TSTP Solution File: NUM459+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM459+1 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n073.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 23.17s
% Output   : CNFRefutation 23.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   54
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  341 (  62 unt;   0 def)
%            Number of atoms       : 1110 ( 242 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives : 1312 ( 543   ~; 675   |;  69   &)
%                                         (   2 <=>;  23  =>;   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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  316 (   0 sgn 133   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/sel_theBenchmark.p_1',mMulCanc) ).

fof(5,axiom,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/sel_theBenchmark.p_1',mAddAsso) ).

fof(10,axiom,
    ( aNaturalNumber0(sz10)
    & ~ equal(sz10,sz00) ),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/sel_theBenchmark.p_1',mSortsC_01) ).

fof(11,conjecture,
    ( ( sdtlseqdt0(xm,xn)
      & sdtlseqdt0(xn,xm) )
   => equal(xm,xn) ),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/sel_theBenchmark.p_1',mZeroAdd) ).

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/tmpyAR6Vf/sel_theBenchmark.p_1',mDefDiff) ).

fof(16,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/sel_theBenchmark.p_1',mSortsB_02) ).

fof(17,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/sel_theBenchmark.p_1',mSortsC) ).

fof(18,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/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/tmpyAR6Vf/sel_theBenchmark.p_1',m_MulUnit) ).

fof(23,negated_conjecture,
    ~ ( ( sdtlseqdt0(xm,xn)
        & 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]) ).

cnf(28,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ 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,
    ( sdtlseqdt0(xm,xn)
    & sdtlseqdt0(xn,xm)
    & ~ equal(xm,xn) ),
    inference(fof_nnf,[status(thm)],[23]) ).

cnf(65,negated_conjecture,
    xm != xn,
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(66,negated_conjecture,
    sdtlseqdt0(xn,xm),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(67,negated_conjecture,
    sdtlseqdt0(xm,xn),
    inference(split_conjunct,[status(thm)],[64]) ).

fof(68,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(69,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)],[68]) ).

cnf(70,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[69]) ).

fof(71,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(72,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | ~ equal(sdtpldt0(X3,X4),sz00)
      | ( equal(X3,sz00)
        & equal(X4,sz00) ) ),
    inference(variable_rename,[status(thm)],[71]) ).

fof(73,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)],[72]) ).

cnf(75,plain,
    ( X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X1) != sz00 ),
    inference(split_conjunct,[status(thm)],[73]) ).

fof(79,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(80,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)],[79]) ).

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

fof(82,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)],[81]) ).

cnf(83,plain,
    ( X3 = sdtmndt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[82]) ).

cnf(84,plain,
    ( sdtpldt0(X2,X3) = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[82]) ).

cnf(85,plain,
    ( aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | X3 != sdtmndt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[82]) ).

fof(86,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(87,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[86]) ).

cnf(88,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[87]) ).

cnf(89,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(90,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(91,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[90]) ).

cnf(92,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[91]) ).

fof(93,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(94,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)],[93]) ).

fof(95,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)],[94]) ).

cnf(96,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X2,X3) != sdtpldt0(X1,X3) ),
    inference(split_conjunct,[status(thm)],[95]) ).

cnf(97,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
    inference(split_conjunct,[status(thm)],[95]) ).

fof(98,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(99,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[98]) ).

cnf(100,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[99]) ).

fof(101,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(102,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtpldt0(X2,sz00),X2)
        & equal(X2,sdtpldt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[101]) ).

fof(103,plain,
    ! [X2] :
      ( ( equal(sdtpldt0(X2,sz00),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtpldt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[102]) ).

cnf(104,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[103]) ).

cnf(105,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[103]) ).

fof(106,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(107,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz10),X2)
        & equal(X2,sdtasdt0(sz10,X2)) ) ),
    inference(variable_rename,[status(thm)],[106]) ).

fof(108,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz10),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtasdt0(sz10,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[107]) ).

cnf(109,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[108]) ).

cnf(110,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[108]) ).

cnf(181,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[57,67,theory(equality)]) ).

cnf(182,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xn,xm))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[57,66,theory(equality)]) ).

cnf(184,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xn))
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[181,42,theory(equality)]) ).

cnf(185,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[184,41,theory(equality)]) ).

cnf(186,negated_conjecture,
    aNaturalNumber0(esk1_2(xm,xn)),
    inference(cn,[status(thm)],[185,theory(equality)]) ).

cnf(187,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xn,xm))
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[182,41,theory(equality)]) ).

cnf(188,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xn,xm))
    | $false
    | $false ),
    inference(rw,[status(thm)],[187,42,theory(equality)]) ).

cnf(189,negated_conjecture,
    aNaturalNumber0(esk1_2(xn,xm)),
    inference(cn,[status(thm)],[188,theory(equality)]) ).

cnf(198,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xn)) = xn
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[56,67,theory(equality)]) ).

cnf(199,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(xn,xm)) = xm
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[56,66,theory(equality)]) ).

cnf(201,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xn)) = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[198,42,theory(equality)]) ).

cnf(202,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xn)) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[201,41,theory(equality)]) ).

cnf(203,negated_conjecture,
    sdtpldt0(xm,esk1_2(xm,xn)) = xn,
    inference(cn,[status(thm)],[202,theory(equality)]) ).

cnf(204,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(xn,xm)) = xm
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[199,41,theory(equality)]) ).

cnf(205,negated_conjecture,
    ( sdtpldt0(xn,esk1_2(xn,xm)) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[204,42,theory(equality)]) ).

cnf(206,negated_conjecture,
    sdtpldt0(xn,esk1_2(xn,xm)) = xm,
    inference(cn,[status(thm)],[205,theory(equality)]) ).

cnf(207,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(er,[status(thm)],[58,theory(equality)]) ).

cnf(218,plain,
    ( aNaturalNumber0(sdtmndt0(X1,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[85,theory(equality)]) ).

cnf(220,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[97,105,theory(equality)]) ).

cnf(228,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[220,89,theory(equality)]) ).

cnf(229,plain,
    ( sz00 = X1
    | X2 != sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[228,theory(equality)]) ).

cnf(253,plain,
    ( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[84,theory(equality)]) ).

cnf(257,plain,
    ( sz00 = sz10
    | X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[39,110,theory(equality)]) ).

cnf(269,plain,
    ( sz00 = sz10
    | X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[257,63,theory(equality)]) ).

cnf(270,plain,
    ( sz00 = sz10
    | X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[269,theory(equality)]) ).

cnf(271,plain,
    ( X1 = X2
    | X1 != sdtasdt0(X2,sz10)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[270,62,theory(equality)]) ).

cnf(336,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[61,104,theory(equality)]) ).

cnf(340,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(355,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[336,89,theory(equality)]) ).

cnf(356,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[355,theory(equality)]) ).

cnf(357,plain,
    ( sdtmndt0(X1,X2) = X3
    | sdtpldt0(X2,X3) != X1
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[83,58]) ).

cnf(358,plain,
    ( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(er,[status(thm)],[357,theory(equality)]) ).

cnf(374,plain,
    ( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[47,110,theory(equality)]) ).

cnf(376,plain,
    ( sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[47,109,theory(equality)]) ).

cnf(404,plain,
    ( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[374,63,theory(equality)]) ).

cnf(405,plain,
    ( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[404,theory(equality)]) ).

cnf(408,plain,
    ( sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2))
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[376,63,theory(equality)]) ).

cnf(409,plain,
    ( sdtpldt0(X1,sdtasdt0(sz10,X2)) = sdtasdt0(sz10,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[408,theory(equality)]) ).

cnf(416,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(sdtpldt0(X1,X2),sz10)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[46,110,theory(equality)]) ).

cnf(447,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(sdtpldt0(X1,X2),sz10)
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(rw,[status(thm)],[416,63,theory(equality)]) ).

cnf(448,plain,
    ( sdtpldt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(sdtpldt0(X1,X2),sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[447,theory(equality)]) ).

cnf(461,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)],[271,70,theory(equality)]) ).

cnf(471,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)],[461,63,theory(equality)]) ).

cnf(472,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)],[471,theory(equality)]) ).

cnf(495,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk1_2(xm,xn))
    | ~ aNaturalNumber0(esk1_2(xm,xn))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[96,203,theory(equality)]) ).

cnf(498,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk1_2(xm,xn)
    | xn != X1
    | ~ aNaturalNumber0(esk1_2(xm,xn))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[357,203,theory(equality)]) ).

cnf(518,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk1_2(xm,xn))
    | $false
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[495,186,theory(equality)]) ).

cnf(519,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk1_2(xm,xn))
    | $false
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[518,42,theory(equality)]) ).

cnf(520,negated_conjecture,
    ( xm = X1
    | xn != sdtpldt0(X1,esk1_2(xm,xn))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[519,theory(equality)]) ).

cnf(527,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk1_2(xm,xn)
    | xn != X1
    | $false
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[498,186,theory(equality)]) ).

cnf(528,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk1_2(xm,xn)
    | xn != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[527,42,theory(equality)]) ).

cnf(529,negated_conjecture,
    ( sdtmndt0(X1,xm) = esk1_2(xm,xn)
    | xn != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[528,theory(equality)]) ).

cnf(578,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X1 != sdtasdt0(X2,sdtasdt0(X3,sz10))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[472,88]) ).

cnf(579,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(sdtasdt0(X1,sdtasdt0(X2,sz10)))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[578,theory(equality)]) ).

cnf(615,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,sz10))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[579,109,theory(equality)]) ).

cnf(625,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,sz10))
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[615,63,theory(equality)]) ).

cnf(626,plain,
    ( sdtasdt0(X1,sz10) = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,sz10))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[625,theory(equality)]) ).

cnf(634,plain,
    ( sz00 = sdtasdt0(sz10,sz00)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[626,27,theory(equality)]) ).

cnf(636,plain,
    ( sz10 = sdtasdt0(sz10,sz10)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[626,109,theory(equality)]) ).

cnf(639,plain,
    ( sz00 = sdtasdt0(sz10,sz00)
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[634,89,theory(equality)]) ).

cnf(640,plain,
    ( sz00 = sdtasdt0(sz10,sz00)
    | $false
    | $false ),
    inference(rw,[status(thm)],[639,63,theory(equality)]) ).

cnf(641,plain,
    sz00 = sdtasdt0(sz10,sz00),
    inference(cn,[status(thm)],[640,theory(equality)]) ).

cnf(642,plain,
    ( sz10 = sdtasdt0(sz10,sz10)
    | $false ),
    inference(rw,[status(thm)],[636,63,theory(equality)]) ).

cnf(643,plain,
    sz10 = sdtasdt0(sz10,sz10),
    inference(cn,[status(thm)],[642,theory(equality)]) ).

cnf(654,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[47,641,theory(equality)]) ).

cnf(680,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | $false
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[654,63,theory(equality)]) ).

cnf(681,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[680,89,theory(equality)]) ).

cnf(682,plain,
    ( sdtpldt0(sz00,sdtasdt0(sz10,X1)) = sdtasdt0(sz10,sdtpldt0(sz00,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[681,theory(equality)]) ).

cnf(875,negated_conjecture,
    ( xm = X1
    | sdtpldt0(esk1_2(xm,xn),X1) != xn
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk1_2(xm,xn)) ),
    inference(spm,[status(thm)],[520,31,theory(equality)]) ).

cnf(881,negated_conjecture,
    ( xm = X1
    | sdtpldt0(esk1_2(xm,xn),X1) != xn
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[875,186,theory(equality)]) ).

cnf(882,negated_conjecture,
    ( xm = X1
    | sdtpldt0(esk1_2(xm,xn),X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[881,theory(equality)]) ).

cnf(1620,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[207,92]) ).

cnf(1626,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,X1))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[1620,31,theory(equality)]) ).

cnf(1694,negated_conjecture,
    ( sdtlseqdt0(esk1_2(xm,xn),xn)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(esk1_2(xm,xn)) ),
    inference(spm,[status(thm)],[1626,203,theory(equality)]) ).

cnf(1703,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,sdtpldt0(X3,X1)))
    | ~ aNaturalNumber0(sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[1626,61,theory(equality)]) ).

cnf(1708,negated_conjecture,
    ( sdtlseqdt0(esk1_2(xm,xn),xn)
    | $false
    | ~ aNaturalNumber0(esk1_2(xm,xn)) ),
    inference(rw,[status(thm)],[1694,42,theory(equality)]) ).

cnf(1709,negated_conjecture,
    ( sdtlseqdt0(esk1_2(xm,xn),xn)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1708,186,theory(equality)]) ).

cnf(1710,negated_conjecture,
    sdtlseqdt0(esk1_2(xm,xn),xn),
    inference(cn,[status(thm)],[1709,theory(equality)]) ).

cnf(1780,negated_conjecture,
    ( sdtpldt0(esk1_2(xm,xn),esk1_2(esk1_2(xm,xn),xn)) = xn
    | ~ aNaturalNumber0(esk1_2(xm,xn))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[56,1710,theory(equality)]) ).

cnf(1784,negated_conjecture,
    ( sdtpldt0(esk1_2(xm,xn),esk1_2(esk1_2(xm,xn),xn)) = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[1780,186,theory(equality)]) ).

cnf(1785,negated_conjecture,
    ( sdtpldt0(esk1_2(xm,xn),esk1_2(esk1_2(xm,xn),xn)) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[1784,41,theory(equality)]) ).

cnf(1786,negated_conjecture,
    sdtpldt0(esk1_2(xm,xn),esk1_2(esk1_2(xm,xn),xn)) = xn,
    inference(cn,[status(thm)],[1785,theory(equality)]) ).

cnf(1795,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[218,67,theory(equality)]) ).

cnf(1796,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[218,66,theory(equality)]) ).

cnf(1804,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xn,xm))
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[1795,42,theory(equality)]) ).

cnf(1805,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xn,xm))
    | $false
    | $false ),
    inference(rw,[status(thm)],[1804,41,theory(equality)]) ).

cnf(1806,negated_conjecture,
    aNaturalNumber0(sdtmndt0(xn,xm)),
    inference(cn,[status(thm)],[1805,theory(equality)]) ).

cnf(1807,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xm,xn))
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[1796,41,theory(equality)]) ).

cnf(1808,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xm,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[1807,42,theory(equality)]) ).

cnf(1809,negated_conjecture,
    aNaturalNumber0(sdtmndt0(xm,xn)),
    inference(cn,[status(thm)],[1808,theory(equality)]) ).

cnf(1845,plain,
    ( sdtasdt0(sz10,X1) = sdtpldt0(sz00,sdtasdt0(sz10,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[682,104,theory(equality)]) ).

cnf(1910,plain,
    ( sdtpldt0(sz00,sz10) = sz10
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[1845,643,theory(equality)]) ).

cnf(1941,plain,
    ( sdtpldt0(sz00,sz10) = sz10
    | $false ),
    inference(rw,[status(thm)],[1910,63,theory(equality)]) ).

cnf(1942,plain,
    sdtpldt0(sz00,sz10) = sz10,
    inference(cn,[status(thm)],[1941,theory(equality)]) ).

cnf(1995,plain,
    ( sdtlseqdt0(sz10,sz10)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[1626,1942,theory(equality)]) ).

cnf(2034,plain,
    ( sdtlseqdt0(sz10,sz10)
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[1995,89,theory(equality)]) ).

cnf(2035,plain,
    ( sdtlseqdt0(sz10,sz10)
    | $false
    | $false ),
    inference(rw,[status(thm)],[2034,63,theory(equality)]) ).

cnf(2036,plain,
    sdtlseqdt0(sz10,sz10),
    inference(cn,[status(thm)],[2035,theory(equality)]) ).

cnf(2056,plain,
    ( aNaturalNumber0(esk1_2(sz10,sz10))
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[57,2036,theory(equality)]) ).

cnf(2057,plain,
    ( sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[56,2036,theory(equality)]) ).

cnf(2059,plain,
    ( aNaturalNumber0(esk1_2(sz10,sz10))
    | $false ),
    inference(rw,[status(thm)],[2056,63,theory(equality)]) ).

cnf(2060,plain,
    aNaturalNumber0(esk1_2(sz10,sz10)),
    inference(cn,[status(thm)],[2059,theory(equality)]) ).

cnf(2061,plain,
    ( sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10
    | $false ),
    inference(rw,[status(thm)],[2057,63,theory(equality)]) ).

cnf(2062,plain,
    sdtpldt0(sz10,esk1_2(sz10,sz10)) = sz10,
    inference(cn,[status(thm)],[2061,theory(equality)]) ).

cnf(2192,plain,
    ( sz00 = esk1_2(sz10,sz10)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(esk1_2(sz10,sz10)) ),
    inference(spm,[status(thm)],[229,2062,theory(equality)]) ).

cnf(2221,plain,
    ( sz00 = esk1_2(sz10,sz10)
    | $false
    | ~ aNaturalNumber0(esk1_2(sz10,sz10)) ),
    inference(rw,[status(thm)],[2192,63,theory(equality)]) ).

cnf(2222,plain,
    ( sz00 = esk1_2(sz10,sz10)
    | ~ aNaturalNumber0(esk1_2(sz10,sz10)) ),
    inference(cn,[status(thm)],[2221,theory(equality)]) ).

cnf(2487,plain,
    esk1_2(sz10,sz10) = sz00,
    inference(spm,[status(thm)],[2222,2060,theory(equality)]) ).

cnf(2493,plain,
    sdtpldt0(sz10,sz00) = sz10,
    inference(rw,[status(thm)],[2062,2487,theory(equality)]) ).

cnf(3173,negated_conjecture,
    ( sdtmndt0(xn,xm) = esk1_2(xm,xn)
    | ~ aNaturalNumber0(xn) ),
    inference(er,[status(thm)],[529,theory(equality)]) ).

cnf(3174,negated_conjecture,
    ( sdtmndt0(xn,xm) = esk1_2(xm,xn)
    | $false ),
    inference(rw,[status(thm)],[3173,41,theory(equality)]) ).

cnf(3175,negated_conjecture,
    sdtmndt0(xn,xm) = esk1_2(xm,xn),
    inference(cn,[status(thm)],[3174,theory(equality)]) ).

cnf(3176,negated_conjecture,
    sdtpldt0(sdtmndt0(xn,xm),esk1_2(sdtmndt0(xn,xm),xn)) = xn,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1786,3175,theory(equality)]),3175,theory(equality)]) ).

cnf(3179,negated_conjecture,
    sdtlseqdt0(sdtmndt0(xn,xm),xn),
    inference(rw,[status(thm)],[1710,3175,theory(equality)]) ).

cnf(3180,negated_conjecture,
    sdtpldt0(xm,sdtmndt0(xn,xm)) = xn,
    inference(rw,[status(thm)],[203,3175,theory(equality)]) ).

cnf(3184,negated_conjecture,
    ( xm = X1
    | sdtpldt0(sdtmndt0(xn,xm),X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[882,3175,theory(equality)]) ).

cnf(3189,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[57,3179,theory(equality)]) ).

cnf(3192,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn))
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[3189,1806,theory(equality)]) ).

cnf(3193,negated_conjecture,
    ( aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[3192,41,theory(equality)]) ).

cnf(3194,negated_conjecture,
    aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn)),
    inference(cn,[status(thm)],[3193,theory(equality)]) ).

cnf(3282,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[61,3180,theory(equality)]) ).

cnf(3315,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[3282,1806,theory(equality)]) ).

cnf(3316,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3315,42,theory(equality)]) ).

cnf(3317,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(xm,sdtpldt0(sdtmndt0(xn,xm),X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3316,theory(equality)]) ).

cnf(3346,negated_conjecture,
    ( xm = esk1_2(sdtmndt0(xn,xm),xn)
    | ~ aNaturalNumber0(esk1_2(sdtmndt0(xn,xm),xn)) ),
    inference(spm,[status(thm)],[3184,3176,theory(equality)]) ).

cnf(3351,negated_conjecture,
    ( xm = esk1_2(sdtmndt0(xn,xm),xn)
    | $false ),
    inference(rw,[status(thm)],[3346,3194,theory(equality)]) ).

cnf(3352,negated_conjecture,
    xm = esk1_2(sdtmndt0(xn,xm),xn),
    inference(cn,[status(thm)],[3351,theory(equality)]) ).

cnf(3413,negated_conjecture,
    sdtpldt0(sdtmndt0(xn,xm),xm) = xn,
    inference(rw,[status(thm)],[3176,3352,theory(equality)]) ).

cnf(3424,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sdtmndt0(xn,xm),sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(spm,[status(thm)],[61,3413,theory(equality)]) ).

cnf(3466,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sdtmndt0(xn,xm),sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(rw,[status(thm)],[3424,42,theory(equality)]) ).

cnf(3467,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sdtmndt0(xn,xm),sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3466,1806,theory(equality)]) ).

cnf(3468,negated_conjecture,
    ( sdtpldt0(xn,X1) = sdtpldt0(sdtmndt0(xn,xm),sdtpldt0(xm,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3467,theory(equality)]) ).

cnf(3496,negated_conjecture,
    ( sdtpldt0(xn,sdtmndt0(xm,xn)) = xm
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[253,66,theory(equality)]) ).

cnf(3510,negated_conjecture,
    ( sdtpldt0(xn,sdtmndt0(xm,xn)) = xm
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[3496,41,theory(equality)]) ).

cnf(3511,negated_conjecture,
    ( sdtpldt0(xn,sdtmndt0(xm,xn)) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[3510,42,theory(equality)]) ).

cnf(3512,negated_conjecture,
    sdtpldt0(xn,sdtmndt0(xm,xn)) = xm,
    inference(cn,[status(thm)],[3511,theory(equality)]) ).

cnf(3545,negated_conjecture,
    ( sdtpldt0(xm,X1) = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[61,3512,theory(equality)]) ).

cnf(3578,negated_conjecture,
    ( sdtpldt0(xm,X1) = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[3545,1809,theory(equality)]) ).

cnf(3579,negated_conjecture,
    ( sdtpldt0(xm,X1) = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),X1))
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[3578,41,theory(equality)]) ).

cnf(3580,negated_conjecture,
    ( sdtpldt0(xm,X1) = sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3579,theory(equality)]) ).

cnf(8719,negated_conjecture,
    ( sdtpldt0(sz00,xm) = xm
    | ~ aNaturalNumber0(esk1_2(xn,xm))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[356,206,theory(equality)]) ).

cnf(8777,negated_conjecture,
    ( sdtpldt0(sz00,xm) = xm
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[8719,189,theory(equality)]) ).

cnf(8778,negated_conjecture,
    ( sdtpldt0(sz00,xm) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[8777,41,theory(equality)]) ).

cnf(8779,negated_conjecture,
    sdtpldt0(sz00,xm) = xm,
    inference(cn,[status(thm)],[8778,theory(equality)]) ).

cnf(8901,negated_conjecture,
    ( sdtlseqdt0(xm,xm)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[1626,8779,theory(equality)]) ).

cnf(8944,negated_conjecture,
    ( sdtlseqdt0(xm,xm)
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[8901,89,theory(equality)]) ).

cnf(8945,negated_conjecture,
    ( sdtlseqdt0(xm,xm)
    | $false
    | $false ),
    inference(rw,[status(thm)],[8944,42,theory(equality)]) ).

cnf(8946,negated_conjecture,
    sdtlseqdt0(xm,xm),
    inference(cn,[status(thm)],[8945,theory(equality)]) ).

cnf(8963,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xm))
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[57,8946,theory(equality)]) ).

cnf(8964,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xm)) = xm
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[56,8946,theory(equality)]) ).

cnf(8967,negated_conjecture,
    ( aNaturalNumber0(esk1_2(xm,xm))
    | $false ),
    inference(rw,[status(thm)],[8963,42,theory(equality)]) ).

cnf(8968,negated_conjecture,
    aNaturalNumber0(esk1_2(xm,xm)),
    inference(cn,[status(thm)],[8967,theory(equality)]) ).

cnf(8969,negated_conjecture,
    ( sdtpldt0(xm,esk1_2(xm,xm)) = xm
    | $false ),
    inference(rw,[status(thm)],[8964,42,theory(equality)]) ).

cnf(8970,negated_conjecture,
    sdtpldt0(xm,esk1_2(xm,xm)) = xm,
    inference(cn,[status(thm)],[8969,theory(equality)]) ).

cnf(9161,negated_conjecture,
    ( sz00 = esk1_2(xm,xm)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(esk1_2(xm,xm)) ),
    inference(spm,[status(thm)],[229,8970,theory(equality)]) ).

cnf(9207,negated_conjecture,
    ( sz00 = esk1_2(xm,xm)
    | $false
    | ~ aNaturalNumber0(esk1_2(xm,xm)) ),
    inference(rw,[status(thm)],[9161,42,theory(equality)]) ).

cnf(9208,negated_conjecture,
    ( sz00 = esk1_2(xm,xm)
    | $false
    | $false ),
    inference(rw,[status(thm)],[9207,8968,theory(equality)]) ).

cnf(9209,negated_conjecture,
    sz00 = esk1_2(xm,xm),
    inference(cn,[status(thm)],[9208,theory(equality)]) ).

cnf(9225,negated_conjecture,
    sdtpldt0(xm,sz00) = xm,
    inference(rw,[status(thm)],[8970,9209,theory(equality)]) ).

cnf(9881,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[340,92]) ).

cnf(9978,plain,
    ( sz00 = sdtpldt0(X1,X2)
    | sdtpldt0(X2,sdtpldt0(X3,X1)) != X3
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[229,9881,theory(equality)]) ).

cnf(13104,plain,
    ( sdtmndt0(sdtpldt0(X1,X2),X1) = X2
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[358,92]) ).

cnf(15347,plain,
    ( sdtpldt0(X1,sz00) = sdtasdt0(X1,sdtpldt0(sz10,sz00))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[405,28,theory(equality)]) ).

cnf(15475,plain,
    ( sdtpldt0(X1,sz00) = sdtasdt0(X1,sz10)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[15347,2493,theory(equality)]) ).

cnf(15476,plain,
    ( sdtpldt0(X1,sz00) = sdtasdt0(X1,sz10)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[15475,89,theory(equality)]) ).

cnf(15477,plain,
    ( sdtpldt0(X1,sz00) = sdtasdt0(X1,sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[15476,theory(equality)]) ).

cnf(15925,negated_conjecture,
    ( sdtasdt0(sz10,xm) = sdtpldt0(xm,sdtasdt0(sz10,sz00))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[409,9225,theory(equality)]) ).

cnf(16034,negated_conjecture,
    ( sdtasdt0(sz10,xm) = xm
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[15925,641,theory(equality)]),9225,theory(equality)]) ).

cnf(16035,negated_conjecture,
    ( sdtasdt0(sz10,xm) = xm
    | $false
    | ~ aNaturalNumber0(sz00) ),
    inference(rw,[status(thm)],[16034,42,theory(equality)]) ).

cnf(16036,negated_conjecture,
    ( sdtasdt0(sz10,xm) = xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[16035,89,theory(equality)]) ).

cnf(16037,negated_conjecture,
    sdtasdt0(sz10,xm) = xm,
    inference(cn,[status(thm)],[16036,theory(equality)]) ).

cnf(16148,negated_conjecture,
    ( xm = sdtasdt0(xm,sz10)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz10) ),
    inference(spm,[status(thm)],[100,16037,theory(equality)]) ).

cnf(16187,negated_conjecture,
    ( xm = sdtasdt0(xm,sz10)
    | $false
    | ~ aNaturalNumber0(sz10) ),
    inference(rw,[status(thm)],[16148,42,theory(equality)]) ).

cnf(16188,negated_conjecture,
    ( xm = sdtasdt0(xm,sz10)
    | $false
    | $false ),
    inference(rw,[status(thm)],[16187,63,theory(equality)]) ).

cnf(16189,negated_conjecture,
    xm = sdtasdt0(xm,sz10),
    inference(cn,[status(thm)],[16188,theory(equality)]) ).

cnf(23454,negated_conjecture,
    ( sdtasdt0(xm,sz10) = sdtpldt0(xn,sdtasdt0(sdtmndt0(xm,xn),sz10))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
    inference(spm,[status(thm)],[448,3512,theory(equality)]) ).

cnf(23580,negated_conjecture,
    ( xm = sdtpldt0(xn,sdtasdt0(sdtmndt0(xm,xn),sz10))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
    inference(rw,[status(thm)],[23454,16189,theory(equality)]) ).

cnf(23581,negated_conjecture,
    ( xm = sdtpldt0(xn,sdtasdt0(sdtmndt0(xm,xn),sz10))
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
    inference(rw,[status(thm)],[23580,41,theory(equality)]) ).

cnf(23582,negated_conjecture,
    ( xm = sdtpldt0(xn,sdtasdt0(sdtmndt0(xm,xn),sz10))
    | $false
    | $false ),
    inference(rw,[status(thm)],[23581,1809,theory(equality)]) ).

cnf(23583,negated_conjecture,
    xm = sdtpldt0(xn,sdtasdt0(sdtmndt0(xm,xn),sz10)),
    inference(cn,[status(thm)],[23582,theory(equality)]) ).

cnf(26155,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sz00)) = xm
    | ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
    inference(spm,[status(thm)],[23583,15477,theory(equality)]) ).

cnf(26262,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sz00)) = xm
    | $false ),
    inference(rw,[status(thm)],[26155,1809,theory(equality)]) ).

cnf(26263,negated_conjecture,
    sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sz00)) = xm,
    inference(cn,[status(thm)],[26262,theory(equality)]) ).

cnf(87566,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X2,sdtpldt0(X3,X1)))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[1703,92]) ).

cnf(87572,negated_conjecture,
    ( sdtlseqdt0(sdtmndt0(xm,xn),sdtpldt0(X1,xm))
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[87566,3512,theory(equality)]) ).

cnf(87722,negated_conjecture,
    ( sdtlseqdt0(sdtmndt0(xm,xn),sdtpldt0(X1,xm))
    | $false
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[87572,1809,theory(equality)]) ).

cnf(87723,negated_conjecture,
    ( sdtlseqdt0(sdtmndt0(xm,xn),sdtpldt0(X1,xm))
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[87722,41,theory(equality)]) ).

cnf(87724,negated_conjecture,
    ( sdtlseqdt0(sdtmndt0(xm,xn),sdtpldt0(X1,xm))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[87723,theory(equality)]) ).

cnf(107873,negated_conjecture,
    ( sdtlseqdt0(sdtmndt0(xm,xn),xn)
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(spm,[status(thm)],[87724,3413,theory(equality)]) ).

cnf(107891,negated_conjecture,
    ( sdtlseqdt0(sdtmndt0(xm,xn),xn)
    | $false ),
    inference(rw,[status(thm)],[107873,1806,theory(equality)]) ).

cnf(107892,negated_conjecture,
    sdtlseqdt0(sdtmndt0(xm,xn),xn),
    inference(cn,[status(thm)],[107891,theory(equality)]) ).

cnf(107925,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xn,sdtmndt0(xm,xn)))
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[218,107892,theory(equality)]) ).

cnf(107926,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,sdtmndt0(xm,xn))) = xn
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[253,107892,theory(equality)]) ).

cnf(107933,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xn,sdtmndt0(xm,xn)))
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[107925,1809,theory(equality)]) ).

cnf(107934,negated_conjecture,
    ( aNaturalNumber0(sdtmndt0(xn,sdtmndt0(xm,xn)))
    | $false
    | $false ),
    inference(rw,[status(thm)],[107933,41,theory(equality)]) ).

cnf(107935,negated_conjecture,
    aNaturalNumber0(sdtmndt0(xn,sdtmndt0(xm,xn))),
    inference(cn,[status(thm)],[107934,theory(equality)]) ).

cnf(107936,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,sdtmndt0(xm,xn))) = xn
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[107926,1809,theory(equality)]) ).

cnf(107937,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,sdtmndt0(xm,xn))) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[107936,41,theory(equality)]) ).

cnf(107938,negated_conjecture,
    sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,sdtmndt0(xm,xn))) = xn,
    inference(cn,[status(thm)],[107937,theory(equality)]) ).

cnf(138111,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xn,xm),xn) = sdtpldt0(xn,sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(spm,[status(thm)],[3468,3180,theory(equality)]) ).

cnf(138257,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xn,xm),xn) = sdtpldt0(xn,sdtmndt0(xn,xm))
    | $false ),
    inference(rw,[status(thm)],[138111,1806,theory(equality)]) ).

cnf(138258,negated_conjecture,
    sdtpldt0(sdtmndt0(xn,xm),xn) = sdtpldt0(xn,sdtmndt0(xn,xm)),
    inference(cn,[status(thm)],[138257,theory(equality)]) ).

cnf(141713,negated_conjecture,
    ( sdtpldt0(xn,xn) = sdtpldt0(xm,sdtmndt0(xn,sdtmndt0(xm,xn)))
    | ~ aNaturalNumber0(sdtmndt0(xn,sdtmndt0(xm,xn))) ),
    inference(spm,[status(thm)],[3580,107938,theory(equality)]) ).

cnf(141868,negated_conjecture,
    ( sdtpldt0(xn,xn) = sdtpldt0(xm,sdtmndt0(xn,sdtmndt0(xm,xn)))
    | $false ),
    inference(rw,[status(thm)],[141713,107935,theory(equality)]) ).

cnf(141869,negated_conjecture,
    sdtpldt0(xn,xn) = sdtpldt0(xm,sdtmndt0(xn,sdtmndt0(xm,xn))),
    inference(cn,[status(thm)],[141868,theory(equality)]) ).

cnf(149751,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(xn,sdtmndt0(xn,xm)))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(spm,[status(thm)],[92,138258,theory(equality)]) ).

cnf(149853,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xn,sdtmndt0(xn,xm))) = sdtpldt0(xn,xn)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[3317,138258,theory(equality)]) ).

cnf(149860,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(xn,sdtmndt0(xn,xm)))
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(rw,[status(thm)],[149751,41,theory(equality)]) ).

cnf(149861,negated_conjecture,
    ( aNaturalNumber0(sdtpldt0(xn,sdtmndt0(xn,xm)))
    | $false
    | $false ),
    inference(rw,[status(thm)],[149860,1806,theory(equality)]) ).

cnf(149862,negated_conjecture,
    aNaturalNumber0(sdtpldt0(xn,sdtmndt0(xn,xm))),
    inference(cn,[status(thm)],[149861,theory(equality)]) ).

cnf(150159,negated_conjecture,
    ( sdtpldt0(xm,sdtpldt0(xn,sdtmndt0(xn,xm))) = sdtpldt0(xn,xn)
    | $false ),
    inference(rw,[status(thm)],[149853,41,theory(equality)]) ).

cnf(150160,negated_conjecture,
    sdtpldt0(xm,sdtpldt0(xn,sdtmndt0(xn,xm))) = sdtpldt0(xn,xn),
    inference(cn,[status(thm)],[150159,theory(equality)]) ).

cnf(168579,negated_conjecture,
    ( sdtmndt0(sdtpldt0(xn,xn),xm) = sdtmndt0(xn,sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,sdtmndt0(xm,xn)))
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[13104,141869,theory(equality)]) ).

cnf(168746,negated_conjecture,
    ( sdtmndt0(sdtpldt0(xn,xn),xm) = sdtmndt0(xn,sdtmndt0(xm,xn))
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[168579,107935,theory(equality)]) ).

cnf(168747,negated_conjecture,
    ( sdtmndt0(sdtpldt0(xn,xn),xm) = sdtmndt0(xn,sdtmndt0(xm,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[168746,42,theory(equality)]) ).

cnf(168748,negated_conjecture,
    sdtmndt0(sdtpldt0(xn,xn),xm) = sdtmndt0(xn,sdtmndt0(xm,xn)),
    inference(cn,[status(thm)],[168747,theory(equality)]) ).

cnf(173207,negated_conjecture,
    sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(sdtpldt0(xn,xn),xm)) = xn,
    inference(rw,[status(thm)],[107938,168748,theory(equality)]) ).

cnf(176351,negated_conjecture,
    ( sdtmndt0(sdtpldt0(xn,xn),xm) = sdtpldt0(xn,sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(sdtpldt0(xn,sdtmndt0(xn,xm)))
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[13104,150160,theory(equality)]) ).

cnf(176559,negated_conjecture,
    ( sdtmndt0(sdtpldt0(xn,xn),xm) = sdtpldt0(xn,sdtmndt0(xn,xm))
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[176351,149862,theory(equality)]) ).

cnf(176560,negated_conjecture,
    ( sdtmndt0(sdtpldt0(xn,xn),xm) = sdtpldt0(xn,sdtmndt0(xn,xm))
    | $false
    | $false ),
    inference(rw,[status(thm)],[176559,42,theory(equality)]) ).

cnf(176561,negated_conjecture,
    sdtmndt0(sdtpldt0(xn,xn),xm) = sdtpldt0(xn,sdtmndt0(xn,xm)),
    inference(cn,[status(thm)],[176560,theory(equality)]) ).

cnf(185489,negated_conjecture,
    sdtpldt0(sdtmndt0(xm,xn),sdtpldt0(xn,sdtmndt0(xn,xm))) = xn,
    inference(rw,[status(thm)],[173207,176561,theory(equality)]) ).

cnf(186158,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn))) = xn
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[9881,185489,theory(equality)]) ).

cnf(186335,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn))) = xn
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[186158,1809,theory(equality)]) ).

cnf(186336,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn))) = xn
    | $false
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[186335,1806,theory(equality)]) ).

cnf(186337,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn))) = xn
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[186336,41,theory(equality)]) ).

cnf(186338,negated_conjecture,
    sdtpldt0(xn,sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn))) = xn,
    inference(cn,[status(thm)],[186337,theory(equality)]) ).

cnf(552432,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) = xn
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(spm,[status(thm)],[186338,31,theory(equality)]) ).

cnf(552569,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) = xn
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(rw,[status(thm)],[552432,1809,theory(equality)]) ).

cnf(552570,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) = xn
    | $false
    | $false ),
    inference(rw,[status(thm)],[552569,1806,theory(equality)]) ).

cnf(552571,negated_conjecture,
    sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) = xn,
    inference(cn,[status(thm)],[552570,theory(equality)]) ).

cnf(1326366,plain,
    ( sdtpldt0(X1,X2) = sz00
    | sdtpldt0(X2,sdtpldt0(X3,X1)) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(csr,[status(thm)],[9978,92]) ).

cnf(1326469,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sz00
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(spm,[status(thm)],[1326366,185489,theory(equality)]) ).

cnf(1327189,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sz00
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xm,xn))
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(rw,[status(thm)],[1326469,41,theory(equality)]) ).

cnf(1327190,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sz00
    | $false
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
    inference(rw,[status(thm)],[1327189,1809,theory(equality)]) ).

cnf(1327191,negated_conjecture,
    ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sz00
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[1327190,1806,theory(equality)]) ).

cnf(1327192,negated_conjecture,
    sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sz00,
    inference(cn,[status(thm)],[1327191,theory(equality)]) ).

cnf(1329952,negated_conjecture,
    ( sz00 = sdtmndt0(xn,xm)
    | ~ aNaturalNumber0(sdtmndt0(xn,xm))
    | ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
    inference(spm,[status(thm)],[75,1327192,theory(equality)]) ).

cnf(1330146,negated_conjecture,
    ( sz00 = sdtmndt0(xn,xm)
    | $false
    | ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
    inference(rw,[status(thm)],[1329952,1806,theory(equality)]) ).

cnf(1330147,negated_conjecture,
    ( sz00 = sdtmndt0(xn,xm)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1330146,1809,theory(equality)]) ).

cnf(1330148,negated_conjecture,
    sz00 = sdtmndt0(xn,xm),
    inference(cn,[status(thm)],[1330147,theory(equality)]) ).

cnf(1330805,negated_conjecture,
    sdtpldt0(xn,sdtpldt0(sdtmndt0(xm,xn),sz00)) = xn,
    inference(rw,[status(thm)],[552571,1330148,theory(equality)]) ).

cnf(1330806,negated_conjecture,
    xm = xn,
    inference(rw,[status(thm)],[1330805,26263,theory(equality)]) ).

cnf(1330807,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1330806,65,theory(equality)]) ).

cnf(1330808,negated_conjecture,
    $false,
    1330807,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.03  % Problem  : NUM459+1 : TPTP v7.0.0. Released v4.0.0.
% 0.01/0.03  % Command  : Source/sine.py -e eprover -t %d %s
% 0.03/0.23  % Computer : n073.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 04:32:29 CST 2018
% 0.03/0.23  % CPUTime  : 
% 0.07/0.27  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27  --creating new selector for []
% 23.17/24.43  -running prover on /export/starexec/sandbox/tmp/tmpyAR6Vf/sel_theBenchmark.p_1 with time limit 29
% 23.17/24.43  -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/tmpyAR6Vf/sel_theBenchmark.p_1']
% 23.17/24.43  -prover status Theorem
% 23.17/24.43  Problem theBenchmark.p solved in phase 0.
% 23.17/24.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.17/24.43  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.17/24.43  Solved 1 out of 1.
% 23.17/24.43  # Problem is unsatisfiable (or provable), constructing proof object
% 23.17/24.43  # SZS status Theorem
% 23.17/24.43  # SZS output start CNFRefutation.
% See solution above
% 23.17/24.44  # SZS output end CNFRefutation
%------------------------------------------------------------------------------