TSTP Solution File: NUM469+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM469+2 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n135.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 15:21:27 EST 2018

% Result   : Theorem 0.07s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   75 (  23 unt;   0 def)
%            Number of atoms       :  230 (  34 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  249 (  94   ~;  94   |;  55   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   55 (   0 sgn  34   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',m_MulZero) ).

fof(2,axiom,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',m__1240) ).

fof(8,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & equal(X2,sdtasdt0(X1,X3)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',mDefDiv) ).

fof(12,axiom,
    ( ~ equal(xl,sz00)
   => ( aNaturalNumber0(sdtsldt0(xm,xl))
      & equal(xm,sdtasdt0(xl,sdtsldt0(xm,xl)))
      & aNaturalNumber0(sdtsldt0(xn,xl))
      & equal(xn,sdtasdt0(xl,sdtsldt0(xn,xl)))
      & equal(sdtpldt0(xm,xn),sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))) ) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',m__1298) ).

fof(13,axiom,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(xm,sdtasdt0(xl,X1)) )
    & doDivides0(xl,xm)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(xn,sdtasdt0(xl,X1)) )
    & doDivides0(xl,xn) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',m__1240_04) ).

fof(24,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & equal(sdtpldt0(xm,xn),sdtasdt0(xl,X1)) )
    | doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',m__) ).

fof(30,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',mSortsC) ).

fof(31,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',mSortsB) ).

fof(35,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1',m_AddZero) ).

fof(37,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & equal(sdtpldt0(xm,xn),sdtasdt0(xl,X1)) )
      | doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(assume_negation,[status(cth)],[24]) ).

fof(38,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(39,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[38]) ).

fof(40,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz00),sz00)
        | ~ aNaturalNumber0(X2) )
      & ( equal(sz00,sdtasdt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[39]) ).

cnf(41,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(43,plain,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[2]) ).

cnf(44,plain,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[2]) ).

cnf(45,plain,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[2]) ).

fof(66,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ( ( ~ doDivides0(X1,X2)
          | ? [X3] :
              ( aNaturalNumber0(X3)
              & equal(X2,sdtasdt0(X1,X3)) ) )
        & ( ! [X3] :
              ( ~ aNaturalNumber0(X3)
              | ~ equal(X2,sdtasdt0(X1,X3)) )
          | doDivides0(X1,X2) ) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(67,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ doDivides0(X4,X5)
          | ? [X6] :
              ( aNaturalNumber0(X6)
              & equal(X5,sdtasdt0(X4,X6)) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(X5,sdtasdt0(X4,X7)) )
          | doDivides0(X4,X5) ) ) ),
    inference(variable_rename,[status(thm)],[66]) ).

fof(68,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ doDivides0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(X5,sdtasdt0(X4,X7)) )
          | doDivides0(X4,X5) ) ) ),
    inference(skolemize,[status(esa)],[67]) ).

fof(69,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ aNaturalNumber0(X7)
          | ~ equal(X5,sdtasdt0(X4,X7))
          | doDivides0(X4,X5) )
        & ( ~ doDivides0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) ) )
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[68]) ).

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

cnf(73,plain,
    ( doDivides0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 != sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(85,plain,
    ( equal(xl,sz00)
    | ( aNaturalNumber0(sdtsldt0(xm,xl))
      & equal(xm,sdtasdt0(xl,sdtsldt0(xm,xl)))
      & aNaturalNumber0(sdtsldt0(xn,xl))
      & equal(xn,sdtasdt0(xl,sdtsldt0(xn,xl)))
      & equal(sdtpldt0(xm,xn),sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(86,plain,
    ( ( aNaturalNumber0(sdtsldt0(xm,xl))
      | equal(xl,sz00) )
    & ( equal(xm,sdtasdt0(xl,sdtsldt0(xm,xl)))
      | equal(xl,sz00) )
    & ( aNaturalNumber0(sdtsldt0(xn,xl))
      | equal(xl,sz00) )
    & ( equal(xn,sdtasdt0(xl,sdtsldt0(xn,xl)))
      | equal(xl,sz00) )
    & ( equal(sdtpldt0(xm,xn),sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))))
      | equal(xl,sz00) ) ),
    inference(distribute,[status(thm)],[85]) ).

cnf(87,plain,
    ( xl = sz00
    | sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
    inference(split_conjunct,[status(thm)],[86]) ).

cnf(89,plain,
    ( xl = sz00
    | aNaturalNumber0(sdtsldt0(xn,xl)) ),
    inference(split_conjunct,[status(thm)],[86]) ).

cnf(91,plain,
    ( xl = sz00
    | aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(split_conjunct,[status(thm)],[86]) ).

fof(92,plain,
    ( ? [X2] :
        ( aNaturalNumber0(X2)
        & equal(xm,sdtasdt0(xl,X2)) )
    & doDivides0(xl,xm)
    & ? [X3] :
        ( aNaturalNumber0(X3)
        & equal(xn,sdtasdt0(xl,X3)) )
    & doDivides0(xl,xn) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(93,plain,
    ( aNaturalNumber0(esk2_0)
    & equal(xm,sdtasdt0(xl,esk2_0))
    & doDivides0(xl,xm)
    & aNaturalNumber0(esk3_0)
    & equal(xn,sdtasdt0(xl,esk3_0))
    & doDivides0(xl,xn) ),
    inference(skolemize,[status(esa)],[92]) ).

cnf(95,plain,
    xn = sdtasdt0(xl,esk3_0),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(96,plain,
    aNaturalNumber0(esk3_0),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(98,plain,
    xm = sdtasdt0(xl,esk2_0),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(99,plain,
    aNaturalNumber0(esk2_0),
    inference(split_conjunct,[status(thm)],[93]) ).

fof(149,negated_conjecture,
    ( ! [X1] :
        ( ~ aNaturalNumber0(X1)
        | ~ equal(sdtpldt0(xm,xn),sdtasdt0(xl,X1)) )
    & ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(fof_nnf,[status(thm)],[37]) ).

fof(150,negated_conjecture,
    ( ! [X2] :
        ( ~ aNaturalNumber0(X2)
        | ~ equal(sdtpldt0(xm,xn),sdtasdt0(xl,X2)) )
    & ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(variable_rename,[status(thm)],[149]) ).

fof(151,negated_conjecture,
    ! [X2] :
      ( ( ~ aNaturalNumber0(X2)
        | ~ equal(sdtpldt0(xm,xn),sdtasdt0(xl,X2)) )
      & ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(shift_quantors,[status(thm)],[150]) ).

cnf(152,negated_conjecture,
    ~ doDivides0(xl,sdtpldt0(xm,xn)),
    inference(split_conjunct,[status(thm)],[151]) ).

cnf(153,negated_conjecture,
    ( sdtpldt0(xm,xn) != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[151]) ).

cnf(175,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(176,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtpldt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(177,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[176]) ).

cnf(178,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[177]) ).

fof(190,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtpldt0(X1,sz00),X1)
        & equal(X1,sdtpldt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(191,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtpldt0(X2,sz00),X2)
        & equal(X2,sdtpldt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[190]) ).

fof(192,plain,
    ! [X2] :
      ( ( equal(sdtpldt0(X2,sz00),X2)
        | ~ aNaturalNumber0(X2) )
      & ( equal(X2,sdtpldt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[191]) ).

cnf(194,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[192]) ).

cnf(332,plain,
    ( doDivides0(xl,X1)
    | xm != X1
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[73,98,theory(equality)]) ).

cnf(342,plain,
    ( doDivides0(xl,X1)
    | xm != X1
    | $false
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[332,99,theory(equality)]) ).

cnf(343,plain,
    ( doDivides0(xl,X1)
    | xm != X1
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[342,45,theory(equality)]) ).

cnf(344,plain,
    ( doDivides0(xl,X1)
    | xm != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[343,theory(equality)]) ).

cnf(432,plain,
    ( xl = sz00
    | ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
    inference(spm,[status(thm)],[153,87,theory(equality)]) ).

cnf(1108,plain,
    ( xm != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
    inference(spm,[status(thm)],[152,344,theory(equality)]) ).

cnf(1116,plain,
    ( sdtpldt0(xm,xn) != xm
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xm) ),
    inference(spm,[status(thm)],[1108,178,theory(equality)]) ).

cnf(1117,plain,
    ( sdtpldt0(xm,xn) != xm
    | $false
    | ~ aNaturalNumber0(xm) ),
    inference(rw,[status(thm)],[1116,43,theory(equality)]) ).

cnf(1118,plain,
    ( sdtpldt0(xm,xn) != xm
    | $false
    | $false ),
    inference(rw,[status(thm)],[1117,44,theory(equality)]) ).

cnf(1119,plain,
    sdtpldt0(xm,xn) != xm,
    inference(cn,[status(thm)],[1118,theory(equality)]) ).

cnf(1459,plain,
    ( xl = sz00
    | ~ aNaturalNumber0(sdtsldt0(xn,xl))
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(spm,[status(thm)],[432,178,theory(equality)]) ).

cnf(1460,plain,
    ( xl = sz00
    | ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
    inference(csr,[status(thm)],[1459,91]) ).

cnf(1461,plain,
    xl = sz00,
    inference(csr,[status(thm)],[1460,89]) ).

cnf(1462,plain,
    sdtasdt0(sz00,esk3_0) = xn,
    inference(rw,[status(thm)],[95,1461,theory(equality)]) ).

cnf(1465,plain,
    sdtasdt0(sz00,esk2_0) = xm,
    inference(rw,[status(thm)],[98,1461,theory(equality)]) ).

cnf(1510,plain,
    ( xn = sz00
    | ~ aNaturalNumber0(esk3_0) ),
    inference(spm,[status(thm)],[41,1462,theory(equality)]) ).

cnf(1523,plain,
    ( xn = sz00
    | $false ),
    inference(rw,[status(thm)],[1510,96,theory(equality)]) ).

cnf(1524,plain,
    xn = sz00,
    inference(cn,[status(thm)],[1523,theory(equality)]) ).

cnf(1568,plain,
    sdtpldt0(xm,sz00) != xm,
    inference(rw,[status(thm)],[1119,1524,theory(equality)]) ).

cnf(1580,plain,
    ( xm = sz00
    | ~ aNaturalNumber0(esk2_0) ),
    inference(spm,[status(thm)],[41,1465,theory(equality)]) ).

cnf(1593,plain,
    ( xm = sz00
    | $false ),
    inference(rw,[status(thm)],[1580,99,theory(equality)]) ).

cnf(1594,plain,
    xm = sz00,
    inference(cn,[status(thm)],[1593,theory(equality)]) ).

cnf(1650,plain,
    sdtpldt0(sz00,sz00) != xm,
    inference(rw,[status(thm)],[1568,1594,theory(equality)]) ).

cnf(1651,plain,
    sdtpldt0(sz00,sz00) != sz00,
    inference(rw,[status(thm)],[1650,1594,theory(equality)]) ).

cnf(1652,plain,
    ~ aNaturalNumber0(sz00),
    inference(spm,[status(thm)],[1651,194,theory(equality)]) ).

cnf(1656,plain,
    $false,
    inference(rw,[status(thm)],[1652,175,theory(equality)]) ).

cnf(1657,plain,
    $false,
    inference(cn,[status(thm)],[1656,theory(equality)]) ).

cnf(1658,plain,
    $false,
    1657,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM469+2 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.03/0.23  % Computer : n135.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
% 0.07/0.23  % CPULimit : 300
% 0.07/0.23  % DateTime : Fri Jan  5 04:55:00 CST 2018
% 0.07/0.23  % CPUTime  : 
% 0.07/0.28  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.28  --creating new selector for []
% 0.07/0.37  -running prover on /export/starexec/sandbox2/tmp/tmp6XI7vm/sel_theBenchmark.p_1 with time limit 29
% 0.07/0.37  -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/tmp6XI7vm/sel_theBenchmark.p_1']
% 0.07/0.37  -prover status Theorem
% 0.07/0.37  Problem theBenchmark.p solved in phase 0.
% 0.07/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.37  Solved 1 out of 1.
% 0.07/0.37  # Problem is unsatisfiable (or provable), constructing proof object
% 0.07/0.37  # SZS status Theorem
% 0.07/0.37  # SZS output start CNFRefutation.
% See solution above
% 0.07/0.37  # SZS output end CNFRefutation
%------------------------------------------------------------------------------