TSTP Solution File: GEO084+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO084+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 08:04:21 EST 2010

% Result   : Theorem 0.27s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   51 (   9 unt;   0 def)
%            Number of atoms       :  203 (  23 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  231 (  79   ~;  98   |;  48   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  117 (   6 sgn  50   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X2,X3] :
      ( part_of(X3,X2)
    <=> ! [X1] :
          ( incident_c(X1,X3)
         => incident_c(X1,X2) ) ),
    file('/tmp/tmpktOb6T/sel_GEO084+1.p_1',part_of_defn) ).

fof(5,axiom,
    ! [X2,X3,X4] :
      ( X2 = sum(X3,X4)
    <=> ! [X5] :
          ( incident_c(X5,X2)
        <=> ( incident_c(X5,X3)
            | incident_c(X5,X4) ) ) ),
    file('/tmp/tmpktOb6T/sel_GEO084+1.p_1',sum_defn) ).

fof(10,conjecture,
    ! [X3,X4,X6,X1] :
      ( ( part_of(X3,X6)
        & part_of(X4,X6)
        & meet(X1,X3,X4) )
     => part_of(sum(X3,X4),X6) ),
    file('/tmp/tmpktOb6T/sel_GEO084+1.p_1',corollary_2_6_2) ).

fof(11,negated_conjecture,
    ~ ! [X3,X4,X6,X1] :
        ( ( part_of(X3,X6)
          & part_of(X4,X6)
          & meet(X1,X3,X4) )
       => part_of(sum(X3,X4),X6) ),
    inference(assume_negation,[status(cth)],[10]) ).

fof(25,plain,
    ! [X2,X3] :
      ( ( ~ part_of(X3,X2)
        | ! [X1] :
            ( ~ incident_c(X1,X3)
            | incident_c(X1,X2) ) )
      & ( ? [X1] :
            ( incident_c(X1,X3)
            & ~ incident_c(X1,X2) )
        | part_of(X3,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(26,plain,
    ! [X4,X5] :
      ( ( ~ part_of(X5,X4)
        | ! [X6] :
            ( ~ incident_c(X6,X5)
            | incident_c(X6,X4) ) )
      & ( ? [X7] :
            ( incident_c(X7,X5)
            & ~ incident_c(X7,X4) )
        | part_of(X5,X4) ) ),
    inference(variable_rename,[status(thm)],[25]) ).

fof(27,plain,
    ! [X4,X5] :
      ( ( ~ part_of(X5,X4)
        | ! [X6] :
            ( ~ incident_c(X6,X5)
            | incident_c(X6,X4) ) )
      & ( ( incident_c(esk3_2(X4,X5),X5)
          & ~ incident_c(esk3_2(X4,X5),X4) )
        | part_of(X5,X4) ) ),
    inference(skolemize,[status(esa)],[26]) ).

fof(28,plain,
    ! [X4,X5,X6] :
      ( ( ~ incident_c(X6,X5)
        | incident_c(X6,X4)
        | ~ part_of(X5,X4) )
      & ( ( incident_c(esk3_2(X4,X5),X5)
          & ~ incident_c(esk3_2(X4,X5),X4) )
        | part_of(X5,X4) ) ),
    inference(shift_quantors,[status(thm)],[27]) ).

fof(29,plain,
    ! [X4,X5,X6] :
      ( ( ~ incident_c(X6,X5)
        | incident_c(X6,X4)
        | ~ part_of(X5,X4) )
      & ( incident_c(esk3_2(X4,X5),X5)
        | part_of(X5,X4) )
      & ( ~ incident_c(esk3_2(X4,X5),X4)
        | part_of(X5,X4) ) ),
    inference(distribute,[status(thm)],[28]) ).

cnf(30,plain,
    ( part_of(X1,X2)
    | ~ incident_c(esk3_2(X2,X1),X2) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(31,plain,
    ( part_of(X1,X2)
    | incident_c(esk3_2(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(32,plain,
    ( incident_c(X3,X2)
    | ~ part_of(X1,X2)
    | ~ incident_c(X3,X1) ),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(44,plain,
    ! [X2,X3,X4] :
      ( ( X2 != sum(X3,X4)
        | ! [X5] :
            ( ( ~ incident_c(X5,X2)
              | incident_c(X5,X3)
              | incident_c(X5,X4) )
            & ( ( ~ incident_c(X5,X3)
                & ~ incident_c(X5,X4) )
              | incident_c(X5,X2) ) ) )
      & ( ? [X5] :
            ( ( ~ incident_c(X5,X2)
              | ( ~ incident_c(X5,X3)
                & ~ incident_c(X5,X4) ) )
            & ( incident_c(X5,X2)
              | incident_c(X5,X3)
              | incident_c(X5,X4) ) )
        | X2 = sum(X3,X4) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(45,plain,
    ! [X6,X7,X8] :
      ( ( X6 != sum(X7,X8)
        | ! [X9] :
            ( ( ~ incident_c(X9,X6)
              | incident_c(X9,X7)
              | incident_c(X9,X8) )
            & ( ( ~ incident_c(X9,X7)
                & ~ incident_c(X9,X8) )
              | incident_c(X9,X6) ) ) )
      & ( ? [X10] :
            ( ( ~ incident_c(X10,X6)
              | ( ~ incident_c(X10,X7)
                & ~ incident_c(X10,X8) ) )
            & ( incident_c(X10,X6)
              | incident_c(X10,X7)
              | incident_c(X10,X8) ) )
        | X6 = sum(X7,X8) ) ),
    inference(variable_rename,[status(thm)],[44]) ).

fof(46,plain,
    ! [X6,X7,X8] :
      ( ( X6 != sum(X7,X8)
        | ! [X9] :
            ( ( ~ incident_c(X9,X6)
              | incident_c(X9,X7)
              | incident_c(X9,X8) )
            & ( ( ~ incident_c(X9,X7)
                & ~ incident_c(X9,X8) )
              | incident_c(X9,X6) ) ) )
      & ( ( ( ~ incident_c(esk6_3(X6,X7,X8),X6)
            | ( ~ incident_c(esk6_3(X6,X7,X8),X7)
              & ~ incident_c(esk6_3(X6,X7,X8),X8) ) )
          & ( incident_c(esk6_3(X6,X7,X8),X6)
            | incident_c(esk6_3(X6,X7,X8),X7)
            | incident_c(esk6_3(X6,X7,X8),X8) ) )
        | X6 = sum(X7,X8) ) ),
    inference(skolemize,[status(esa)],[45]) ).

fof(47,plain,
    ! [X6,X7,X8,X9] :
      ( ( ( ( ~ incident_c(X9,X6)
            | incident_c(X9,X7)
            | incident_c(X9,X8) )
          & ( ( ~ incident_c(X9,X7)
              & ~ incident_c(X9,X8) )
            | incident_c(X9,X6) ) )
        | X6 != sum(X7,X8) )
      & ( ( ( ~ incident_c(esk6_3(X6,X7,X8),X6)
            | ( ~ incident_c(esk6_3(X6,X7,X8),X7)
              & ~ incident_c(esk6_3(X6,X7,X8),X8) ) )
          & ( incident_c(esk6_3(X6,X7,X8),X6)
            | incident_c(esk6_3(X6,X7,X8),X7)
            | incident_c(esk6_3(X6,X7,X8),X8) ) )
        | X6 = sum(X7,X8) ) ),
    inference(shift_quantors,[status(thm)],[46]) ).

fof(48,plain,
    ! [X6,X7,X8,X9] :
      ( ( ~ incident_c(X9,X6)
        | incident_c(X9,X7)
        | incident_c(X9,X8)
        | X6 != sum(X7,X8) )
      & ( ~ incident_c(X9,X7)
        | incident_c(X9,X6)
        | X6 != sum(X7,X8) )
      & ( ~ incident_c(X9,X8)
        | incident_c(X9,X6)
        | X6 != sum(X7,X8) )
      & ( ~ incident_c(esk6_3(X6,X7,X8),X7)
        | ~ incident_c(esk6_3(X6,X7,X8),X6)
        | X6 = sum(X7,X8) )
      & ( ~ incident_c(esk6_3(X6,X7,X8),X8)
        | ~ incident_c(esk6_3(X6,X7,X8),X6)
        | X6 = sum(X7,X8) )
      & ( incident_c(esk6_3(X6,X7,X8),X6)
        | incident_c(esk6_3(X6,X7,X8),X7)
        | incident_c(esk6_3(X6,X7,X8),X8)
        | X6 = sum(X7,X8) ) ),
    inference(distribute,[status(thm)],[47]) ).

cnf(49,plain,
    ( X1 = sum(X2,X3)
    | incident_c(esk6_3(X1,X2,X3),X3)
    | incident_c(esk6_3(X1,X2,X3),X2)
    | incident_c(esk6_3(X1,X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,plain,
    ( X1 = sum(X2,X3)
    | ~ incident_c(esk6_3(X1,X2,X3),X1)
    | ~ incident_c(esk6_3(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(52,plain,
    ( incident_c(X4,X1)
    | X1 != sum(X2,X3)
    | ~ incident_c(X4,X3) ),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(54,plain,
    ( incident_c(X4,X3)
    | incident_c(X4,X2)
    | X1 != sum(X2,X3)
    | ~ incident_c(X4,X1) ),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(80,negated_conjecture,
    ? [X3,X4,X6,X1] :
      ( part_of(X3,X6)
      & part_of(X4,X6)
      & meet(X1,X3,X4)
      & ~ part_of(sum(X3,X4),X6) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(81,negated_conjecture,
    ? [X7,X8,X9,X10] :
      ( part_of(X7,X9)
      & part_of(X8,X9)
      & meet(X10,X7,X8)
      & ~ part_of(sum(X7,X8),X9) ),
    inference(variable_rename,[status(thm)],[80]) ).

fof(82,negated_conjecture,
    ( part_of(esk9_0,esk11_0)
    & part_of(esk10_0,esk11_0)
    & meet(esk12_0,esk9_0,esk10_0)
    & ~ part_of(sum(esk9_0,esk10_0),esk11_0) ),
    inference(skolemize,[status(esa)],[81]) ).

cnf(83,negated_conjecture,
    ~ part_of(sum(esk9_0,esk10_0),esk11_0),
    inference(split_conjunct,[status(thm)],[82]) ).

cnf(85,negated_conjecture,
    part_of(esk10_0,esk11_0),
    inference(split_conjunct,[status(thm)],[82]) ).

cnf(86,negated_conjecture,
    part_of(esk9_0,esk11_0),
    inference(split_conjunct,[status(thm)],[82]) ).

cnf(91,negated_conjecture,
    ( incident_c(X1,esk11_0)
    | ~ incident_c(X1,esk9_0) ),
    inference(spm,[status(thm)],[32,86,theory(equality)]) ).

cnf(92,negated_conjecture,
    ( incident_c(X1,esk11_0)
    | ~ incident_c(X1,esk10_0) ),
    inference(spm,[status(thm)],[32,85,theory(equality)]) ).

cnf(94,plain,
    ( incident_c(X1,sum(X2,X3))
    | ~ incident_c(X1,X3) ),
    inference(er,[status(thm)],[52,theory(equality)]) ).

cnf(101,plain,
    ( incident_c(X1,X2)
    | incident_c(X1,X3)
    | ~ incident_c(X1,sum(X2,X3)) ),
    inference(er,[status(thm)],[54,theory(equality)]) ).

cnf(112,plain,
    ( sum(X4,X5) = X4
    | incident_c(esk6_3(X4,X4,X5),X4)
    | incident_c(esk6_3(X4,X4,X5),X5) ),
    inference(ef,[status(thm)],[49,theory(equality)]) ).

cnf(128,negated_conjecture,
    ( incident_c(esk3_2(X1,esk9_0),esk11_0)
    | part_of(esk9_0,X1) ),
    inference(spm,[status(thm)],[91,31,theory(equality)]) ).

cnf(141,negated_conjecture,
    ( incident_c(esk3_2(X1,esk10_0),esk11_0)
    | part_of(esk10_0,X1) ),
    inference(spm,[status(thm)],[92,31,theory(equality)]) ).

cnf(153,plain,
    ( part_of(X1,sum(X2,X3))
    | ~ incident_c(esk3_2(sum(X2,X3),X1),X3) ),
    inference(spm,[status(thm)],[30,94,theory(equality)]) ).

cnf(176,plain,
    ( incident_c(esk3_2(X1,sum(X2,X3)),X3)
    | incident_c(esk3_2(X1,sum(X2,X3)),X2)
    | part_of(sum(X2,X3),X1) ),
    inference(spm,[status(thm)],[101,31,theory(equality)]) ).

cnf(188,negated_conjecture,
    part_of(esk9_0,sum(X1,esk11_0)),
    inference(spm,[status(thm)],[153,128,theory(equality)]) ).

cnf(190,negated_conjecture,
    part_of(esk10_0,sum(X1,esk11_0)),
    inference(spm,[status(thm)],[153,141,theory(equality)]) ).

cnf(203,negated_conjecture,
    ( incident_c(X1,sum(X2,esk11_0))
    | ~ incident_c(X1,esk9_0) ),
    inference(spm,[status(thm)],[32,188,theory(equality)]) ).

cnf(204,negated_conjecture,
    ( incident_c(X1,sum(X2,esk11_0))
    | ~ incident_c(X1,esk10_0) ),
    inference(spm,[status(thm)],[32,190,theory(equality)]) ).

cnf(205,negated_conjecture,
    ( part_of(X1,sum(X2,esk11_0))
    | ~ incident_c(esk3_2(sum(X2,esk11_0),X1),esk9_0) ),
    inference(spm,[status(thm)],[30,203,theory(equality)]) ).

cnf(212,negated_conjecture,
    ( part_of(X1,sum(X2,esk11_0))
    | ~ incident_c(esk3_2(sum(X2,esk11_0),X1),esk10_0) ),
    inference(spm,[status(thm)],[30,204,theory(equality)]) ).

cnf(510,plain,
    ( sum(X3,X3) = X3
    | incident_c(esk6_3(X3,X3,X3),X3) ),
    inference(ef,[status(thm)],[112,theory(equality)]) ).

cnf(534,plain,
    ( sum(X1,X1) = X1
    | ~ incident_c(esk6_3(X1,X1,X1),X1) ),
    inference(spm,[status(thm)],[50,510,theory(equality)]) ).

cnf(592,plain,
    sum(X1,X1) = X1,
    inference(csr,[status(thm)],[534,510]) ).

cnf(608,negated_conjecture,
    ( part_of(X1,esk11_0)
    | ~ incident_c(esk3_2(esk11_0,X1),esk9_0) ),
    inference(spm,[status(thm)],[205,592,theory(equality)]) ).

cnf(612,negated_conjecture,
    ( part_of(X1,esk11_0)
    | ~ incident_c(esk3_2(esk11_0,X1),esk10_0) ),
    inference(spm,[status(thm)],[212,592,theory(equality)]) ).

cnf(680,negated_conjecture,
    ( part_of(sum(esk9_0,X1),esk11_0)
    | incident_c(esk3_2(esk11_0,sum(esk9_0,X1)),X1) ),
    inference(spm,[status(thm)],[608,176,theory(equality)]) ).

cnf(697,negated_conjecture,
    part_of(sum(esk9_0,esk10_0),esk11_0),
    inference(spm,[status(thm)],[612,680,theory(equality)]) ).

cnf(704,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[697,83,theory(equality)]) ).

cnf(705,negated_conjecture,
    $false,
    704,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO084+1.p
% --creating new selector for [GEO004+0.ax]
% -running prover on /tmp/tmpktOb6T/sel_GEO084+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO084+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO084+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO084+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
% 
%------------------------------------------------------------------------------