TSTP Solution File: NUM468+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM468+2 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n127.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 0.47s
% Output   : CNFRefutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   57 (  19 unt;   0 def)
%            Number of atoms       :  207 (  54 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  238 (  88   ~; 102   |;  37   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   51 (   0 sgn  27   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/tmp/tmphyyVxt/sel_theBenchmark.p_1',m__1240) ).

fof(6,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/tmphyyVxt/sel_theBenchmark.p_1',mMulCanc) ).

fof(7,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/tmphyyVxt/sel_theBenchmark.p_1',mAMDistr) ).

fof(12,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/sandbox/tmp/tmphyyVxt/sel_theBenchmark.p_1',m__1240_04) ).

fof(23,conjecture,
    ( ~ 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/sandbox/tmp/tmphyyVxt/sel_theBenchmark.p_1',m__) ).

fof(36,negated_conjecture,
    ~ ( ~ 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(assume_negation,[status(cth)],[23]) ).

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

fof(54,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)],[6]) ).

fof(55,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)],[54]) ).

fof(56,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)],[55]) ).

fof(57,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)],[56]) ).

cnf(59,plain,
    ( X1 = sz00
    | X3 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[57]) ).

fof(60,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)],[7]) ).

fof(61,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)],[60]) ).

fof(62,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)],[61]) ).

cnf(64,plain,
    ( sdtasdt0(X3,sdtpldt0(X2,X1)) = sdtpldt0(sdtasdt0(X3,X2),sdtasdt0(X3,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(84,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)],[12]) ).

fof(85,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)],[84]) ).

cnf(87,plain,
    xn = sdtasdt0(xl,esk3_0),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(88,plain,
    aNaturalNumber0(esk3_0),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(90,plain,
    xm = sdtasdt0(xl,esk2_0),
    inference(split_conjunct,[status(thm)],[85]) ).

cnf(91,plain,
    aNaturalNumber0(esk2_0),
    inference(split_conjunct,[status(thm)],[85]) ).

fof(141,negated_conjecture,
    ( ~ 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)],[36]) ).

cnf(142,negated_conjecture,
    sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(143,negated_conjecture,
    xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(144,negated_conjecture,
    aNaturalNumber0(sdtsldt0(xn,xl)),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(145,negated_conjecture,
    xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(146,negated_conjecture,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(147,negated_conjecture,
    xl != sz00,
    inference(split_conjunct,[status(thm)],[141]) ).

cnf(520,plain,
    ( sz00 = xl
    | esk2_0 = X1
    | xm != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(xl) ),
    inference(spm,[status(thm)],[59,90,theory(equality)]) ).

cnf(522,plain,
    ( sz00 = xl
    | esk3_0 = X1
    | xn != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(esk3_0)
    | ~ aNaturalNumber0(xl) ),
    inference(spm,[status(thm)],[59,87,theory(equality)]) ).

cnf(540,plain,
    ( sz00 = xl
    | esk2_0 = X1
    | xm != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xl) ),
    inference(rw,[status(thm)],[520,91,theory(equality)]) ).

cnf(541,plain,
    ( sz00 = xl
    | esk2_0 = X1
    | xm != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[540,44,theory(equality)]) ).

cnf(542,plain,
    ( sz00 = xl
    | esk2_0 = X1
    | xm != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[541,theory(equality)]) ).

cnf(543,plain,
    ( esk2_0 = X1
    | sdtasdt0(xl,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[542,147,theory(equality)]) ).

cnf(548,plain,
    ( sz00 = xl
    | esk3_0 = X1
    | xn != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1)
    | $false
    | ~ aNaturalNumber0(xl) ),
    inference(rw,[status(thm)],[522,88,theory(equality)]) ).

cnf(549,plain,
    ( sz00 = xl
    | esk3_0 = X1
    | xn != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[548,44,theory(equality)]) ).

cnf(550,plain,
    ( sz00 = xl
    | esk3_0 = X1
    | xn != sdtasdt0(xl,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[549,theory(equality)]) ).

cnf(551,plain,
    ( esk3_0 = X1
    | sdtasdt0(xl,X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[550,147,theory(equality)]) ).

cnf(671,plain,
    ( sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[64,90,theory(equality)]) ).

cnf(706,plain,
    ( sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(esk2_0,X1))
    | $false
    | ~ aNaturalNumber0(esk2_0)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[671,44,theory(equality)]) ).

cnf(707,plain,
    ( sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(esk2_0,X1))
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[706,91,theory(equality)]) ).

cnf(708,plain,
    ( sdtpldt0(xm,sdtasdt0(xl,X1)) = sdtasdt0(xl,sdtpldt0(esk2_0,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[707,theory(equality)]) ).

cnf(1558,negated_conjecture,
    ( esk2_0 = sdtsldt0(xm,xl)
    | ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
    inference(spm,[status(thm)],[543,145,theory(equality)]) ).

cnf(1571,negated_conjecture,
    ( esk2_0 = sdtsldt0(xm,xl)
    | $false ),
    inference(rw,[status(thm)],[1558,146,theory(equality)]) ).

cnf(1572,negated_conjecture,
    esk2_0 = sdtsldt0(xm,xl),
    inference(cn,[status(thm)],[1571,theory(equality)]) ).

cnf(1597,negated_conjecture,
    sdtasdt0(xl,sdtpldt0(esk2_0,sdtsldt0(xn,xl))) != sdtpldt0(xm,xn),
    inference(rw,[status(thm)],[142,1572,theory(equality)]) ).

cnf(1888,negated_conjecture,
    ( esk3_0 = sdtsldt0(xn,xl)
    | ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
    inference(spm,[status(thm)],[551,143,theory(equality)]) ).

cnf(1902,negated_conjecture,
    ( esk3_0 = sdtsldt0(xn,xl)
    | $false ),
    inference(rw,[status(thm)],[1888,144,theory(equality)]) ).

cnf(1903,negated_conjecture,
    esk3_0 = sdtsldt0(xn,xl),
    inference(cn,[status(thm)],[1902,theory(equality)]) ).

cnf(1926,negated_conjecture,
    sdtasdt0(xl,esk3_0) = xn,
    inference(rw,[status(thm)],[143,1903,theory(equality)]) ).

cnf(1929,negated_conjecture,
    sdtasdt0(xl,sdtpldt0(esk2_0,esk3_0)) != sdtpldt0(xm,xn),
    inference(rw,[status(thm)],[1597,1903,theory(equality)]) ).

cnf(19746,negated_conjecture,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(esk2_0,esk3_0))
    | ~ aNaturalNumber0(esk3_0) ),
    inference(spm,[status(thm)],[708,1926,theory(equality)]) ).

cnf(19826,negated_conjecture,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(esk2_0,esk3_0))
    | $false ),
    inference(rw,[status(thm)],[19746,88,theory(equality)]) ).

cnf(19827,negated_conjecture,
    sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(esk2_0,esk3_0)),
    inference(cn,[status(thm)],[19826,theory(equality)]) ).

cnf(19828,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[19827,1929,theory(equality)]) ).

cnf(19829,negated_conjecture,
    $false,
    19828,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM468+2 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.03  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.24  % Computer : n127.star.cs.uiowa.edu
% 0.02/0.24  % Model    : x86_64 x86_64
% 0.02/0.24  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24  % Memory   : 32218.625MB
% 0.02/0.24  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24  % CPULimit : 300
% 0.02/0.24  % DateTime : Fri Jan  5 04:50:29 CST 2018
% 0.02/0.24  % CPUTime  : 
% 0.06/0.30  % SZS status Started for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.30  --creating new selector for []
% 0.47/0.68  -running prover on /export/starexec/sandbox/tmp/tmphyyVxt/sel_theBenchmark.p_1 with time limit 29
% 0.47/0.68  -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/tmphyyVxt/sel_theBenchmark.p_1']
% 0.47/0.68  -prover status Theorem
% 0.47/0.68  Problem theBenchmark.p solved in phase 0.
% 0.47/0.68  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.68  % SZS status Ended for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.68  Solved 1 out of 1.
% 0.47/0.68  # Problem is unsatisfiable (or provable), constructing proof object
% 0.47/0.68  # SZS status Theorem
% 0.47/0.68  # SZS output start CNFRefutation.
% See solution above
% 0.47/0.69  # SZS output end CNFRefutation
%------------------------------------------------------------------------------