TSTP Solution File: ALG210+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : ALG210+1 : TPTP v5.0.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sat Dec 25 04:16:46 EST 2010

% Result   : Theorem 0.31s
% Output   : CNFRefutation 0.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   91 (  38 unt;   0 def)
%            Number of atoms       :  176 (  95 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  145 (  60   ~;  63   |;  19   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   89 (   0 sgn  21   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( element(X1)
    <=> ? [X2] :
          ( times(X1,X2) = X1
          & times(X1,X1) = X2 ) ),
    file('/tmp/tmpcveeQI/sel_ALG210+1.p_1',axiom_2) ).

fof(2,conjecture,
    ! [X3,X1] :
      ( ( element(X3)
        & element(X1) )
     => element(times(X3,X1)) ),
    file('/tmp/tmpcveeQI/sel_ALG210+1.p_1',conjecture_1) ).

fof(3,axiom,
    ! [X3,X1,X2] : times(times(X3,X1),X2) = times(X1,times(X2,X3)),
    file('/tmp/tmpcveeQI/sel_ALG210+1.p_1',axiom_1) ).

fof(4,negated_conjecture,
    ~ ! [X3,X1] :
        ( ( element(X3)
          & element(X1) )
       => element(times(X3,X1)) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(5,plain,
    ! [X1] :
      ( ( ~ element(X1)
        | ? [X2] :
            ( times(X1,X2) = X1
            & times(X1,X1) = X2 ) )
      & ( ! [X2] :
            ( times(X1,X2) != X1
            | times(X1,X1) != X2 )
        | element(X1) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(6,plain,
    ! [X3] :
      ( ( ~ element(X3)
        | ? [X4] :
            ( times(X3,X4) = X3
            & times(X3,X3) = X4 ) )
      & ( ! [X5] :
            ( times(X3,X5) != X3
            | times(X3,X3) != X5 )
        | element(X3) ) ),
    inference(variable_rename,[status(thm)],[5]) ).

fof(7,plain,
    ! [X3] :
      ( ( ~ element(X3)
        | ( times(X3,esk1_1(X3)) = X3
          & times(X3,X3) = esk1_1(X3) ) )
      & ( ! [X5] :
            ( times(X3,X5) != X3
            | times(X3,X3) != X5 )
        | element(X3) ) ),
    inference(skolemize,[status(esa)],[6]) ).

fof(8,plain,
    ! [X3,X5] :
      ( ( times(X3,X5) != X3
        | times(X3,X3) != X5
        | element(X3) )
      & ( ~ element(X3)
        | ( times(X3,esk1_1(X3)) = X3
          & times(X3,X3) = esk1_1(X3) ) ) ),
    inference(shift_quantors,[status(thm)],[7]) ).

fof(9,plain,
    ! [X3,X5] :
      ( ( times(X3,X5) != X3
        | times(X3,X3) != X5
        | element(X3) )
      & ( times(X3,esk1_1(X3)) = X3
        | ~ element(X3) )
      & ( times(X3,X3) = esk1_1(X3)
        | ~ element(X3) ) ),
    inference(distribute,[status(thm)],[8]) ).

cnf(10,plain,
    ( times(X1,X1) = esk1_1(X1)
    | ~ element(X1) ),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(11,plain,
    ( times(X1,esk1_1(X1)) = X1
    | ~ element(X1) ),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(12,plain,
    ( element(X1)
    | times(X1,X1) != X2
    | times(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[9]) ).

fof(13,negated_conjecture,
    ? [X3,X1] :
      ( element(X3)
      & element(X1)
      & ~ element(times(X3,X1)) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(14,negated_conjecture,
    ? [X4,X5] :
      ( element(X4)
      & element(X5)
      & ~ element(times(X4,X5)) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ( element(esk2_0)
    & element(esk3_0)
    & ~ element(times(esk2_0,esk3_0)) ),
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    ~ element(times(esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    element(esk3_0),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(18,negated_conjecture,
    element(esk2_0),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(19,plain,
    ! [X4,X5,X6] : times(times(X4,X5),X6) = times(X5,times(X6,X4)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(20,plain,
    times(times(X1,X2),X3) = times(X2,times(X3,X1)),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(21,plain,
    ( times(X1,times(X1,X1)) = X1
    | ~ element(X1) ),
    inference(spm,[status(thm)],[11,10,theory(equality)]) ).

cnf(22,plain,
    times(times(X2,times(X3,X1)),X4) = times(X3,times(X4,times(X1,X2))),
    inference(spm,[status(thm)],[20,20,theory(equality)]) ).

cnf(23,plain,
    times(times(X1,X2),times(X3,X4)) = times(X2,times(X4,times(X1,X3))),
    inference(spm,[status(thm)],[20,20,theory(equality)]) ).

cnf(28,plain,
    ( times(X1,X2) = times(esk1_1(X1),times(X2,X1))
    | ~ element(X1) ),
    inference(spm,[status(thm)],[20,11,theory(equality)]) ).

cnf(29,plain,
    ( element(X1)
    | times(X1,times(X1,X1)) != X1 ),
    inference(er,[status(thm)],[12,theory(equality)]) ).

cnf(30,plain,
    ( element(times(X1,X2))
    | times(times(X1,X2),X3) != times(X1,X2)
    | times(X2,times(times(X1,X2),X1)) != X3 ),
    inference(spm,[status(thm)],[12,20,theory(equality)]) ).

cnf(31,plain,
    ( element(times(X1,X2))
    | times(times(X1,X2),X3) != times(X1,X2)
    | times(X2,times(X2,times(X1,X1))) != X3 ),
    inference(rw,[status(thm)],[30,20,theory(equality)]) ).

cnf(32,negated_conjecture,
    times(esk2_0,times(esk2_0,esk2_0)) = esk2_0,
    inference(spm,[status(thm)],[21,18,theory(equality)]) ).

cnf(33,negated_conjecture,
    times(esk3_0,times(esk3_0,esk3_0)) = esk3_0,
    inference(spm,[status(thm)],[21,17,theory(equality)]) ).

cnf(34,negated_conjecture,
    times(esk2_0,X1) = times(times(esk2_0,esk2_0),times(X1,esk2_0)),
    inference(spm,[status(thm)],[20,32,theory(equality)]) ).

cnf(35,negated_conjecture,
    times(esk3_0,X1) = times(times(esk3_0,esk3_0),times(X1,esk3_0)),
    inference(spm,[status(thm)],[20,33,theory(equality)]) ).

cnf(38,plain,
    ( element(times(X1,X2))
    | times(times(X1,X2),times(X2,times(times(X1,X2),X1))) != times(X1,X2) ),
    inference(spm,[status(thm)],[29,20,theory(equality)]) ).

cnf(41,plain,
    ( element(times(X1,X2))
    | times(times(X1,X2),times(X2,times(X2,times(X1,X1)))) != times(X1,X2) ),
    inference(rw,[status(thm)],[38,20,theory(equality)]) ).

cnf(43,negated_conjecture,
    ( element(times(esk2_0,esk2_0))
    | times(times(esk2_0,esk2_0),X1) != times(esk2_0,esk2_0)
    | times(esk2_0,esk2_0) != X1 ),
    inference(spm,[status(thm)],[31,32,theory(equality)]) ).

cnf(44,negated_conjecture,
    ( element(times(esk3_0,esk3_0))
    | times(times(esk3_0,esk3_0),X1) != times(esk3_0,esk3_0)
    | times(esk3_0,esk3_0) != X1 ),
    inference(spm,[status(thm)],[31,33,theory(equality)]) ).

cnf(48,negated_conjecture,
    ( element(times(esk2_0,esk2_0))
    | times(times(esk2_0,esk2_0),times(esk2_0,esk2_0)) != times(esk2_0,esk2_0) ),
    inference(er,[status(thm)],[43,theory(equality)]) ).

cnf(49,negated_conjecture,
    ( element(times(esk2_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[48,20,theory(equality)]),20,theory(equality)]),32,theory(equality)]) ).

cnf(50,negated_conjecture,
    element(times(esk2_0,esk2_0)),
    inference(cn,[status(thm)],[49,theory(equality)]) ).

cnf(51,negated_conjecture,
    ( element(times(esk3_0,esk3_0))
    | times(times(esk3_0,esk3_0),times(esk3_0,esk3_0)) != times(esk3_0,esk3_0) ),
    inference(er,[status(thm)],[44,theory(equality)]) ).

cnf(52,negated_conjecture,
    ( element(times(esk3_0,esk3_0))
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[51,20,theory(equality)]),20,theory(equality)]),33,theory(equality)]) ).

cnf(53,negated_conjecture,
    element(times(esk3_0,esk3_0)),
    inference(cn,[status(thm)],[52,theory(equality)]) ).

cnf(67,plain,
    ( element(times(X1,X2))
    | times(X2,times(times(X2,times(X2,times(X1,X1))),X1)) != times(X1,X2) ),
    inference(spm,[status(thm)],[41,20,theory(equality)]) ).

cnf(84,plain,
    ( element(times(X1,X2))
    | times(X2,times(times(X2,times(X1,X1)),times(X1,X2))) != times(X1,X2) ),
    inference(rw,[status(thm)],[67,20,theory(equality)]) ).

cnf(92,plain,
    ( element(times(X1,X2))
    | times(X2,times(times(X1,X1),times(times(X1,X2),X2))) != times(X1,X2) ),
    inference(spm,[status(thm)],[84,20,theory(equality)]) ).

cnf(109,plain,
    ( element(times(X1,X2))
    | times(X2,times(times(X1,X1),times(X2,times(X2,X1)))) != times(X1,X2) ),
    inference(rw,[status(thm)],[92,20,theory(equality)]) ).

cnf(139,negated_conjecture,
    times(esk2_0,X1) = times(esk2_0,times(times(X1,esk2_0),esk2_0)),
    inference(spm,[status(thm)],[20,34,theory(equality)]) ).

cnf(155,negated_conjecture,
    times(esk2_0,X1) = times(esk2_0,times(esk2_0,times(esk2_0,X1))),
    inference(rw,[status(thm)],[139,20,theory(equality)]) ).

cnf(181,negated_conjecture,
    times(esk3_0,X1) = times(esk3_0,times(times(X1,esk3_0),esk3_0)),
    inference(spm,[status(thm)],[20,35,theory(equality)]) ).

cnf(197,negated_conjecture,
    times(esk3_0,X1) = times(esk3_0,times(esk3_0,times(esk3_0,X1))),
    inference(rw,[status(thm)],[181,20,theory(equality)]) ).

cnf(323,negated_conjecture,
    times(esk2_0,X1) = times(esk2_0,times(X1,times(esk2_0,esk2_0))),
    inference(spm,[status(thm)],[22,32,theory(equality)]) ).

cnf(326,negated_conjecture,
    times(esk3_0,X1) = times(esk3_0,times(X1,times(esk3_0,esk3_0))),
    inference(spm,[status(thm)],[22,33,theory(equality)]) ).

cnf(525,negated_conjecture,
    ( times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = times(times(esk2_0,esk2_0),esk2_0)
    | ~ element(times(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[28,32,theory(equality)]) ).

cnf(526,negated_conjecture,
    ( times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = times(times(esk3_0,esk3_0),esk3_0)
    | ~ element(times(esk3_0,esk3_0)) ),
    inference(spm,[status(thm)],[28,33,theory(equality)]) ).

cnf(561,negated_conjecture,
    ( times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = esk2_0
    | ~ element(times(esk2_0,esk2_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[525,20,theory(equality)]),32,theory(equality)]) ).

cnf(562,negated_conjecture,
    ( times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = esk2_0
    | $false ),
    inference(rw,[status(thm)],[561,50,theory(equality)]) ).

cnf(563,negated_conjecture,
    times(esk1_1(times(esk2_0,esk2_0)),esk2_0) = esk2_0,
    inference(cn,[status(thm)],[562,theory(equality)]) ).

cnf(564,negated_conjecture,
    ( times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = esk3_0
    | ~ element(times(esk3_0,esk3_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[526,20,theory(equality)]),33,theory(equality)]) ).

cnf(565,negated_conjecture,
    ( times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = esk3_0
    | $false ),
    inference(rw,[status(thm)],[564,53,theory(equality)]) ).

cnf(566,negated_conjecture,
    times(esk1_1(times(esk3_0,esk3_0)),esk3_0) = esk3_0,
    inference(cn,[status(thm)],[565,theory(equality)]) ).

cnf(1217,negated_conjecture,
    ( times(esk1_1(esk2_0),esk2_0) = times(esk2_0,esk1_1(times(esk2_0,esk2_0)))
    | ~ element(esk2_0) ),
    inference(spm,[status(thm)],[28,563,theory(equality)]) ).

cnf(1235,negated_conjecture,
    ( times(esk1_1(esk2_0),esk2_0) = times(esk2_0,esk1_1(times(esk2_0,esk2_0)))
    | $false ),
    inference(rw,[status(thm)],[1217,18,theory(equality)]) ).

cnf(1236,negated_conjecture,
    times(esk1_1(esk2_0),esk2_0) = times(esk2_0,esk1_1(times(esk2_0,esk2_0))),
    inference(cn,[status(thm)],[1235,theory(equality)]) ).

cnf(1254,negated_conjecture,
    ( times(esk1_1(esk3_0),esk3_0) = times(esk3_0,esk1_1(times(esk3_0,esk3_0)))
    | ~ element(esk3_0) ),
    inference(spm,[status(thm)],[28,566,theory(equality)]) ).

cnf(1271,negated_conjecture,
    ( times(esk1_1(esk3_0),esk3_0) = times(esk3_0,esk1_1(times(esk3_0,esk3_0)))
    | $false ),
    inference(rw,[status(thm)],[1254,17,theory(equality)]) ).

cnf(1272,negated_conjecture,
    times(esk1_1(esk3_0),esk3_0) = times(esk3_0,esk1_1(times(esk3_0,esk3_0))),
    inference(cn,[status(thm)],[1271,theory(equality)]) ).

cnf(1387,plain,
    ( element(times(X1,X2))
    | times(times(X2,X2),times(times(X2,X1),times(X1,X1))) != times(X1,X2) ),
    inference(spm,[status(thm)],[109,23,theory(equality)]) ).

cnf(1449,plain,
    ( element(times(X1,X2))
    | times(times(X2,X2),times(X1,times(X1,times(X2,X1)))) != times(X1,X2) ),
    inference(rw,[status(thm)],[1387,23,theory(equality)]) ).

cnf(1609,negated_conjecture,
    ( times(esk2_0,times(times(esk2_0,esk2_0),times(esk2_0,esk2_0))) = times(esk1_1(esk2_0),esk2_0)
    | ~ element(times(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[1236,10,theory(equality)]) ).

cnf(1621,negated_conjecture,
    ( esk2_0 = times(esk1_1(esk2_0),esk2_0)
    | ~ element(times(esk2_0,esk2_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1609,20,theory(equality)]),20,theory(equality)]),32,theory(equality)]),32,theory(equality)]) ).

cnf(1622,negated_conjecture,
    ( esk2_0 = times(esk1_1(esk2_0),esk2_0)
    | $false ),
    inference(rw,[status(thm)],[1621,50,theory(equality)]) ).

cnf(1623,negated_conjecture,
    esk2_0 = times(esk1_1(esk2_0),esk2_0),
    inference(cn,[status(thm)],[1622,theory(equality)]) ).

cnf(1649,negated_conjecture,
    times(times(esk2_0,X1),esk1_1(esk2_0)) = times(X1,esk2_0),
    inference(spm,[status(thm)],[20,1623,theory(equality)]) ).

cnf(1788,negated_conjecture,
    times(times(esk2_0,X1),esk1_1(esk2_0)) = times(times(X1,times(esk2_0,esk2_0)),esk2_0),
    inference(spm,[status(thm)],[1649,323,theory(equality)]) ).

cnf(1819,negated_conjecture,
    times(X1,esk2_0) = times(times(X1,times(esk2_0,esk2_0)),esk2_0),
    inference(rw,[status(thm)],[1788,1649,theory(equality)]) ).

cnf(1820,negated_conjecture,
    times(X1,esk2_0) = times(esk2_0,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[1819,22,theory(equality)]),155,theory(equality)]) ).

cnf(2070,negated_conjecture,
    ( times(esk3_0,times(times(esk3_0,esk3_0),times(esk3_0,esk3_0))) = times(esk1_1(esk3_0),esk3_0)
    | ~ element(times(esk3_0,esk3_0)) ),
    inference(spm,[status(thm)],[1272,10,theory(equality)]) ).

cnf(2084,negated_conjecture,
    ( esk3_0 = times(esk1_1(esk3_0),esk3_0)
    | ~ element(times(esk3_0,esk3_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[2070,20,theory(equality)]),20,theory(equality)]),33,theory(equality)]),33,theory(equality)]) ).

cnf(2085,negated_conjecture,
    ( esk3_0 = times(esk1_1(esk3_0),esk3_0)
    | $false ),
    inference(rw,[status(thm)],[2084,53,theory(equality)]) ).

cnf(2086,negated_conjecture,
    esk3_0 = times(esk1_1(esk3_0),esk3_0),
    inference(cn,[status(thm)],[2085,theory(equality)]) ).

cnf(2111,negated_conjecture,
    times(times(esk3_0,X1),esk1_1(esk3_0)) = times(X1,esk3_0),
    inference(spm,[status(thm)],[20,2086,theory(equality)]) ).

cnf(2440,negated_conjecture,
    ( element(times(esk2_0,X1))
    | times(times(X1,X1),times(esk2_0,times(esk2_0,times(esk2_0,X1)))) != times(esk2_0,X1) ),
    inference(spm,[status(thm)],[1449,1820,theory(equality)]) ).

cnf(2447,negated_conjecture,
    ~ element(times(esk3_0,esk2_0)),
    inference(rw,[status(thm)],[16,1820,theory(equality)]) ).

cnf(2485,negated_conjecture,
    ( element(times(esk2_0,X1))
    | times(X1,times(X1,times(X1,esk2_0))) != times(esk2_0,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2440,155,theory(equality)]),23,theory(equality)]) ).

cnf(2586,negated_conjecture,
    times(times(esk3_0,X1),esk1_1(esk3_0)) = times(times(X1,times(esk3_0,esk3_0)),esk3_0),
    inference(spm,[status(thm)],[2111,326,theory(equality)]) ).

cnf(2624,negated_conjecture,
    times(X1,esk3_0) = times(times(X1,times(esk3_0,esk3_0)),esk3_0),
    inference(rw,[status(thm)],[2586,2111,theory(equality)]) ).

cnf(2625,negated_conjecture,
    times(X1,esk3_0) = times(esk3_0,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[2624,22,theory(equality)]),197,theory(equality)]) ).

cnf(3003,negated_conjecture,
    ( element(times(esk3_0,esk2_0))
    | times(esk3_0,times(esk3_0,times(esk3_0,esk2_0))) != times(esk3_0,esk2_0) ),
    inference(spm,[status(thm)],[2485,2625,theory(equality)]) ).

cnf(3015,negated_conjecture,
    ( element(times(esk3_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[3003,197,theory(equality)]) ).

cnf(3016,negated_conjecture,
    element(times(esk3_0,esk2_0)),
    inference(cn,[status(thm)],[3015,theory(equality)]) ).

cnf(3017,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[3016,2447,theory(equality)]) ).

cnf(3018,negated_conjecture,
    $false,
    3017,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/ALG/ALG210+1.p
% --creating new selector for []
% -running prover on /tmp/tmpcveeQI/sel_ALG210+1.p_1 with time limit 29
% -prover status Theorem
% Problem ALG210+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/ALG/ALG210+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/ALG/ALG210+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------