TSTP Solution File: NUM528+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM528+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n068.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 15:21:40 EST 2018

% Result   : Theorem 0.38s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   37
%            Number of leaves      :   21
% Syntax   : Number of formulae    :  169 (  30 unt;   0 def)
%            Number of atoms       :  617 ( 113 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  736 ( 288   ~; 335   |;  94   &)
%                                         (   0 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :  164 (   0 sgn  94   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( equal(sdtasdt0(X1,X2),sz00)
       => ( equal(X1,sz00)
          | equal(X2,sz00) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mZeroMul) ).

fof(5,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/tmpWCBu73/sel_theBenchmark.p_1',mMulCanc) ).

fof(6,axiom,
    ( ( ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(xn,X1),xm) )
      | sdtlseqdt0(xn,xm) )
   => ( ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(sdtasdt0(xn,xn),X1),sdtasdt0(xm,xm)) )
      & sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__3152) ).

fof(12,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( ~ equal(X2,X1)
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mLETotal) ).

fof(15,axiom,
    equal(sdtasdt0(xp,sdtasdt0(xm,xm)),sdtasdt0(xn,xn)),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__3014) ).

fof(19,axiom,
    ( aNaturalNumber0(xq)
    & equal(xn,sdtasdt0(xp,xq))
    & equal(xq,sdtsldt0(xn,xp)) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__3059) ).

fof(23,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/tmpWCBu73/sel_theBenchmark.p_1',mAddAsso) ).

fof(24,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => equal(X1,X2) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mLEAsym) ).

fof(27,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ~ equal(X1,sz00)
       => sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mMonMul2) ).

fof(28,axiom,
    ( aNaturalNumber0(sz10)
    & ~ equal(sz10,sz00) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mSortsC_01) ).

fof(29,conjecture,
    ( ~ equal(xm,xn)
    & ( ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(xm,X1),xn) )
      | sdtlseqdt0(xm,xn) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__) ).

fof(34,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mSortsB_02) ).

fof(36,axiom,
    equal(sdtasdt0(xm,xm),sdtasdt0(xp,sdtasdt0(xq,xq))),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__3082) ).

fof(37,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mSortsC) ).

fof(38,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mSortsB) ).

fof(42,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',mMulComm) ).

fof(44,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & ~ equal(xn,sz00)
    & ~ equal(xm,sz00)
    & ~ equal(xp,sz00) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__2987) ).

fof(45,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m_AddZero) ).

fof(46,axiom,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(sdtasdt0(xn,xn),sdtasdt0(xp,X1)) )
    & doDivides0(xp,sdtasdt0(xn,xn))
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(xn,sdtasdt0(xp,X1)) )
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__3046) ).

fof(47,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m_MulUnit) ).

fof(48,axiom,
    ( ~ equal(xp,sz10)
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & equal(xp,sdtasdt0(X1,X2)) )
            | doDivides0(X1,xp) ) )
       => ( equal(X1,sz10)
          | equal(X1,xp) ) )
    & isPrime0(xp) ),
    file('/export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1',m__3025) ).

fof(49,negated_conjecture,
    ~ ( ~ equal(xm,xn)
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & equal(sdtpldt0(xm,X1),xn) )
        | sdtlseqdt0(xm,xn) ) ),
    inference(assume_negation,[status(cth)],[29]) ).

fof(61,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ equal(sdtasdt0(X1,X2),sz00)
      | equal(X1,sz00)
      | equal(X2,sz00) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(62,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | ~ equal(sdtasdt0(X3,X4),sz00)
      | equal(X3,sz00)
      | equal(X4,sz00) ),
    inference(variable_rename,[status(thm)],[61]) ).

cnf(63,plain,
    ( X1 = sz00
    | X2 = sz00
    | sdtasdt0(X2,X1) != sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(64,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)],[5]) ).

fof(65,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)],[64]) ).

fof(66,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)],[65]) ).

fof(67,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)],[66]) ).

cnf(68,plain,
    ( X1 = sz00
    | X3 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(69,plain,
    ( X1 = sz00
    | X3 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(70,plain,
    ( ( ! [X1] :
          ( ~ aNaturalNumber0(X1)
          | ~ equal(sdtpldt0(xn,X1),xm) )
      & ~ sdtlseqdt0(xn,xm) )
    | ( ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(sdtasdt0(xn,xn),X1),sdtasdt0(xm,xm)) )
      & sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(71,plain,
    ( ( ! [X2] :
          ( ~ aNaturalNumber0(X2)
          | ~ equal(sdtpldt0(xn,X2),xm) )
      & ~ sdtlseqdt0(xn,xm) )
    | ( ? [X3] :
          ( aNaturalNumber0(X3)
          & equal(sdtpldt0(sdtasdt0(xn,xn),X3),sdtasdt0(xm,xm)) )
      & sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    inference(variable_rename,[status(thm)],[70]) ).

fof(72,plain,
    ( ( ! [X2] :
          ( ~ aNaturalNumber0(X2)
          | ~ equal(sdtpldt0(xn,X2),xm) )
      & ~ sdtlseqdt0(xn,xm) )
    | ( aNaturalNumber0(esk1_0)
      & equal(sdtpldt0(sdtasdt0(xn,xn),esk1_0),sdtasdt0(xm,xm))
      & sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    inference(skolemize,[status(esa)],[71]) ).

fof(73,plain,
    ! [X2] :
      ( ( ( ~ aNaturalNumber0(X2)
          | ~ equal(sdtpldt0(xn,X2),xm) )
        & ~ sdtlseqdt0(xn,xm) )
      | ( aNaturalNumber0(esk1_0)
        & equal(sdtpldt0(sdtasdt0(xn,xn),esk1_0),sdtasdt0(xm,xm))
        & sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    inference(shift_quantors,[status(thm)],[72]) ).

fof(74,plain,
    ! [X2] :
      ( ( aNaturalNumber0(esk1_0)
        | ~ aNaturalNumber0(X2)
        | ~ equal(sdtpldt0(xn,X2),xm) )
      & ( equal(sdtpldt0(sdtasdt0(xn,xn),esk1_0),sdtasdt0(xm,xm))
        | ~ aNaturalNumber0(X2)
        | ~ equal(sdtpldt0(xn,X2),xm) )
      & ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
        | ~ aNaturalNumber0(X2)
        | ~ equal(sdtpldt0(xn,X2),xm) )
      & ( aNaturalNumber0(esk1_0)
        | ~ sdtlseqdt0(xn,xm) )
      & ( equal(sdtpldt0(sdtasdt0(xn,xn),esk1_0),sdtasdt0(xm,xm))
        | ~ sdtlseqdt0(xn,xm) )
      & ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
        | ~ sdtlseqdt0(xn,xm) ) ),
    inference(distribute,[status(thm)],[73]) ).

cnf(75,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
    | ~ sdtlseqdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[74]) ).

cnf(78,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(111,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | sdtlseqdt0(X1,X2)
      | ( ~ equal(X2,X1)
        & sdtlseqdt0(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(112,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtlseqdt0(X3,X4)
      | ( ~ equal(X4,X3)
        & sdtlseqdt0(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[111]) ).

fof(113,plain,
    ! [X3,X4] :
      ( ( ~ equal(X4,X3)
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) )
      & ( sdtlseqdt0(X4,X3)
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[112]) ).

cnf(114,plain,
    ( sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[113]) ).

cnf(122,plain,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(139,plain,
    aNaturalNumber0(xq),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(158,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)],[23]) ).

fof(159,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)],[158]) ).

cnf(160,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[159]) ).

fof(161,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ sdtlseqdt0(X1,X2)
      | ~ sdtlseqdt0(X2,X1)
      | equal(X1,X2) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(162,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | ~ sdtlseqdt0(X3,X4)
      | ~ sdtlseqdt0(X4,X3)
      | equal(X3,X4) ),
    inference(variable_rename,[status(thm)],[161]) ).

cnf(163,plain,
    ( X1 = X2
    | ~ sdtlseqdt0(X2,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[162]) ).

fof(176,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(X1,sz00)
      | sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(177,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(X3,sz00)
      | sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[176]) ).

cnf(178,plain,
    ( sdtlseqdt0(X1,sdtasdt0(X1,X2))
    | X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[177]) ).

cnf(180,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(181,negated_conjecture,
    ( equal(xm,xn)
    | ( ! [X1] :
          ( ~ aNaturalNumber0(X1)
          | ~ equal(sdtpldt0(xm,X1),xn) )
      & ~ sdtlseqdt0(xm,xn) ) ),
    inference(fof_nnf,[status(thm)],[49]) ).

fof(182,negated_conjecture,
    ( equal(xm,xn)
    | ( ! [X2] :
          ( ~ aNaturalNumber0(X2)
          | ~ equal(sdtpldt0(xm,X2),xn) )
      & ~ sdtlseqdt0(xm,xn) ) ),
    inference(variable_rename,[status(thm)],[181]) ).

fof(183,negated_conjecture,
    ! [X2] :
      ( ( ( ~ aNaturalNumber0(X2)
          | ~ equal(sdtpldt0(xm,X2),xn) )
        & ~ sdtlseqdt0(xm,xn) )
      | equal(xm,xn) ),
    inference(shift_quantors,[status(thm)],[182]) ).

fof(184,negated_conjecture,
    ! [X2] :
      ( ( ~ aNaturalNumber0(X2)
        | ~ equal(sdtpldt0(xm,X2),xn)
        | equal(xm,xn) )
      & ( ~ sdtlseqdt0(xm,xn)
        | equal(xm,xn) ) ),
    inference(distribute,[status(thm)],[183]) ).

cnf(185,negated_conjecture,
    ( xm = xn
    | ~ sdtlseqdt0(xm,xn) ),
    inference(split_conjunct,[status(thm)],[184]) ).

fof(205,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(206,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[205]) ).

cnf(207,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[206]) ).

cnf(220,plain,
    sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(221,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(222,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(223,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[222]) ).

cnf(224,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[223]) ).

fof(240,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(241,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[240]) ).

cnf(242,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[241]) ).

cnf(247,plain,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(248,plain,
    xm != sz00,
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(250,plain,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(251,plain,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[44]) ).

cnf(252,plain,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(253,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[45]) ).

fof(254,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtpldt0(X2,sz00),X2)
        & equal(X2,sdtpldt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[253]) ).

fof(255,plain,
    ! [X2] :
      ( ( equal(sdtpldt0(X2,sz00),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtpldt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[254]) ).

cnf(256,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[255]) ).

cnf(257,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[255]) ).

fof(258,plain,
    ( ? [X2] :
        ( aNaturalNumber0(X2)
        & equal(sdtasdt0(xn,xn),sdtasdt0(xp,X2)) )
    & doDivides0(xp,sdtasdt0(xn,xn))
    & ? [X3] :
        ( aNaturalNumber0(X3)
        & equal(xn,sdtasdt0(xp,X3)) )
    & doDivides0(xp,xn) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(259,plain,
    ( aNaturalNumber0(esk8_0)
    & equal(sdtasdt0(xn,xn),sdtasdt0(xp,esk8_0))
    & doDivides0(xp,sdtasdt0(xn,xn))
    & aNaturalNumber0(esk9_0)
    & equal(xn,sdtasdt0(xp,esk9_0))
    & doDivides0(xp,xn) ),
    inference(skolemize,[status(esa)],[258]) ).

cnf(264,plain,
    sdtasdt0(xn,xn) = sdtasdt0(xp,esk8_0),
    inference(split_conjunct,[status(thm)],[259]) ).

cnf(265,plain,
    aNaturalNumber0(esk8_0),
    inference(split_conjunct,[status(thm)],[259]) ).

fof(266,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz10),X1)
        & equal(X1,sdtasdt0(sz10,X1)) ) ),
    inference(fof_nnf,[status(thm)],[47]) ).

fof(267,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz10),X2)
        & equal(X2,sdtasdt0(sz10,X2)) ) ),
    inference(variable_rename,[status(thm)],[266]) ).

fof(268,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz10),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtasdt0(sz10,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[267]) ).

cnf(269,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[268]) ).

fof(271,plain,
    ( ~ equal(xp,sz10)
    & ! [X1] :
        ( ~ aNaturalNumber0(X1)
        | ( ! [X2] :
              ( ~ aNaturalNumber0(X2)
              | ~ equal(xp,sdtasdt0(X1,X2)) )
          & ~ doDivides0(X1,xp) )
        | equal(X1,sz10)
        | equal(X1,xp) )
    & isPrime0(xp) ),
    inference(fof_nnf,[status(thm)],[48]) ).

fof(272,plain,
    ( ~ equal(xp,sz10)
    & ! [X3] :
        ( ~ aNaturalNumber0(X3)
        | ( ! [X4] :
              ( ~ aNaturalNumber0(X4)
              | ~ equal(xp,sdtasdt0(X3,X4)) )
          & ~ doDivides0(X3,xp) )
        | equal(X3,sz10)
        | equal(X3,xp) )
    & isPrime0(xp) ),
    inference(variable_rename,[status(thm)],[271]) ).

fof(273,plain,
    ! [X3,X4] :
      ( ( ( ( ~ aNaturalNumber0(X4)
            | ~ equal(xp,sdtasdt0(X3,X4)) )
          & ~ doDivides0(X3,xp) )
        | ~ aNaturalNumber0(X3)
        | equal(X3,sz10)
        | equal(X3,xp) )
      & ~ equal(xp,sz10)
      & isPrime0(xp) ),
    inference(shift_quantors,[status(thm)],[272]) ).

fof(274,plain,
    ! [X3,X4] :
      ( ( ~ aNaturalNumber0(X4)
        | ~ equal(xp,sdtasdt0(X3,X4))
        | ~ aNaturalNumber0(X3)
        | equal(X3,sz10)
        | equal(X3,xp) )
      & ( ~ doDivides0(X3,xp)
        | ~ aNaturalNumber0(X3)
        | equal(X3,sz10)
        | equal(X3,xp) )
      & ~ equal(xp,sz10)
      & isPrime0(xp) ),
    inference(distribute,[status(thm)],[273]) ).

cnf(276,plain,
    xp != sz10,
    inference(split_conjunct,[status(thm)],[274]) ).

cnf(301,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(esk8_0)
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[207,264,theory(equality)]) ).

cnf(303,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(sdtasdt0(xq,xq))
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[207,220,theory(equality)]) ).

cnf(316,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | $false
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[301,265,theory(equality)]) ).

cnf(317,plain,
    ( aNaturalNumber0(sdtasdt0(xn,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[316,250,theory(equality)]) ).

cnf(318,plain,
    aNaturalNumber0(sdtasdt0(xn,xn)),
    inference(cn,[status(thm)],[317,theory(equality)]) ).

cnf(321,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(sdtasdt0(xq,xq))
    | $false ),
    inference(rw,[status(thm)],[303,250,theory(equality)]) ).

cnf(322,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
    inference(cn,[status(thm)],[321,theory(equality)]) ).

cnf(334,plain,
    ( sdtlseqdt0(X1,xn)
    | sdtlseqdt0(xn,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[114,252,theory(equality)]) ).

cnf(475,plain,
    ( sz00 = X1
    | sdtlseqdt0(X2,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[178,242,theory(equality)]) ).

cnf(714,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[257,160,theory(equality)]) ).

cnf(716,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[160,256,theory(equality)]) ).

cnf(734,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | $false
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[714,221,theory(equality)]) ).

cnf(735,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[734,theory(equality)]) ).

cnf(738,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[716,221,theory(equality)]) ).

cnf(739,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(sz00,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[738,theory(equality)]) ).

cnf(770,plain,
    ( sz00 = X1
    | sz10 = X2
    | X1 != sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[68,269,theory(equality)]) ).

cnf(812,plain,
    ( sz00 = X1
    | sz10 = X2
    | X1 != sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[770,180,theory(equality)]) ).

cnf(813,plain,
    ( sz00 = X1
    | sz10 = X2
    | X1 != sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[812,theory(equality)]) ).

cnf(825,plain,
    ( sz00 = xp
    | esk8_0 = X1
    | sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk8_0)
    | ~ aNaturalNumber0(xp) ),
    inference(spm,[status(thm)],[69,264,theory(equality)]) ).

cnf(859,plain,
    ( sz00 = xp
    | esk8_0 = X1
    | sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xp) ),
    inference(rw,[status(thm)],[825,265,theory(equality)]) ).

cnf(860,plain,
    ( sz00 = xp
    | esk8_0 = X1
    | sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[859,250,theory(equality)]) ).

cnf(861,plain,
    ( sz00 = xp
    | esk8_0 = X1
    | sdtasdt0(xn,xn) != sdtasdt0(xp,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[860,theory(equality)]) ).

cnf(862,plain,
    ( esk8_0 = X1
    | sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[861,247,theory(equality)]) ).

cnf(1960,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(xq) ),
    inference(spm,[status(thm)],[322,207,theory(equality)]) ).

cnf(1964,plain,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | $false ),
    inference(rw,[status(thm)],[1960,139,theory(equality)]) ).

cnf(1965,plain,
    aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(cn,[status(thm)],[1964,theory(equality)]) ).

cnf(2025,plain,
    ( sdtlseqdt0(xn,xm)
    | sdtlseqdt0(xm,xn) ),
    inference(spm,[status(thm)],[334,251,theory(equality)]) ).

cnf(2153,plain,
    ( xm = xn
    | sdtlseqdt0(xn,xm) ),
    inference(spm,[status(thm)],[185,2025,theory(equality)]) ).

cnf(3287,plain,
    ( esk8_0 = sdtasdt0(xm,xm)
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(spm,[status(thm)],[862,122,theory(equality)]) ).

cnf(3299,plain,
    ( esk8_0 = sdtasdt0(xm,xm)
    | $false ),
    inference(rw,[status(thm)],[3287,1965,theory(equality)]) ).

cnf(3300,plain,
    esk8_0 = sdtasdt0(xm,xm),
    inference(cn,[status(thm)],[3299,theory(equality)]) ).

cnf(3321,plain,
    ( sz00 = xm
    | esk8_0 != sz00
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[63,3300,theory(equality)]) ).

cnf(3349,plain,
    sdtasdt0(xp,esk8_0) = sdtasdt0(xn,xn),
    inference(rw,[status(thm)],[122,3300,theory(equality)]) ).

cnf(3357,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[78,3300,theory(equality)]) ).

cnf(3359,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | ~ sdtlseqdt0(xn,xm) ),
    inference(rw,[status(thm)],[75,3300,theory(equality)]) ).

cnf(3372,plain,
    ( sz00 = xm
    | esk8_0 != sz00
    | $false ),
    inference(rw,[status(thm)],[3321,251,theory(equality)]) ).

cnf(3373,plain,
    ( sz00 = xm
    | esk8_0 != sz00 ),
    inference(cn,[status(thm)],[3372,theory(equality)]) ).

cnf(3374,plain,
    esk8_0 != sz00,
    inference(sr,[status(thm)],[3373,248,theory(equality)]) ).

cnf(4427,plain,
    ( sz00 = xp
    | sdtlseqdt0(esk8_0,sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[475,3349,theory(equality)]) ).

cnf(4452,plain,
    ( sz00 = xp
    | sdtlseqdt0(esk8_0,sdtasdt0(xn,xn))
    | $false
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[4427,250,theory(equality)]) ).

cnf(4453,plain,
    ( sz00 = xp
    | sdtlseqdt0(esk8_0,sdtasdt0(xn,xn))
    | $false
    | $false ),
    inference(rw,[status(thm)],[4452,265,theory(equality)]) ).

cnf(4454,plain,
    ( sz00 = xp
    | sdtlseqdt0(esk8_0,sdtasdt0(xn,xn)) ),
    inference(cn,[status(thm)],[4453,theory(equality)]) ).

cnf(4455,plain,
    sdtlseqdt0(esk8_0,sdtasdt0(xn,xn)),
    inference(sr,[status(thm)],[4454,247,theory(equality)]) ).

cnf(8234,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[735,224]) ).

cnf(8509,plain,
    ( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[8234,739,theory(equality)]) ).

cnf(8573,plain,
    ( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[8509,221,theory(equality)]) ).

cnf(8574,plain,
    ( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[8573,theory(equality)]) ).

cnf(10785,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | sdtpldt0(sz00,xn) != xm
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[3357,8574,theory(equality)]) ).

cnf(10913,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | sdtpldt0(sz00,xn) != xm
    | $false
    | ~ aNaturalNumber0(xn) ),
    inference(rw,[status(thm)],[10785,221,theory(equality)]) ).

cnf(10914,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | sdtpldt0(sz00,xn) != xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[10913,252,theory(equality)]) ).

cnf(10915,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | sdtpldt0(sz00,xn) != xm ),
    inference(cn,[status(thm)],[10914,theory(equality)]) ).

cnf(12418,plain,
    ( sz10 = xp
    | sz00 = esk8_0
    | sdtasdt0(xn,xn) != esk8_0
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[813,3349,theory(equality)]) ).

cnf(12442,plain,
    ( sz10 = xp
    | sz00 = esk8_0
    | sdtasdt0(xn,xn) != esk8_0
    | $false
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[12418,250,theory(equality)]) ).

cnf(12443,plain,
    ( sz10 = xp
    | sz00 = esk8_0
    | sdtasdt0(xn,xn) != esk8_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[12442,265,theory(equality)]) ).

cnf(12444,plain,
    ( sz10 = xp
    | sz00 = esk8_0
    | sdtasdt0(xn,xn) != esk8_0 ),
    inference(cn,[status(thm)],[12443,theory(equality)]) ).

cnf(12445,plain,
    ( esk8_0 = sz00
    | sdtasdt0(xn,xn) != esk8_0 ),
    inference(sr,[status(thm)],[12444,276,theory(equality)]) ).

cnf(12446,plain,
    sdtasdt0(xn,xn) != esk8_0,
    inference(sr,[status(thm)],[12445,3374,theory(equality)]) ).

cnf(13704,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | ~ sdtlseqdt0(esk8_0,sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(esk8_0)
    | sdtpldt0(sz00,xn) != xm ),
    inference(spm,[status(thm)],[163,10915,theory(equality)]) ).

cnf(13716,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | $false
    | ~ aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(esk8_0)
    | sdtpldt0(sz00,xn) != xm ),
    inference(rw,[status(thm)],[13704,4455,theory(equality)]) ).

cnf(13717,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | $false
    | $false
    | ~ aNaturalNumber0(esk8_0)
    | sdtpldt0(sz00,xn) != xm ),
    inference(rw,[status(thm)],[13716,318,theory(equality)]) ).

cnf(13718,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | $false
    | $false
    | $false
    | sdtpldt0(sz00,xn) != xm ),
    inference(rw,[status(thm)],[13717,265,theory(equality)]) ).

cnf(13719,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | sdtpldt0(sz00,xn) != xm ),
    inference(cn,[status(thm)],[13718,theory(equality)]) ).

cnf(13720,plain,
    sdtpldt0(sz00,xn) != xm,
    inference(sr,[status(thm)],[13719,12446,theory(equality)]) ).

cnf(13733,plain,
    ( xn != xm
    | ~ aNaturalNumber0(xn) ),
    inference(spm,[status(thm)],[13720,256,theory(equality)]) ).

cnf(13734,plain,
    ( xn != xm
    | $false ),
    inference(rw,[status(thm)],[13733,252,theory(equality)]) ).

cnf(13735,plain,
    xn != xm,
    inference(cn,[status(thm)],[13734,theory(equality)]) ).

cnf(13736,plain,
    sdtlseqdt0(xn,xm),
    inference(sr,[status(thm)],[2153,13735,theory(equality)]) ).

cnf(13771,plain,
    ( sdtlseqdt0(sdtasdt0(xn,xn),esk8_0)
    | $false ),
    inference(rw,[status(thm)],[3359,13736,theory(equality)]) ).

cnf(13772,plain,
    sdtlseqdt0(sdtasdt0(xn,xn),esk8_0),
    inference(cn,[status(thm)],[13771,theory(equality)]) ).

cnf(13918,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | ~ sdtlseqdt0(esk8_0,sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[163,13772,theory(equality)]) ).

cnf(13935,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | $false
    | ~ aNaturalNumber0(sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[13918,4455,theory(equality)]) ).

cnf(13936,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | $false
    | $false
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[13935,318,theory(equality)]) ).

cnf(13937,plain,
    ( esk8_0 = sdtasdt0(xn,xn)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[13936,265,theory(equality)]) ).

cnf(13938,plain,
    esk8_0 = sdtasdt0(xn,xn),
    inference(cn,[status(thm)],[13937,theory(equality)]) ).

cnf(13939,plain,
    $false,
    inference(sr,[status(thm)],[13938,12446,theory(equality)]) ).

cnf(13940,plain,
    $false,
    13939,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM528+3 : TPTP v7.0.0. Released v4.0.0.
% 0.02/0.03  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.22  % Computer : n068.star.cs.uiowa.edu
% 0.02/0.22  % Model    : x86_64 x86_64
% 0.02/0.22  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.22  % Memory   : 32218.625MB
% 0.02/0.22  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.22  % CPULimit : 300
% 0.02/0.22  % DateTime : Fri Jan  5 08:29:59 CST 2018
% 0.02/0.22  % CPUTime  : 
% 0.06/0.27  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.27  --creating new selector for []
% 0.38/0.59  -running prover on /export/starexec/sandbox/tmp/tmpWCBu73/sel_theBenchmark.p_1 with time limit 29
% 0.38/0.59  -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/tmpWCBu73/sel_theBenchmark.p_1']
% 0.38/0.59  -prover status Theorem
% 0.38/0.59  Problem theBenchmark.p solved in phase 0.
% 0.38/0.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.59  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.59  Solved 1 out of 1.
% 0.38/0.59  # Problem is unsatisfiable (or provable), constructing proof object
% 0.38/0.59  # SZS status Theorem
% 0.38/0.59  # SZS output start CNFRefutation.
% See solution above
% 0.38/0.60  # SZS output end CNFRefutation
%------------------------------------------------------------------------------