X2,sdtpldt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[107]) ).

fof(109,plain,
    ! [X2] :
      ( ( equal(sdtpldt0(X2,sz00),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtpldt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[108]) ).

cnf(110,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[109]) ).

cnf(111,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[109]) ).

fof(112,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(113,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz10),X2)
        & equal(X2,sdtasdt0(sz10,X2)) ) ),
    inference(variable_rename,[status(thm)],[112]) ).

fof(114,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz10),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtasdt0(sz10,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[113]) ).

cnf(115,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[114]) ).

cnf(116,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[114]) ).

cnf(213,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[57,71,theory(equality)]) ).

cnf(214,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xn,xm))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[57,68,theory(equality)]) ).

cnf(215,plain,
    ( aNaturalNumber0(esk1_2(X1,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[57,84,theory(equality)]) ).

cnf(216,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xn))
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[213,42,theory(equality)]) ).

cnf(217,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[216,41,theory(equality)]) ).

cnf(218,negated_conjecture,
    aNaturalNumber0(esk1_2(xm,xn)),
    inference(cn,[status(thm)],[217,theory(equality)]) ).

cnf(219,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xn,xm))
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[214,41,theory(equality)]) ).

cnf(220,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xn,xm))
    | $false
    | $false ),
    inference(rw,[status(thm)],[219,42,theory(equality)]) ).

cnf(221,negated_conjecture,
    aNaturalNumber0(esk1_2(xn,xm)),
    inference(cn,[status(thm)],[220,theory(equality)]) ).

cnf(230,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(er,[status(thm)],[58,theory(equality)]) ).

cnf(235,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtpldt0(X3,X1) != X2
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[58,31,theory(equality)]) ).

cnf(249,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xn)) = xn
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[56,71,theory(equality)]) ).

cnf(250,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(xn,xm)) = xm
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[56,68,theory(equality)]) ).

cnf(251,plain,
    ( sdtpldt0(X1,esk1_2(X1,X1)) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[56,84,theory(equality)]) ).

cnf(252,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xn)) = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[249,42,theory(equality)]) ).

cnf(253,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xn)) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[252,41,theory(equality)]) ).

cnf(254,negated_conjecture,
    sdtpldt0(xm,esk1_2(xm,xn)) = xn,
    inference(cn,[status(thm)],[253,theory(equality)]) ).

cnf(255,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(xn,xm)) = xm
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[250,41,theory(equality)]) ).

cnf(256,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(xn,xm)) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[255,42,theory(equality)]) ).

cnf(257,negated_conjecture,
    sdtpldt0(xn,esk1_2(xn,xm)) = xm,
    inference(cn,[status(thm)],[256,theory(equality)]) ).

cnf(260,negated_conjecture,
    ( esk2_0 = X1
    | xn != sdtpldt0(xm,X1)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[103,72,theory(equality)]) ).

cnf(262,negated_conjecture,
    ( esk3_0 = X1
    | xm != sdtpldt0(xn,X1)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk3_0) ),
    inference(spm,[status(thm)],[103,69,theory(equality)]) ).

cnf(264,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[103,111,theory(equality)]) ).

cnf(272,negated_conjecture,
    ( esk2_0 = X1
    | xn != sdtpldt0(xm,X1)
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[260,42,theory(equality)]) ).

cnf(273,negated_conjecture,
    ( esk2_0 = X1
    | xn != sdtpldt0(xm,X1)
    | $false
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[272,73,theory(equality)]) ).

cnf(274,negated_conjecture,
    ( esk2_0 = X1
    | xn != sdtpldt0(xm,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[273,theory(equality)]) ).

cnf(278,negated_conjecture,
    ( esk3_0 = X1
    | xm != sdtpldt0(xn,X1)
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk3_0) ),
    inference(rw,[status(thm)],[262,41,theory(equality)]) ).

cnf(279,negated_conjecture,
    ( esk3_0 = X1
    | xm != sdtpldt0(xn,X1)
    | $false
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[278,70,theory(equality)]) ).

cnf(280,negated_conjecture,
    ( esk3_0 = X1
    | xm != sdtpldt0(xn,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[279,theory(equality)]) ).

cnf(284,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[264,95,theory(equality)]) ).

cnf(285,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[284,theory(equality)]) ).

cnf(329,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[61,110,theory(equality)]) ).

cnf(330,plain,
    ( aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3)))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[98,61,theory(equality)]) ).

cnf(331,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)],[31,61,theory(equality)]) ).

cnf(354,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[329,95,theory(equality)]) ).

cnf(355,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[354,theory(equality)]) ).

cnf(356,plain,
    ( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[90,theory(equality)]) ).

cnf(362,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[76,115,theory(equality)]) ).

cnf(381,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[362,63,theory(equality)]) ).

cnf(382,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(sz10,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[381,theory(equality)]) ).

cnf(386,plain,
    ( sz00 = sz10
    | X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[39,116,theory(equality)]) ).

cnf(400,plain,
    ( sz00 = sz10
    | X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[386,63,theory(equality)]) ).

cnf(401,plain,
    ( sz00 = sz10
    | X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[400,theory(equality)]) ).

cnf(402,plain,
    ( X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[401,62,theory(equality)]) ).

cnf(437,plain,
    ( sdtmndt0(X1,X2) = X3
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[89,58]) ).

cnf(464,plain,
    ( sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[47,115,theory(equality)]) ).

cnf(496,plain,
    ( sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2))
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[464,63,theory(equality)]) ).

cnf(497,plain,
    ( sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[496,theory(equality)]) ).

cnf(504,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(sdtpldt0(X1,X2),sz10)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[46,116,theory(equality)]) ).

cnf(535,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(sdtpldt0(X1,X2),sz10)
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[504,63,theory(equality)]) ).

cnf(536,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(sdtpldt0(X1,X2),sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[535,theory(equality)]) ).

cnf(549,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X1 != sdtasdt0(X2,sdtasdt0(X3,sz10))
    | ~ aNaturalNumber0(sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[402,76,theory(equality)]) ).

cnf(559,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X1 != sdtasdt0(X2,sdtasdt0(X3,sz10))
    | ~ aNaturalNumber0(sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[549,63,theory(equality)]) ).

cnf(560,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X1 != sdtasdt0(X2,sdtasdt0(X3,sz10))
    | ~ aNaturalNumber0(sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[559,theory(equality)]) ).

cnf(666,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X1 != sdtasdt0(X2,sdtasdt0(X3,sz10))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[560,94]) ).

cnf(667,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,sz10)))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[666,theory(equality)]) ).

cnf(699,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,sz10))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[667,115,theory(equality)]) ).

cnf(709,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,sz10))
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[699,63,theory(equality)]) ).

cnf(710,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,sz10))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[709,theory(equality)]) ).

cnf(718,plain,
    ( sz00 = sdtasdt0(sz10,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[710,27,theory(equality)]) ).

cnf(720,plain,
    ( sz10 = sdtasdt0(sz10,sz10)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[710,115,theory(equality)]) ).

cnf(721,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[710,94,theory(equality)]) ).

cnf(723,plain,
    ( sz00 = sdtasdt0(sz10,sz00)
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[718,95,theory(equality)]) ).

cnf(724,plain,
    ( sz00 = sdtasdt0(sz10,sz00)
    | $false
    | $false ),
    inference(rw,[status(thm)],[723,63,theory(equality)]) ).

cnf(725,plain,
    sz00 = sdtasdt0(sz10,sz00),
    inference(cn,[status(thm)],[724,theory(equality)]) ).

cnf(726,plain,
    ( sz10 = sdtasdt0(sz10,sz10)
    | $false ),
    inference(rw,[status(thm)],[720,63,theory(equality)]) ).

cnf(727,plain,
    sz10 = sdtasdt0(sz10,sz10),
    inference(cn,[status(thm)],[726,theory(equality)]) ).

cnf(728,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[721,63,theory(equality)]) ).

cnf(729,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[728,theory(equality)]) ).

cnf(733,plain,
    ( sz00 = sdtasdt0(sz00,sz10)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[106,725,theory(equality)]) ).

cnf(738,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[47,725,theory(equality)]) ).

cnf(747,plain,
    ( sz00 = sdtasdt0(sz00,sz10)
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[733,95,theory(equality)]) ).

cnf(748,plain,
    ( sz00 = sdtasdt0(sz00,sz10)
    | $false
    | $false ),
    inference(rw,[status(thm)],[747,63,theory(equality)]) ).

cnf(749,plain,
    sz00 = sdtasdt0(sz00,sz10),
    inference(cn,[status(thm)],[748,theory(equality)]) ).

cnf(764,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | $false
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[738,63,theory(equality)]) ).

cnf(765,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[764,95,theory(equality)]) ).

cnf(766,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[765,theory(equality)]) ).

cnf(921,negated_conjecture,
    ( esk2_0 = esk1_2(xm,xn)
    | ~ aNaturalNumber0(esk1_2(xm,xn)) ),
    inference(spm,[status(thm)],[274,254,theory(equality)]) ).

cnf(925,negated_conjecture,
    ( esk2_0 = esk1_2(xm,xn)
    | $false ),
    inference(rw,[status(thm)],[921,218,theory(equality)]) ).

cnf(926,negated_conjecture,
    esk2_0 = esk1_2(xm,xn),
    inference(cn,[status(thm)],[925,theory(equality)]) ).

cnf(934,negated_conjecture,
    sdtpldt0(xm,esk2_0) = xn,
    inference(rw,[status(thm)],[254,926,theory(equality)]) ).

cnf(944,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk2_0)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[102,934,theory(equality)]) ).

cnf(946,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[61,934,theory(equality)]) ).

cnf(947,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk2_0
    | xn != X1
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[437,934,theory(equality)]) ).

cnf(968,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk2_0)
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[944,73,theory(equality)]) ).

cnf(969,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk2_0)
    | $false
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[968,42,theory(equality)]) ).

cnf(970,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[969,theory(equality)]) ).

cnf(974,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[946,73,theory(equality)]) ).

cnf(975,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[974,42,theory(equality)]) ).

cnf(976,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[975,theory(equality)]) ).

cnf(977,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk2_0
    | xn != X1
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[947,73,theory(equality)]) ).

cnf(978,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk2_0
    | xn != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[977,42,theory(equality)]) ).

cnf(979,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk2_0
    | xn != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[978,theory(equality)]) ).

cnf(1010,negated_conjecture,
    ( esk3_0 = esk1_2(xn,xm)
    | ~ aNaturalNumber0(esk1_2(xn,xm)) ),
    inference(spm,[status(thm)],[280,257,theory(equality)]) ).

cnf(1014,negated_conjecture,
    ( esk3_0 = esk1_2(xn,xm)
    | $false ),
    inference(rw,[status(thm)],[1010,221,theory(equality)]) ).

cnf(1015,negated_conjecture,
    esk3_0 = esk1_2(xn,xm),
    inference(cn,[status(thm)],[1014,theory(equality)]) ).

cnf(1023,negated_conjecture,
    sdtpldt0(xn,esk3_0) = xm,
    inference(rw,[status(thm)],[257,1015,theory(equality)]) ).

cnf(1105,plain,
    ( sdtpldt0(sdtasdt0(sz10,X1),sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[47,729,theory(equality)]) ).

cnf(1182,plain,
    ( sdtpldt0(sdtasdt0(sz10,X1),sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[1105,63,theory(equality)]) ).

cnf(1183,plain,
    ( sdtpldt0(sdtasdt0(sz10,X1),sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[1182,theory(equality)]) ).

cnf(1282,negated_conjecture,
    ( xm = X1
    | sdtpldt0(esk2_0,X1) != xn
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[970,31,theory(equality)]) ).

cnf(1288,negated_conjecture,
    ( xm = X1
    | sdtpldt0(esk2_0,X1) != xn
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[1282,73,theory(equality)]) ).

cnf(1289,negated_conjecture,
    ( xm = X1
    | sdtpldt0(esk2_0,X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[1288,theory(equality)]) ).

cnf(1854,plain,
    ( sdtasdt0(sz10,sz00) = sdtpldt0(sz00,sdtasdt0(sz10,sz00))
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[766,111,theory(equality)]) ).

cnf(1855,plain,
    ( sdtasdt0(sz10,X1) = sdtpldt0(sz00,sdtasdt0(sz10,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[766,110,theory(equality)]) ).

cnf(1878,plain,
    ( sz00 = sdtpldt0(sz00,sdtasdt0(sz10,sz00))
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[1854,725,theory(equality)]) ).

cnf(1879,plain,
    ( sz00 = sdtpldt0(sz00,sz00)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[1878,725,theory(equality)]) ).

cnf(1880,plain,
    ( sz00 = sdtpldt0(sz00,sz00)
    | $false ),
    inference(rw,[status(thm)],[1879,95,theory(equality)]) ).

cnf(1881,plain,
    sz00 = sdtpldt0(sz00,sz00),
    inference(cn,[status(thm)],[1880,theory(equality)]) ).

cnf(1922,plain,
    ( sdtpldt0(sz00,X1) = sdtpldt0(sz00,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[61,1881,theory(equality)]) ).

cnf(1944,plain,
    ( sdtpldt0(sz00,X1) = sdtpldt0(sz00,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[1922,95,theory(equality)]) ).

cnf(1945,plain,
    ( sdtpldt0(sz00,X1) = sdtpldt0(sz00,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[1944,theory(equality)]) ).

cnf(1952,negated_conjecture,
    ( sdtmndt0(xn,xm) = esk2_0
    | ~ aNaturalNumber0(xn) ),
    inference(er,[status(thm)],[979,theory(equality)]) ).

cnf(1953,negated_conjecture,
    ( sdtmndt0(xn,xm) = esk2_0
    | $false ),
    inference(rw,[status(thm)],[1952,41,theory(equality)]) ).

cnf(1954,negated_conjecture,
    sdtmndt0(xn,xm) = esk2_0,
    inference(cn,[status(thm)],[1953,theory(equality)]) ).

cnf(1967,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[230,98]) ).

cnf(1973,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,X1))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[1967,31,theory(equality)]) ).

cnf(2077,negated_conjecture,
    ( sdtlseqdt0(esk2_0,X1)
    | xn != X1
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[235,934,theory(equality)]) ).

cnf(2089,negated_conjecture,
    ( sdtlseqdt0(esk2_0,X1)
    | xn != X1
    | $false
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2077,42,theory(equality)]) ).

cnf(2090,negated_conjecture,
    ( sdtlseqdt0(esk2_0,X1)
    | xn != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2089,73,theory(equality)]) ).

cnf(2091,negated_conjecture,
    ( sdtlseqdt0(esk2_0,X1)
    | xn != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[2090,theory(equality)]) ).

cnf(2131,negated_conjecture,
    ( sdtlseqdt0(esk2_0,xn)
    | ~ aNaturalNumber0(xn) ),
    inference(er,[status(thm)],[2091,theory(equality)]) ).

cnf(2132,negated_conjecture,
    ( sdtlseqdt0(esk2_0,xn)
    | $false ),
    inference(rw,[status(thm)],[2131,41,theory(equality)]) ).

cnf(2133,negated_conjecture,
    sdtlseqdt0(esk2_0,xn),
    inference(cn,[status(thm)],[2132,theory(equality)]) ).

cnf(2134,negated_conjecture,
    ( aNaturalNumber0(esk1_2(esk2_0,xn))
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[57,2133,theory(equality)]) ).

cnf(2135,negated_conjecture,
    ( sdtpldt0(esk2_0,esk1_2(esk2_0,xn)) = xn
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[56,2133,theory(equality)]) ).

cnf(2136,negated_conjecture,
    ( aNaturalNumber0(esk1_2(esk2_0,xn))
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[2134,73,theory(equality)]) ).

cnf(2137,negated_conjecture,
    ( aNaturalNumber0(esk1_2(esk2_0,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[2136,41,theory(equality)]) ).

cnf(2138,negated_conjecture,
    aNaturalNumber0(esk1_2(esk2_0,xn)),
    inference(cn,[status(thm)],[2137,theory(equality)]) ).

cnf(2139,negated_conjecture,
    ( sdtpldt0(esk2_0,esk1_2(esk2_0,xn)) = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[2135,73,theory(equality)]) ).

cnf(2140,negated_conjecture,
    ( sdtpldt0(esk2_0,esk1_2(esk2_0,xn)) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[2139,41,theory(equality)]) ).

cnf(2141,negated_conjecture,
    sdtpldt0(esk2_0,esk1_2(esk2_0,xn)) = xn,
    inference(cn,[status(thm)],[2140,theory(equality)]) ).

cnf(2152,negated_conjecture,
    ( xm = esk1_2(esk2_0,xn)
    | ~ aNaturalNumber0(esk1_2(esk2_0,xn)) ),
    inference(spm,[status(thm)],[1289,2141,theory(equality)]) ).

cnf(2186,negated_conjecture,
    ( xm = esk1_2(esk2_0,xn)
    | $false ),
    inference(rw,[status(thm)],[2152,2138,theory(equality)]) ).

cnf(2187,negated_conjecture,
    xm = esk1_2(esk2_0,xn),
    inference(cn,[status(thm)],[2186,theory(equality)]) ).

cnf(2195,negated_conjecture,
    sdtpldt0(esk2_0,xm) = xn,
    inference(rw,[status(thm)],[2141,2187,theory(equality)]) ).

cnf(2208,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(esk2_0,sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[61,2195,theory(equality)]) ).

cnf(2209,negated_conjecture,
    ( sdtmndt0(X1,esk2_0) = xm
    | xn != X1
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[437,2195,theory(equality)]) ).

cnf(2245,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(esk2_0,sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[2208,42,theory(equality)]) ).

cnf(2246,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(esk2_0,sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[2245,73,theory(equality)]) ).

cnf(2247,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(esk2_0,sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[2246,theory(equality)]) ).

cnf(2248,negated_conjecture,
    ( sdtmndt0(X1,esk2_0) = xm
    | xn != X1
    | $false
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2209,42,theory(equality)]) ).

cnf(2249,negated_conjecture,
    ( sdtmndt0(X1,esk2_0) = xm
    | xn != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2248,73,theory(equality)]) ).

cnf(2250,negated_conjecture,
    ( sdtmndt0(X1,esk2_0) = xm
    | xn != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[2249,theory(equality)]) ).

cnf(2332,plain,
    ( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[1945,31,theory(equality)]) ).

cnf(2359,plain,
    ( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[2332,95,theory(equality)]) ).

cnf(2360,plain,
    ( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[2359,theory(equality)]) ).

cnf(2486,plain,
    ( sdtpldt0(sz00,sz10) = sz10
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[1855,727,theory(equality)]) ).

cnf(2518,plain,
    ( sdtpldt0(sz00,sz10) = sz10
    | $false ),
    inference(rw,[status(thm)],[2486,63,theory(equality)]) ).

cnf(2519,plain,
    sdtpldt0(sz00,sz10) = sz10,
    inference(cn,[status(thm)],[2518,theory(equality)]) ).

cnf(2569,plain,
    ( sdtlseqdt0(sz10,X1)
    | sz10 != X1
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[235,2519,theory(equality)]) ).

cnf(2609,plain,
    ( sdtlseqdt0(sz10,X1)
    | sz10 != X1
    | $false
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2569,95,theory(equality)]) ).

cnf(2610,plain,
    ( sdtlseqdt0(sz10,X1)
    | sz10 != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2609,63,theory(equality)]) ).

cnf(2611,plain,
    ( sdtlseqdt0(sz10,X1)
    | sz10 != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[2610,theory(equality)]) ).

cnf(2915,plain,
    ( sdtlseqdt0(sz10,sz10)
    | ~ aNaturalNumber0(sz10) ),
    inference(er,[status(thm)],[2611,theory(equality)]) ).

cnf(2916,plain,
    ( sdtlseqdt0(sz10,sz10)
    | $false ),
    inference(rw,[status(thm)],[2915,63,theory(equality)]) ).

cnf(2917,plain,
    sdtlseqdt0(sz10,sz10),
    inference(cn,[status(thm)],[2916,theory(equality)]) ).

cnf(2918,plain,
    ( aNaturalNumber0(esk1_2(sz10,sz10))
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[57,2917,theory(equality)]) ).

cnf(2919,plain,
    ( sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[56,2917,theory(equality)]) ).

cnf(2921,plain,
    ( aNaturalNumber0(esk1_2(sz10,sz10))
    | $false ),
    inference(rw,[status(thm)],[2918,63,theory(equality)]) ).

cnf(2922,plain,
    aNaturalNumber0(esk1_2(sz10,sz10)),
    inference(cn,[status(thm)],[2921,theory(equality)]) ).

cnf(2923,plain,
    ( sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10
    | $false ),
    inference(rw,[status(thm)],[2919,63,theory(equality)]) ).

cnf(2924,plain,
    sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10,
    inference(cn,[status(thm)],[2923,theory(equality)]) ).

cnf(2943,plain,
    ( sz00 = esk1_2(sz10,sz10)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(esk1_2(sz10,sz10)) ),
    inference(spm,[status(thm)],[285,2924,theory(equality)]) ).

cnf(2983,plain,
    ( sz00 = esk1_2(sz10,sz10)
    | $false
    | ~ aNaturalNumber0(esk1_2(sz10,sz10)) ),
    inference(rw,[status(thm)],[2943,63,theory(equality)]) ).

cnf(2984,plain,
    ( sz00 = esk1_2(sz10,sz10)
    | $false
    | $false ),
    inference(rw,[status(thm)],[2983,2922,theory(equality)]) ).

cnf(2985,plain,
    sz00 = esk1_2(sz10,sz10),
    inference(cn,[status(thm)],[2984,theory(equality)]) ).

cnf(2991,plain,
    sdtpldt0(sz10,sz00) = sz10,
    inference(rw,[status(thm)],[2924,2985,theory(equality)]) ).

cnf(3008,plain,
    ( sdtpldt0(sz10,X1) = sdtpldt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[61,2991,theory(equality)]) ).

cnf(3046,plain,
    ( sdtpldt0(sz10,X1) = sdtpldt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[3008,95,theory(equality)]) ).

cnf(3047,plain,
    ( sdtpldt0(sz10,X1) = sdtpldt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3046,63,theory(equality)]) ).

cnf(3048,plain,
    ( sdtpldt0(sz10,X1) = sdtpldt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3047,theory(equality)]) ).

cnf(3262,negated_conjecture,
    ( sdtmndt0(xn,esk2_0) = xm
    | ~ aNaturalNumber0(xn) ),
    inference(er,[status(thm)],[2250,theory(equality)]) ).

cnf(3263,negated_conjecture,
    ( sdtmndt0(xn,esk2_0) = xm
    | $false ),
    inference(rw,[status(thm)],[3262,41,theory(equality)]) ).

cnf(3264,negated_conjecture,
    sdtmndt0(xn,esk2_0) = xm,
    inference(cn,[status(thm)],[3263,theory(equality)]) ).

cnf(3265,negated_conjecture,
    ( aNaturalNumber0(X1)
    | xm != X1
    | ~ sdtlseqdt0(esk2_0,xn)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[91,3264,theory(equality)]) ).

cnf(3269,negated_conjecture,
    ( aNaturalNumber0(X1)
    | xm != X1
    | $false
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[3265,2133,theory(equality)]) ).

cnf(3270,negated_conjecture,
    ( aNaturalNumber0(X1)
    | xm != X1
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[3269,73,theory(equality)]) ).

cnf(3271,negated_conjecture,
    ( aNaturalNumber0(X1)
    | xm != X1
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[3270,41,theory(equality)]) ).

cnf(3272,negated_conjecture,
    ( aNaturalNumber0(X1)
    | xm != X1 ),
    inference(cn,[status(thm)],[3271,theory(equality)]) ).

cnf(3341,plain,
    ( aNaturalNumber0(sdtpldt0(sz10,X1))
    | ~ aNaturalNumber0(sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[98,3048,theory(equality)]) ).

cnf(3362,plain,
    ( aNaturalNumber0(sdtpldt0(sz10,X1))
    | ~ aNaturalNumber0(sdtpldt0(sz00,X1))
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[3341,63,theory(equality)]) ).

cnf(3363,plain,
    ( aNaturalNumber0(sdtpldt0(sz10,X1))
    | ~ aNaturalNumber0(sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3362,theory(equality)]) ).

cnf(3466,plain,
    ( aNaturalNumber0(sdtpldt0(sz10,sz10))
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[3363,2519,theory(equality)]) ).

cnf(3481,plain,
    ( aNaturalNumber0(sdtpldt0(sz10,sz10))
    | $false ),
    inference(rw,[status(thm)],[3466,63,theory(equality)]) ).

cnf(3482,plain,
    aNaturalNumber0(sdtpldt0(sz10,sz10)),
    inference(cn,[status(thm)],[3481,theory(equality)]) ).

cnf(3607,negated_conjecture,
    ( sdtpldt0(xm,esk2_0) = sdtpldt0(xn,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[976,111,theory(equality)]) ).

cnf(3618,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,X1),X2) = sdtpldt0(xm,sdtpldt0(sdtpldt0(esk2_0,X1),X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[61,976,theory(equality)]) ).

cnf(3621,negated_conjecture,
    ( sdtpldt0(xm,esk2_0) = sdtpldt0(xn,esk1_2(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk1_2(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[976,251,theory(equality)]) ).

cnf(3624,negated_conjecture,
    ( sz00 = sdtpldt0(esk2_0,X1)
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[285,976,theory(equality)]) ).

cnf(3629,negated_conjecture,
    ( xn = sdtpldt0(xn,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[3607,934,theory(equality)]) ).

cnf(3630,negated_conjecture,
    ( xn = sdtpldt0(xn,sz00)
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[3629,95,theory(equality)]) ).

cnf(3631,negated_conjecture,
    ( xn = sdtpldt0(xn,sz00)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3630,73,theory(equality)]) ).

cnf(3632,negated_conjecture,
    xn = sdtpldt0(xn,sz00),
    inference(cn,[status(thm)],[3631,theory(equality)]) ).

cnf(3653,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,X1),X2) = sdtpldt0(xm,sdtpldt0(sdtpldt0(esk2_0,X1),X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[3618,42,theory(equality)]) ).

cnf(3654,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,X1),X2) = sdtpldt0(xm,sdtpldt0(sdtpldt0(esk2_0,X1),X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3653,theory(equality)]) ).

cnf(3657,negated_conjecture,
    ( xn = sdtpldt0(xn,esk1_2(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk1_2(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[3621,934,theory(equality)]) ).

cnf(3658,negated_conjecture,
    ( xn = sdtpldt0(xn,esk1_2(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk1_2(esk2_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[3657,73,theory(equality)]) ).

cnf(3659,negated_conjecture,
    ( xn = sdtpldt0(xn,esk1_2(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk1_2(esk2_0,esk2_0)) ),
    inference(cn,[status(thm)],[3658,theory(equality)]) ).

cnf(3664,negated_conjecture,
    ( sz00 = sdtpldt0(esk2_0,X1)
    | sdtpldt0(xn,X1) != xm
    | $false
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[3624,42,theory(equality)]) ).

cnf(3665,negated_conjecture,
    ( sz00 = sdtpldt0(esk2_0,X1)
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3664,theory(equality)]) ).

cnf(3685,negated_conjecture,
    ( sdtpldt0(sz00,xn) = xn
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[2360,3632,theory(equality)]) ).

cnf(3735,negated_conjecture,
    ( sdtpldt0(sz00,xn) = xn
    | $false ),
    inference(rw,[status(thm)],[3685,41,theory(equality)]) ).

cnf(3736,negated_conjecture,
    sdtpldt0(sz00,xn) = xn,
    inference(cn,[status(thm)],[3735,theory(equality)]) ).

cnf(3857,negated_conjecture,
    ( sz00 = X1
    | xn != sdtpldt0(X1,xn)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[102,3736,theory(equality)]) ).

cnf(3859,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sz00,sdtpldt0(xn,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[61,3736,theory(equality)]) ).

cnf(3887,negated_conjecture,
    ( sz00 = X1
    | xn != sdtpldt0(X1,xn)
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[3857,41,theory(equality)]) ).

cnf(3888,negated_conjecture,
    ( sz00 = X1
    | xn != sdtpldt0(X1,xn)
    | $false
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[3887,95,theory(equality)]) ).

cnf(3889,negated_conjecture,
    ( sz00 = X1
    | xn != sdtpldt0(X1,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3888,theory(equality)]) ).

cnf(3893,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sz00,sdtpldt0(xn,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[3859,41,theory(equality)]) ).

cnf(3894,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sz00,sdtpldt0(xn,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3893,95,theory(equality)]) ).

cnf(3895,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sz00,sdtpldt0(xn,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3894,theory(equality)]) ).

cnf(4180,negated_conjecture,
    ( sz00 = X1
    | sdtpldt0(xn,X1) != xn
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[3889,31,theory(equality)]) ).

cnf(4185,negated_conjecture,
    ( sz00 = X1
    | sdtpldt0(xn,X1) != xn
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[4180,41,theory(equality)]) ).

cnf(4186,negated_conjecture,
    ( sz00 = X1
    | sdtpldt0(xn,X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[4185,theory(equality)]) ).

cnf(4206,negated_conjecture,
    ( sdtpldt0(sz00,xm) = xm
    | ~ aNaturalNumber0(esk3_0)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[355,1023,theory(equality)]) ).

cnf(4257,negated_conjecture,
    ( sdtpldt0(sz00,xm) = xm
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[4206,70,theory(equality)]) ).

cnf(4258,negated_conjecture,
    ( sdtpldt0(sz00,xm) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[4257,41,theory(equality)]) ).

cnf(4259,negated_conjecture,
    sdtpldt0(sz00,xm) = xm,
    inference(cn,[status(thm)],[4258,theory(equality)]) ).

cnf(4370,negated_conjecture,
    ( sdtlseqdt0(xm,X1)
    | xm != X1
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[235,4259,theory(equality)]) ).

cnf(4413,negated_conjecture,
    ( sdtlseqdt0(xm,X1)
    | xm != X1
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[4370,95,theory(equality)]) ).

cnf(4414,negated_conjecture,
    ( sdtlseqdt0(xm,X1)
    | xm != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[4413,42,theory(equality)]) ).

cnf(4415,negated_conjecture,
    ( sdtlseqdt0(xm,X1)
    | xm != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[4414,theory(equality)]) ).

cnf(4448,plain,
    ( aNaturalNumber0(sdtpldt0(X1,sdtpldt0(X2,X3)))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[330,98]) ).

cnf(4706,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[331,98]) ).

cnf(6796,negated_conjecture,
    ( sdtlseqdt0(xm,X1)
    | xm != X1 ),
    inference(csr,[status(thm)],[4415,3272]) ).

cnf(6797,negated_conjecture,
    sdtlseqdt0(xm,xm),
    inference(er,[status(thm)],[6796,theory(equality)]) ).

cnf(6798,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xm))
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[57,6797,theory(equality)]) ).

cnf(6799,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xm)) = xm
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[56,6797,theory(equality)]) ).

cnf(6801,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xm))
    | $false ),
    inference(rw,[status(thm)],[6798,42,theory(equality)]) ).

cnf(6802,negated_conjecture,
    aNaturalNumber0(esk1_2(xm,xm)),
    inference(cn,[status(thm)],[6801,theory(equality)]) ).

cnf(6803,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xm)) = xm
    | $false ),
    inference(rw,[status(thm)],[6799,42,theory(equality)]) ).

cnf(6804,negated_conjecture,
    sdtpldt0(xm,esk1_2(xm,xm)) = xm,
    inference(cn,[status(thm)],[6803,theory(equality)]) ).

cnf(6825,negated_conjecture,
    ( sz00 = esk1_2(xm,xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(esk1_2(xm,xm)) ),
    inference(spm,[status(thm)],[285,6804,theory(equality)]) ).

cnf(6880,negated_conjecture,
    ( sz00 = esk1_2(xm,xm)
    | $false
    | ~ aNaturalNumber0(esk1_2(xm,xm)) ),
    inference(rw,[status(thm)],[6825,42,theory(equality)]) ).

cnf(6881,negated_conjecture,
    ( sz00 = esk1_2(xm,xm)
    | $false
    | $false ),
    inference(rw,[status(thm)],[6880,6802,theory(equality)]) ).

cnf(6882,negated_conjecture,
    sz00 = esk1_2(xm,xm),
    inference(cn,[status(thm)],[6881,theory(equality)]) ).

cnf(6928,negated_conjecture,
    sdtpldt0(xm,sz00) = xm,
    inference(rw,[status(thm)],[6804,6882,theory(equality)]) ).

cnf(9207,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(X1,sdtpldt0(sz00,xn))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[4706,3895,theory(equality)]) ).

cnf(9296,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(X1,xn)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[9207,3736,theory(equality)]) ).

cnf(9297,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(X1,xn)
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[9296,41,theory(equality)]) ).

cnf(9298,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(X1,xn)
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[9297,95,theory(equality)]) ).

cnf(9299,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(X1,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[9298,theory(equality)]) ).

cnf(33880,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(esk2_0,esk2_0)) = xn
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[3659,215,theory(equality)]) ).

cnf(33881,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(esk2_0,esk2_0)) = xn
    | $false ),
    inference(rw,[status(thm)],[33880,73,theory(equality)]) ).

cnf(33882,negated_conjecture,
    sdtpldt0(xn,esk1_2(esk2_0,esk2_0)) = xn,
    inference(cn,[status(thm)],[33881,theory(equality)]) ).

cnf(33900,negated_conjecture,
    ( sz00 = esk1_2(esk2_0,esk2_0)
    | ~ aNaturalNumber0(esk1_2(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[4186,33882,theory(equality)]) ).

cnf(34550,negated_conjecture,
    ( esk1_2(esk2_0,esk2_0) = sz00
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[33900,215,theory(equality)]) ).

cnf(34551,negated_conjecture,
    ( esk1_2(esk2_0,esk2_0) = sz00
    | $false ),
    inference(rw,[status(thm)],[34550,73,theory(equality)]) ).

cnf(34552,negated_conjecture,
    esk1_2(esk2_0,esk2_0) = sz00,
    inference(cn,[status(thm)],[34551,theory(equality)]) ).

cnf(34554,negated_conjecture,
    ( sdtpldt0(esk2_0,sz00) = esk2_0
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[251,34552,theory(equality)]) ).

cnf(34566,negated_conjecture,
    ( sdtpldt0(esk2_0,sz00) = esk2_0
    | $false ),
    inference(rw,[status(thm)],[34554,73,theory(equality)]) ).

cnf(34567,negated_conjecture,
    sdtpldt0(esk2_0,sz00) = esk2_0,
    inference(cn,[status(thm)],[34566,theory(equality)]) ).

cnf(34591,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(X1,esk2_0))
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[4448,34567,theory(equality)]) ).

cnf(34608,negated_conjecture,
    ( sdtasdt0(sz10,esk2_0) = sdtpldt0(esk2_0,sdtasdt0(sz10,sz00))
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[497,34567,theory(equality)]) ).

cnf(34621,negated_conjecture,
    ( sdtasdt0(esk2_0,sz10) = sdtpldt0(esk2_0,sdtasdt0(sz00,sz10))
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[536,34567,theory(equality)]) ).

cnf(34695,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(X1,esk2_0))
    | $false
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[34591,95,theory(equality)]) ).

cnf(34696,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(X1,esk2_0))
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[34695,73,theory(equality)]) ).

cnf(34697,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(X1,esk2_0))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[34696,theory(equality)]) ).

cnf(34746,negated_conjecture,
    ( sdtasdt0(sz10,esk2_0) = esk2_0
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[34608,725,theory(equality)]),34567,theory(equality)]) ).

cnf(34747,negated_conjecture,
    ( sdtasdt0(sz10,esk2_0) = esk2_0
    | $false
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[34746,73,theory(equality)]) ).

cnf(34748,negated_conjecture,
    ( sdtasdt0(sz10,esk2_0) = esk2_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[34747,95,theory(equality)]) ).

cnf(34749,negated_conjecture,
    sdtasdt0(sz10,esk2_0) = esk2_0,
    inference(cn,[status(thm)],[34748,theory(equality)]) ).

cnf(34786,negated_conjecture,
    ( sdtasdt0(esk2_0,sz10) = esk2_0
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[34621,749,theory(equality)]),34567,theory(equality)]) ).

cnf(34787,negated_conjecture,
    ( sdtasdt0(esk2_0,sz10) = esk2_0
    | $false
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[34786,73,theory(equality)]) ).

cnf(34788,negated_conjecture,
    ( sdtasdt0(esk2_0,sz10) = esk2_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[34787,95,theory(equality)]) ).

cnf(34789,negated_conjecture,
    sdtasdt0(esk2_0,sz10) = esk2_0,
    inference(cn,[status(thm)],[34788,theory(equality)]) ).

cnf(37397,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[34697,31,theory(equality)]) ).

cnf(37412,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[37397,73,theory(equality)]) ).

cnf(37413,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[37412,theory(equality)]) ).

cnf(37574,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(xn,esk2_0))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[37413,9299,theory(equality)]) ).

cnf(37601,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(xn,esk2_0))
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[37574,41,theory(equality)]) ).

cnf(37602,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(xn,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[37601,73,theory(equality)]) ).

cnf(37603,negated_conjecture,
    aNaturalNumber0(sdtpldt0(xn,esk2_0)),
    inference(cn,[status(thm)],[37602,theory(equality)]) ).

cnf(48055,negated_conjecture,
    ( sdtpldt0(sdtasdt0(sz10,esk2_0),esk2_0) = sdtasdt0(esk2_0,sdtpldt0(sz10,sz10))
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[1183,34789,theory(equality)]) ).

cnf(48340,negated_conjecture,
    ( sdtpldt0(esk2_0,esk2_0) = sdtasdt0(esk2_0,sdtpldt0(sz10,sz10))
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[48055,34749,theory(equality)]) ).

cnf(48341,negated_conjecture,
    ( sdtpldt0(esk2_0,esk2_0) = sdtasdt0(esk2_0,sdtpldt0(sz10,sz10))
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[48340,73,theory(equality)]) ).

cnf(48342,negated_conjecture,
    ( sdtpldt0(esk2_0,esk2_0) = sdtasdt0(esk2_0,sdtpldt0(sz10,sz10))
    | $false
    | $false ),
    inference(rw,[status(thm)],[48341,63,theory(equality)]) ).

cnf(48343,negated_conjecture,
    sdtpldt0(esk2_0,esk2_0) = sdtasdt0(esk2_0,sdtpldt0(sz10,sz10)),
    inference(cn,[status(thm)],[48342,theory(equality)]) ).

cnf(65241,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(esk2_0,esk2_0))
    | ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[94,48343,theory(equality)]) ).

cnf(65255,negated_conjecture,
    ( sdtasdt0(sz10,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0)
    | ~ aNaturalNumber0(sdtpldt0(sz10,sz10))
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[382,48343,theory(equality)]) ).

cnf(65313,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(esk2_0,esk2_0))
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[65241,3482,theory(equality)]) ).

cnf(65314,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(esk2_0,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[65313,73,theory(equality)]) ).

cnf(65315,negated_conjecture,
    aNaturalNumber0(sdtpldt0(esk2_0,esk2_0)),
    inference(cn,[status(thm)],[65314,theory(equality)]) ).

cnf(65356,negated_conjecture,
    ( sdtasdt0(sz10,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0)
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[65255,3482,theory(equality)]) ).

cnf(65357,negated_conjecture,
    ( sdtasdt0(sz10,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[65356,73,theory(equality)]) ).

cnf(65358,negated_conjecture,
    sdtasdt0(sz10,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0),
    inference(cn,[status(thm)],[65357,theory(equality)]) ).

cnf(65876,negated_conjecture,
    ( sdtpldt0(sz00,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[1855,65358,theory(equality)]) ).

cnf(66003,negated_conjecture,
    ( sdtpldt0(sz00,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[65876,65315,theory(equality)]) ).

cnf(66004,negated_conjecture,
    sdtpldt0(sz00,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(esk2_0,esk2_0),
    inference(cn,[status(thm)],[66003,theory(equality)]) ).

cnf(90090,negated_conjecture,
    ( sdtlseqdt0(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[1973,66004,theory(equality)]) ).

cnf(90308,negated_conjecture,
    ( sdtlseqdt0(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))
    | $false
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0)) ),
    inference(rw,[status(thm)],[90090,95,theory(equality)]) ).

cnf(90309,negated_conjecture,
    ( sdtlseqdt0(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[90308,65315,theory(equality)]) ).

cnf(90310,negated_conjecture,
    sdtlseqdt0(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0)),
    inference(cn,[status(thm)],[90309,theory(equality)]) ).

cnf(90481,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0)))
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[57,90310,theory(equality)]) ).

cnf(90482,negated_conjecture,
    ( sdtpldt0(sdtpldt0(esk2_0,esk2_0),esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))) = sdtpldt0(esk2_0,esk2_0)
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[56,90310,theory(equality)]) ).

cnf(90491,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0)))
    | $false ),
    inference(rw,[status(thm)],[90481,65315,theory(equality)]) ).

cnf(90492,negated_conjecture,
    aNaturalNumber0(esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))),
    inference(cn,[status(thm)],[90491,theory(equality)]) ).

cnf(90493,negated_conjecture,
    ( sdtpldt0(sdtpldt0(esk2_0,esk2_0),esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))) = sdtpldt0(esk2_0,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[90482,65315,theory(equality)]) ).

cnf(90494,negated_conjecture,
    sdtpldt0(sdtpldt0(esk2_0,esk2_0),esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))) = sdtpldt0(esk2_0,esk2_0),
    inference(cn,[status(thm)],[90493,theory(equality)]) ).

cnf(98208,negated_conjecture,
    ( sz00 = esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0))
    | ~ aNaturalNumber0(esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))) ),
    inference(spm,[status(thm)],[285,90494,theory(equality)]) ).

cnf(98311,negated_conjecture,
    ( sz00 = esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))
    | $false
    | ~ aNaturalNumber0(esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))) ),
    inference(rw,[status(thm)],[98208,65315,theory(equality)]) ).

cnf(98312,negated_conjecture,
    ( sz00 = esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[98311,90492,theory(equality)]) ).

cnf(98313,negated_conjecture,
    sz00 = esk1_2(sdtpldt0(esk2_0,esk2_0),sdtpldt0(esk2_0,esk2_0)),
    inference(cn,[status(thm)],[98312,theory(equality)]) ).

cnf(98500,negated_conjecture,
    sdtpldt0(sdtpldt0(esk2_0,esk2_0),sz00) = sdtpldt0(esk2_0,esk2_0),
    inference(rw,[status(thm)],[90494,98313,theory(equality)]) ).

cnf(104347,negated_conjecture,
    ( sdtpldt0(esk2_0,xn) = sdtpldt0(xn,esk2_0)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[2247,934,theory(equality)]) ).

cnf(104464,negated_conjecture,
    ( sdtpldt0(esk2_0,xn) = sdtpldt0(xn,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[104347,73,theory(equality)]) ).

cnf(104465,negated_conjecture,
    sdtpldt0(esk2_0,xn) = sdtpldt0(xn,esk2_0),
    inference(cn,[status(thm)],[104464,theory(equality)]) ).

cnf(105125,negated_conjecture,
    ( sdtpldt0(sz00,sdtpldt0(xn,esk2_0)) = sdtpldt0(xn,esk2_0)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[355,104465,theory(equality)]) ).

cnf(105280,negated_conjecture,
    ( sdtpldt0(sz00,sdtpldt0(xn,esk2_0)) = sdtpldt0(xn,esk2_0)
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[105125,41,theory(equality)]) ).

cnf(105281,negated_conjecture,
    ( sdtpldt0(sz00,sdtpldt0(xn,esk2_0)) = sdtpldt0(xn,esk2_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[105280,73,theory(equality)]) ).

cnf(105282,negated_conjecture,
    sdtpldt0(sz00,sdtpldt0(xn,esk2_0)) = sdtpldt0(xn,esk2_0),
    inference(cn,[status(thm)],[105281,theory(equality)]) ).

cnf(109870,negated_conjecture,
    ( sdtlseqdt0(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0)) ),
    inference(spm,[status(thm)],[1973,105282,theory(equality)]) ).

cnf(110128,negated_conjecture,
    ( sdtlseqdt0(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))
    | $false
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0)) ),
    inference(rw,[status(thm)],[109870,95,theory(equality)]) ).

cnf(110129,negated_conjecture,
    ( sdtlseqdt0(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[110128,37603,theory(equality)]) ).

cnf(110130,negated_conjecture,
    sdtlseqdt0(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0)),
    inference(cn,[status(thm)],[110129,theory(equality)]) ).

cnf(110215,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0)))
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0)) ),
    inference(spm,[status(thm)],[57,110130,theory(equality)]) ).

cnf(110216,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,esk2_0),esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))) = sdtpldt0(xn,esk2_0)
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0)) ),
    inference(spm,[status(thm)],[56,110130,theory(equality)]) ).

cnf(110219,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0)))
    | $false ),
    inference(rw,[status(thm)],[110215,37603,theory(equality)]) ).

cnf(110220,negated_conjecture,
    aNaturalNumber0(esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))),
    inference(cn,[status(thm)],[110219,theory(equality)]) ).

cnf(110221,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,esk2_0),esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))) = sdtpldt0(xn,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[110216,37603,theory(equality)]) ).

cnf(110222,negated_conjecture,
    sdtpldt0(sdtpldt0(xn,esk2_0),esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))) = sdtpldt0(xn,esk2_0),
    inference(cn,[status(thm)],[110221,theory(equality)]) ).

cnf(116318,negated_conjecture,
    ( sz00 = esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0))
    | ~ aNaturalNumber0(esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))) ),
    inference(spm,[status(thm)],[285,110222,theory(equality)]) ).

cnf(116421,negated_conjecture,
    ( sz00 = esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))
    | $false
    | ~ aNaturalNumber0(esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))) ),
    inference(rw,[status(thm)],[116318,37603,theory(equality)]) ).

cnf(116422,negated_conjecture,
    ( sz00 = esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[116421,110220,theory(equality)]) ).

cnf(116423,negated_conjecture,
    sz00 = esk1_2(sdtpldt0(xn,esk2_0),sdtpldt0(xn,esk2_0)),
    inference(cn,[status(thm)],[116422,theory(equality)]) ).

cnf(116626,negated_conjecture,
    sdtpldt0(sdtpldt0(xn,esk2_0),sz00) = sdtpldt0(xn,esk2_0),
    inference(rw,[status(thm)],[110222,116423,theory(equality)]) ).

cnf(150951,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(sdtpldt0(esk2_0,X1),X2)) = sdtpldt0(sdtpldt0(xn,X1),X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[3654,37413]) ).

cnf(150956,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(sdtpldt0(xn,esk2_0),sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[150951,98500,theory(equality)]) ).

cnf(151127,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(xn,esk2_0)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[150956,116626,theory(equality)]) ).

cnf(151128,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(xn,esk2_0)
    | $false
    | ~ aNaturalNumber0(esk2_0) ),
    inference(rw,[status(thm)],[151127,95,theory(equality)]) ).

cnf(151129,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(xn,esk2_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[151128,73,theory(equality)]) ).

cnf(151130,negated_conjecture,
    sdtpldt0(xm,sdtpldt0(esk2_0,esk2_0)) = sdtpldt0(xn,esk2_0),
    inference(cn,[status(thm)],[151129,theory(equality)]) ).

cnf(151437,negated_conjecture,
    ( sdtlseqdt0(xm,sdtpldt0(xn,esk2_0))
    | ~ aNaturalNumber0(sdtpldt0(esk2_0,esk2_0))
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[1967,151130,theory(equality)]) ).

cnf(151576,negated_conjecture,
    ( sdtlseqdt0(xm,sdtpldt0(xn,esk2_0))
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[151437,65315,theory(equality)]) ).

cnf(151577,negated_conjecture,
    ( sdtlseqdt0(xm,sdtpldt0(xn,esk2_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[151576,42,theory(equality)]) ).

cnf(151578,negated_conjecture,
    sdtlseqdt0(xm,sdtpldt0(xn,esk2_0)),
    inference(cn,[status(thm)],[151577,theory(equality)]) ).

cnf(151897,negated_conjecture,
    ( sdtpldt0(xm,sdtmndt0(sdtpldt0(xn,esk2_0),xm)) = sdtpldt0(xn,esk2_0)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0)) ),
    inference(spm,[status(thm)],[356,151578,theory(equality)]) ).

cnf(151907,negated_conjecture,
    ( sdtpldt0(xm,sdtmndt0(sdtpldt0(xn,esk2_0),xm)) = sdtpldt0(xn,esk2_0)
    | $false
    | ~ aNaturalNumber0(sdtpldt0(xn,esk2_0)) ),
    inference(rw,[status(thm)],[151897,42,theory(equality)]) ).

cnf(151908,negated_conjecture,
    ( sdtpldt0(xm,sdtmndt0(sdtpldt0(xn,esk2_0),xm)) = sdtpldt0(xn,esk2_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[151907,37603,theory(equality)]) ).

cnf(151909,negated_conjecture,
    sdtpldt0(xm,sdtmndt0(sdtpldt0(xn,esk2_0),xm)) = sdtpldt0(xn,esk2_0),
    inference(cn,[status(thm)],[151908,theory(equality)]) ).

cnf(153084,negated_conjecture,
    ( sdtpldt0(esk2_0,X1) = sz00
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[3665,37413]) ).

cnf(153085,negated_conjecture,
    ( sdtpldt0(esk2_0,esk3_0) = sz00
    | ~ aNaturalNumber0(esk3_0) ),
    inference(spm,[status(thm)],[153084,1023,theory(equality)]) ).

cnf(153111,negated_conjecture,
    ( sdtpldt0(esk2_0,esk3_0) = sz00
    | $false ),
    inference(rw,[status(thm)],[153085,70,theory(equality)]) ).

cnf(153112,negated_conjecture,
    sdtpldt0(esk2_0,esk3_0) = sz00,
    inference(cn,[status(thm)],[153111,theory(equality)]) ).

cnf(153173,negated_conjecture,
    ( sz00 = esk2_0
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(esk3_0) ),
    inference(spm,[status(thm)],[81,153112,theory(equality)]) ).

cnf(153273,negated_conjecture,
    ( sz00 = esk2_0
    | $false
    | ~ aNaturalNumber0(esk3_0) ),
    inference(rw,[status(thm)],[153173,73,theory(equality)]) ).

cnf(153274,negated_conjecture,
    ( sz00 = esk2_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[153273,70,theory(equality)]) ).

cnf(153275,negated_conjecture,
    sz00 = esk2_0,
    inference(cn,[status(thm)],[153274,theory(equality)]) ).

cnf(153569,negated_conjecture,
    sdtpldt0(xm,sz00) = sdtpldt0(xn,esk2_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[151909,153275,theory(equality)]),3632,theory(equality)]),1954,theory(equality)]),153275,theory(equality)]) ).

cnf(153570,negated_conjecture,
    sdtpldt0(xm,sz00) = xn,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[153569,153275,theory(equality)]),3632,theory(equality)]) ).

cnf(153571,negated_conjecture,
    xm = xn,
    inference(rw,[status(thm)],[153570,6928,theory(equality)]) ).

cnf(153572,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[153571,67,theory(equality)]) ).

cnf(153573,negated_conjecture,
    $false,
    153572,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM459+2 : 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 : n112.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 05:17:59 CST 2018
% 0.03/0.23  % CPUTime  : 
% 0.06/0.28  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.28  --creating new selector for []
% 2.39/2.60  -running prover on /export/starexec/sandbox/tmp/tmp2ID3DG/sel_theBenchmark.p_1 with time limit 29
% 2.39/2.60  -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/tmp2ID3DG/sel_theBenchmark.p_1']
% 2.39/2.60  -prover status Theorem
% 2.39/2.60  Problem theBenchmark.p solved in phase 0.
% 2.39/2.60  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.39/2.60  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.39/2.60  Solved 1 out of 1.
% 2.39/2.60  # Problem is unsatisfiable (or provable), constructing proof object
% 2.39/2.60  # SZS status Theorem
% 2.39/2.60  # SZS output start CNFRefutation.
% See solution above
% 2.39/2.61  # SZS output end CNFRefutation
%------------------------------------------------------------------------------