TSTP Solution File: NUM500+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM500+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n088.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 15:21:34 EST 2018

% Result   : Theorem 0.06s
% Output   : CNFRefutation 0.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   38 (   7 unt;   0 def)
%            Number of atoms       :  256 (  29 equ)
%            Maximal formula atoms :   73 (   6 avg)
%            Number of connectives :  329 ( 111   ~; 143   |;  72   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   34 (   0 sgn  17   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ~ ( equal(xk,sz00)
      | equal(xk,sz10) ),
    file('/export/starexec/sandbox2/tmp/tmpVLGRJZ/sel_theBenchmark.p_1',m__2315) ).

fof(31,conjecture,
    ? [X1] :
      ( aNaturalNumber0(X1)
      & ( ? [X2] :
            ( aNaturalNumber0(X2)
            & equal(xk,sdtasdt0(X1,X2)) )
        | doDivides0(X1,xk) )
      & ( ( ~ equal(X1,sz00)
          & ~ equal(X1,sz10)
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & ? [X3] :
                    ( aNaturalNumber0(X3)
                    & equal(X1,sdtasdt0(X2,X3)) )
                & doDivides0(X2,X1) )
             => ( equal(X2,sz10)
                | equal(X2,X1) ) ) )
        | isPrime0(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmpVLGRJZ/sel_theBenchmark.p_1',m__) ).

fof(40,axiom,
    ! [X1] :
      ( ( aNaturalNumber0(X1)
        & ~ equal(X1,sz00)
        & ~ equal(X1,sz10) )
     => ? [X2] :
          ( aNaturalNumber0(X2)
          & doDivides0(X2,X1)
          & isPrime0(X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpVLGRJZ/sel_theBenchmark.p_1',mPrimDiv) ).

fof(43,axiom,
    ( aNaturalNumber0(xk)
    & equal(sdtasdt0(xn,xm),sdtasdt0(xp,xk))
    & equal(xk,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
    file('/export/starexec/sandbox2/tmp/tmpVLGRJZ/sel_theBenchmark.p_1',m__2306) ).

fof(49,negated_conjecture,
    ~ ? [X1] :
        ( aNaturalNumber0(X1)
        & ( ? [X2] :
              ( aNaturalNumber0(X2)
              & equal(xk,sdtasdt0(X1,X2)) )
          | doDivides0(X1,xk) )
        & ( ( ~ equal(X1,sz00)
            & ~ equal(X1,sz10)
            & ! [X2] :
                ( ( aNaturalNumber0(X2)
                  & ? [X3] :
                      ( aNaturalNumber0(X3)
                      & equal(X1,sdtasdt0(X2,X3)) )
                  & doDivides0(X2,X1) )
               => ( equal(X2,sz10)
                  | equal(X2,X1) ) ) )
          | isPrime0(X1) ) ),
    inference(assume_negation,[status(cth)],[31]) ).

fof(50,plain,
    ( ~ equal(xk,sz00)
    & ~ equal(xk,sz10) ),
    inference(fof_nnf,[status(thm)],[1]) ).

cnf(51,plain,
    xk != sz10,
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(52,plain,
    xk != sz00,
    inference(split_conjunct,[status(thm)],[50]) ).

fof(319,negated_conjecture,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( ! [X2] :
            ( ~ aNaturalNumber0(X2)
            | ~ equal(xk,sdtasdt0(X1,X2)) )
        & ~ doDivides0(X1,xk) )
      | ( ( equal(X1,sz00)
          | equal(X1,sz10)
          | ? [X2] :
              ( aNaturalNumber0(X2)
              & ? [X3] :
                  ( aNaturalNumber0(X3)
                  & equal(X1,sdtasdt0(X2,X3)) )
              & doDivides0(X2,X1)
              & ~ equal(X2,sz10)
              & ~ equal(X2,X1) ) )
        & ~ isPrime0(X1) ) ),
    inference(fof_nnf,[status(thm)],[49]) ).

fof(320,negated_conjecture,
    ! [X4] :
      ( ~ aNaturalNumber0(X4)
      | ( ! [X5] :
            ( ~ aNaturalNumber0(X5)
            | ~ equal(xk,sdtasdt0(X4,X5)) )
        & ~ doDivides0(X4,xk) )
      | ( ( equal(X4,sz00)
          | equal(X4,sz10)
          | ? [X6] :
              ( aNaturalNumber0(X6)
              & ? [X7] :
                  ( aNaturalNumber0(X7)
                  & equal(X4,sdtasdt0(X6,X7)) )
              & doDivides0(X6,X4)
              & ~ equal(X6,sz10)
              & ~ equal(X6,X4) ) )
        & ~ isPrime0(X4) ) ),
    inference(variable_rename,[status(thm)],[319]) ).

fof(321,negated_conjecture,
    ! [X4] :
      ( ~ aNaturalNumber0(X4)
      | ( ! [X5] :
            ( ~ aNaturalNumber0(X5)
            | ~ equal(xk,sdtasdt0(X4,X5)) )
        & ~ doDivides0(X4,xk) )
      | ( ( equal(X4,sz00)
          | equal(X4,sz10)
          | ( aNaturalNumber0(esk10_1(X4))
            & aNaturalNumber0(esk11_1(X4))
            & equal(X4,sdtasdt0(esk10_1(X4),esk11_1(X4)))
            & doDivides0(esk10_1(X4),X4)
            & ~ equal(esk10_1(X4),sz10)
            & ~ equal(esk10_1(X4),X4) ) )
        & ~ isPrime0(X4) ) ),
    inference(skolemize,[status(esa)],[320]) ).

fof(322,negated_conjecture,
    ! [X4,X5] :
      ( ( ( ~ aNaturalNumber0(X5)
          | ~ equal(xk,sdtasdt0(X4,X5)) )
        & ~ doDivides0(X4,xk) )
      | ~ aNaturalNumber0(X4)
      | ( ( equal(X4,sz00)
          | equal(X4,sz10)
          | ( aNaturalNumber0(esk10_1(X4))
            & aNaturalNumber0(esk11_1(X4))
            & equal(X4,sdtasdt0(esk10_1(X4),esk11_1(X4)))
            & doDivides0(esk10_1(X4),X4)
            & ~ equal(esk10_1(X4),sz10)
            & ~ equal(esk10_1(X4),X4) ) )
        & ~ isPrime0(X4) ) ),
    inference(shift_quantors,[status(thm)],[321]) ).

fof(323,negated_conjecture,
    ! [X4,X5] :
      ( ( aNaturalNumber0(esk10_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( aNaturalNumber0(esk11_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( equal(X4,sdtasdt0(esk10_1(X4),esk11_1(X4)))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( doDivides0(esk10_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk10_1(X4),sz10)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk10_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( ~ isPrime0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( aNaturalNumber0(esk10_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( aNaturalNumber0(esk11_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( equal(X4,sdtasdt0(esk10_1(X4),esk11_1(X4)))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( doDivides0(esk10_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk10_1(X4),sz10)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk10_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( ~ isPrime0(X4)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[322]) ).

cnf(324,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | ~ doDivides0(X1,xk)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[323]) ).

fof(375,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | equal(X1,sz00)
      | equal(X1,sz10)
      | ? [X2] :
          ( aNaturalNumber0(X2)
          & doDivides0(X2,X1)
          & isPrime0(X2) ) ),
    inference(fof_nnf,[status(thm)],[40]) ).

fof(376,plain,
    ! [X3] :
      ( ~ aNaturalNumber0(X3)
      | equal(X3,sz00)
      | equal(X3,sz10)
      | ? [X4] :
          ( aNaturalNumber0(X4)
          & doDivides0(X4,X3)
          & isPrime0(X4) ) ),
    inference(variable_rename,[status(thm)],[375]) ).

fof(377,plain,
    ! [X3] :
      ( ~ aNaturalNumber0(X3)
      | equal(X3,sz00)
      | equal(X3,sz10)
      | ( aNaturalNumber0(esk13_1(X3))
        & doDivides0(esk13_1(X3),X3)
        & isPrime0(esk13_1(X3)) ) ),
    inference(skolemize,[status(esa)],[376]) ).

fof(378,plain,
    ! [X3] :
      ( ( aNaturalNumber0(esk13_1(X3))
        | ~ aNaturalNumber0(X3)
        | equal(X3,sz00)
        | equal(X3,sz10) )
      & ( doDivides0(esk13_1(X3),X3)
        | ~ aNaturalNumber0(X3)
        | equal(X3,sz00)
        | equal(X3,sz10) )
      & ( isPrime0(esk13_1(X3))
        | ~ aNaturalNumber0(X3)
        | equal(X3,sz00)
        | equal(X3,sz10) ) ),
    inference(distribute,[status(thm)],[377]) ).

cnf(379,plain,
    ( X1 = sz10
    | X1 = sz00
    | isPrime0(esk13_1(X1))
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[378]) ).

cnf(380,plain,
    ( X1 = sz10
    | X1 = sz00
    | doDivides0(esk13_1(X1),X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[378]) ).

cnf(381,plain,
    ( X1 = sz10
    | X1 = sz00
    | aNaturalNumber0(esk13_1(X1))
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[378]) ).

cnf(392,plain,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(522,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ isPrime0(esk13_1(xk))
    | ~ aNaturalNumber0(esk13_1(xk))
    | ~ aNaturalNumber0(xk) ),
    inference(spm,[status(thm)],[324,380,theory(equality)]) ).

cnf(527,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ isPrime0(esk13_1(xk))
    | ~ aNaturalNumber0(esk13_1(xk))
    | $false ),
    inference(rw,[status(thm)],[522,392,theory(equality)]) ).

cnf(528,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ isPrime0(esk13_1(xk))
    | ~ aNaturalNumber0(esk13_1(xk)) ),
    inference(cn,[status(thm)],[527,theory(equality)]) ).

cnf(529,negated_conjecture,
    ( xk = sz00
    | ~ isPrime0(esk13_1(xk))
    | ~ aNaturalNumber0(esk13_1(xk)) ),
    inference(sr,[status(thm)],[528,51,theory(equality)]) ).

cnf(530,negated_conjecture,
    ( ~ isPrime0(esk13_1(xk))
    | ~ aNaturalNumber0(esk13_1(xk)) ),
    inference(sr,[status(thm)],[529,52,theory(equality)]) ).

cnf(5613,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(esk13_1(xk))
    | ~ aNaturalNumber0(xk) ),
    inference(spm,[status(thm)],[530,379,theory(equality)]) ).

cnf(5614,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(esk13_1(xk))
    | $false ),
    inference(rw,[status(thm)],[5613,392,theory(equality)]) ).

cnf(5615,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(esk13_1(xk)) ),
    inference(cn,[status(thm)],[5614,theory(equality)]) ).

cnf(5616,negated_conjecture,
    ( xk = sz00
    | ~ aNaturalNumber0(esk13_1(xk)) ),
    inference(sr,[status(thm)],[5615,51,theory(equality)]) ).

cnf(5617,negated_conjecture,
    ~ aNaturalNumber0(esk13_1(xk)),
    inference(sr,[status(thm)],[5616,52,theory(equality)]) ).

cnf(5618,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | ~ aNaturalNumber0(xk) ),
    inference(spm,[status(thm)],[5617,381,theory(equality)]) ).

cnf(5619,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk
    | $false ),
    inference(rw,[status(thm)],[5618,392,theory(equality)]) ).

cnf(5620,negated_conjecture,
    ( sz10 = xk
    | sz00 = xk ),
    inference(cn,[status(thm)],[5619,theory(equality)]) ).

cnf(5621,negated_conjecture,
    xk = sz00,
    inference(sr,[status(thm)],[5620,51,theory(equality)]) ).

cnf(5622,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[5621,52,theory(equality)]) ).

cnf(5623,negated_conjecture,
    $false,
    5622,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM500+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.23  % Computer : n088.star.cs.uiowa.edu
% 0.02/0.23  % Model    : x86_64 x86_64
% 0.02/0.23  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23  % Memory   : 32218.625MB
% 0.02/0.23  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23  % CPULimit : 300
% 0.02/0.23  % DateTime : Fri Jan  5 06:05:30 CST 2018
% 0.02/0.23  % CPUTime  : 
% 0.02/0.28  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.28  --creating new selector for []
% 0.06/0.49  -running prover on /export/starexec/sandbox2/tmp/tmpVLGRJZ/sel_theBenchmark.p_1 with time limit 29
% 0.06/0.49  -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpVLGRJZ/sel_theBenchmark.p_1']
% 0.06/0.49  -prover status Theorem
% 0.06/0.49  Problem theBenchmark.p solved in phase 0.
% 0.06/0.49  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.49  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.49  Solved 1 out of 1.
% 0.06/0.49  # Problem is unsatisfiable (or provable), constructing proof object
% 0.06/0.49  # SZS status Theorem
% 0.06/0.49  # SZS output start CNFRefutation.
% See solution above
% 0.06/0.49  # SZS output end CNFRefutation
%------------------------------------------------------------------------------