TSTP Solution File: GEO093+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO093+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 08:05:21 EST 2010

% Result   : Theorem 11.63s
% Output   : CNFRefutation 11.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   60 (  12 unt;   0 def)
%            Number of atoms       :  229 (  34 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  252 (  83   ~; 108   |;  54   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  133 (   9 sgn  56   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X2,X3] :
      ( part_of(X3,X2)
    <=> ! [X1] :
          ( incident_c(X1,X3)
         => incident_c(X1,X2) ) ),
    file('/tmp/tmpd7R2iT/sel_GEO093+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/tmpd7R2iT/sel_GEO093+1.p_1',sum_defn) ).

fof(8,axiom,
    ! [X2,X3] :
      ( ( part_of(X3,X2)
        & X3 != X2 )
     => open(X3) ),
    file('/tmp/tmpd7R2iT/sel_GEO093+1.p_1',c1) ).

fof(12,conjecture,
    ! [X2,X3,X4,X1] :
      ( ( open(X2)
        & part_of(X3,X2)
        & part_of(X4,X2)
        & meet(X1,X3,X4) )
     => open(sum(X3,X4)) ),
    file('/tmp/tmpd7R2iT/sel_GEO093+1.p_1',proposition_2_14_2) ).

fof(13,negated_conjecture,
    ~ ! [X2,X3,X4,X1] :
        ( ( open(X2)
          & part_of(X3,X2)
          & part_of(X4,X2)
          & meet(X1,X3,X4) )
       => open(sum(X3,X4)) ),
    inference(assume_negation,[status(cth)],[12]) ).

fof(27,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(28,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)],[27]) ).

fof(29,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)],[28]) ).

fof(30,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)],[29]) ).

fof(31,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)],[30]) ).

cnf(32,plain,
    ( part_of(X1,X2)
    | ~ incident_c(esk3_2(X2,X1),X2) ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(33,plain,
    ( part_of(X1,X2)
    | incident_c(esk3_2(X2,X1),X1) ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(34,plain,
    ( incident_c(X3,X2)
    | ~ part_of(X1,X2)
    | ~ incident_c(X3,X1) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(46,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(47,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)],[46]) ).

fof(48,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)],[47]) ).

fof(49,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)],[48]) ).

fof(50,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)],[49]) ).

cnf(51,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)],[50]) ).

cnf(53,plain,
    ( X1 = sum(X2,X3)
    | ~ incident_c(esk6_3(X1,X2,X3),X1)
    | ~ incident_c(esk6_3(X1,X2,X3),X2) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(54,plain,
    ( incident_c(X4,X1)
    | X1 != sum(X2,X3)
    | ~ incident_c(X4,X3) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(55,plain,
    ( incident_c(X4,X1)
    | X1 != sum(X2,X3)
    | ~ incident_c(X4,X2) ),
    inference(split_conjunct,[status(thm)],[50]) ).

cnf(56,plain,
    ( incident_c(X4,X3)
    | incident_c(X4,X2)
    | X1 != sum(X2,X3)
    | ~ incident_c(X4,X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(73,plain,
    ! [X2,X3] :
      ( ~ part_of(X3,X2)
      | X3 = X2
      | open(X3) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(74,plain,
    ! [X4,X5] :
      ( ~ part_of(X5,X4)
      | X5 = X4
      | open(X5) ),
    inference(variable_rename,[status(thm)],[73]) ).

cnf(75,plain,
    ( open(X1)
    | X1 = X2
    | ~ part_of(X1,X2) ),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(91,negated_conjecture,
    ? [X2,X3,X4,X1] :
      ( open(X2)
      & part_of(X3,X2)
      & part_of(X4,X2)
      & meet(X1,X3,X4)
      & ~ open(sum(X3,X4)) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(92,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( open(X5)
      & part_of(X6,X5)
      & part_of(X7,X5)
      & meet(X8,X6,X7)
      & ~ open(sum(X6,X7)) ),
    inference(variable_rename,[status(thm)],[91]) ).

fof(93,negated_conjecture,
    ( open(esk10_0)
    & part_of(esk11_0,esk10_0)
    & part_of(esk12_0,esk10_0)
    & meet(esk13_0,esk11_0,esk12_0)
    & ~ open(sum(esk11_0,esk12_0)) ),
    inference(skolemize,[status(esa)],[92]) ).

cnf(94,negated_conjecture,
    ~ open(sum(esk11_0,esk12_0)),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(96,negated_conjecture,
    part_of(esk12_0,esk10_0),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(97,negated_conjecture,
    part_of(esk11_0,esk10_0),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(98,negated_conjecture,
    open(esk10_0),
    inference(split_conjunct,[status(thm)],[93]) ).

cnf(107,negated_conjecture,
    ( incident_c(X1,esk10_0)
    | ~ incident_c(X1,esk11_0) ),
    inference(spm,[status(thm)],[34,97,theory(equality)]) ).

cnf(108,negated_conjecture,
    ( incident_c(X1,esk10_0)
    | ~ incident_c(X1,esk12_0) ),
    inference(spm,[status(thm)],[34,96,theory(equality)]) ).

cnf(111,plain,
    ( incident_c(X1,sum(X2,X3))
    | ~ incident_c(X1,X3) ),
    inference(er,[status(thm)],[54,theory(equality)]) ).

cnf(112,plain,
    ( incident_c(X1,sum(X2,X3))
    | ~ incident_c(X1,X2) ),
    inference(er,[status(thm)],[55,theory(equality)]) ).

cnf(124,plain,
    ( incident_c(X1,X2)
    | incident_c(X1,X3)
    | ~ incident_c(X1,sum(X2,X3)) ),
    inference(er,[status(thm)],[56,theory(equality)]) ).

cnf(132,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)],[51,theory(equality)]) ).

cnf(149,negated_conjecture,
    ( part_of(X1,esk10_0)
    | ~ incident_c(esk3_2(esk10_0,X1),esk11_0) ),
    inference(spm,[status(thm)],[32,107,theory(equality)]) ).

cnf(171,plain,
    ( part_of(X1,sum(X2,X3))
    | ~ incident_c(esk3_2(sum(X2,X3),X1),X3) ),
    inference(spm,[status(thm)],[32,111,theory(equality)]) ).

cnf(241,plain,
    part_of(X1,sum(X2,X1)),
    inference(spm,[status(thm)],[171,33,theory(equality)]) ).

cnf(249,plain,
    ( X1 = sum(X2,X1)
    | open(X1) ),
    inference(spm,[status(thm)],[75,241,theory(equality)]) ).

cnf(253,negated_conjecture,
    sum(X1,sum(esk11_0,esk12_0)) = sum(esk11_0,esk12_0),
    inference(spm,[status(thm)],[94,249,theory(equality)]) ).

cnf(293,negated_conjecture,
    ( incident_c(X1,sum(esk11_0,esk12_0))
    | ~ incident_c(X1,X2) ),
    inference(spm,[status(thm)],[112,253,theory(equality)]) ).

cnf(301,negated_conjecture,
    ( incident_c(esk3_2(X1,X2),sum(esk11_0,esk12_0))
    | part_of(X2,X1) ),
    inference(spm,[status(thm)],[293,33,theory(equality)]) ).

cnf(341,negated_conjecture,
    ( incident_c(esk3_2(X1,X2),esk12_0)
    | incident_c(esk3_2(X1,X2),esk11_0)
    | part_of(X2,X1) ),
    inference(spm,[status(thm)],[124,301,theory(equality)]) ).

cnf(1031,plain,
    ( sum(X1,X2) = X1
    | incident_c(esk6_3(X1,X1,X2),X2)
    | ~ incident_c(esk6_3(X1,X1,X2),X1) ),
    inference(spm,[status(thm)],[53,132,theory(equality)]) ).

cnf(8500,negated_conjecture,
    ( part_of(X1,sum(X2,esk12_0))
    | incident_c(esk3_2(sum(X2,esk12_0),X1),esk11_0) ),
    inference(spm,[status(thm)],[171,341,theory(equality)]) ).

cnf(51652,plain,
    ( sum(X1,X2) = X1
    | incident_c(esk6_3(X1,X1,X2),X2) ),
    inference(csr,[status(thm)],[1031,132]) ).

cnf(51656,negated_conjecture,
    ( incident_c(esk6_3(X1,X1,esk12_0),esk10_0)
    | sum(X1,esk12_0) = X1 ),
    inference(spm,[status(thm)],[108,51652,theory(equality)]) ).

cnf(62865,negated_conjecture,
    ( sum(esk10_0,esk12_0) = esk10_0
    | ~ incident_c(esk6_3(esk10_0,esk10_0,esk12_0),esk10_0) ),
    inference(spm,[status(thm)],[53,51656,theory(equality)]) ).

cnf(186855,negated_conjecture,
    sum(esk10_0,esk12_0) = esk10_0,
    inference(csr,[status(thm)],[62865,51656]) ).

cnf(186946,negated_conjecture,
    ( part_of(X1,esk10_0)
    | incident_c(esk3_2(esk10_0,X1),esk11_0) ),
    inference(spm,[status(thm)],[8500,186855,theory(equality)]) ).

cnf(187959,negated_conjecture,
    part_of(X1,esk10_0),
    inference(csr,[status(thm)],[186946,149]) ).

cnf(187960,negated_conjecture,
    ( X1 = esk10_0
    | open(X1) ),
    inference(spm,[status(thm)],[75,187959,theory(equality)]) ).

cnf(188079,negated_conjecture,
    sum(esk11_0,esk12_0) = esk10_0,
    inference(spm,[status(thm)],[94,187960,theory(equality)]) ).

cnf(188412,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[94,188079,theory(equality)]),98,theory(equality)]) ).

cnf(188413,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[188412,theory(equality)]) ).

cnf(188414,negated_conjecture,
    $false,
    188413,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GEO/GEO093+1.p
% --creating new selector for [GEO004+0.ax]
% -running prover on /tmp/tmpd7R2iT/sel_GEO093+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO093+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO093+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO093+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
% 
%------------------------------------------------------------------------------