%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET912+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 : Sun Dec 26 03:46:45 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   31 (  16 unt;   0 def)
%            Number of atoms       :   66 (  19 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   57 (  22   ~;  16   |;  15   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   48 (   0 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmpPG0Y3Z/sel_SET912+1.p_1',commutativity_k3_xboole_0) ).

fof(3,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_intersection2(X1,X2) = X1 ),
    file('/tmp/tmpPG0Y3Z/sel_SET912+1.p_1',t28_xboole_1) ).

fof(5,axiom,
    ! [X1,X2,X3] :
      ( subset(unordered_pair(X1,X2),X3)
    <=> ( in(X1,X3)
        & in(X2,X3) ) ),
    file('/tmp/tmpPG0Y3Z/sel_SET912+1.p_1',t38_zfmisc_1) ).

fof(6,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmpPG0Y3Z/sel_SET912+1.p_1',commutativity_k2_tarski) ).

fof(9,conjecture,
    ! [X1,X2,X3] :
      ( ( in(X1,X2)
        & in(X3,X2) )
     => set_intersection2(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
    file('/tmp/tmpPG0Y3Z/sel_SET912+1.p_1',t53_zfmisc_1) ).

fof(11,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( in(X1,X2)
          & in(X3,X2) )
       => set_intersection2(unordered_pair(X1,X3),X2) = unordered_pair(X1,X3) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(14,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(15,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(18,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | set_intersection2(X1,X2) = X1 ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(19,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | set_intersection2(X3,X4) = X3 ),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(20,plain,
    ( set_intersection2(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(24,plain,
    ! [X1,X2,X3] :
      ( ( ~ subset(unordered_pair(X1,X2),X3)
        | ( in(X1,X3)
          & in(X2,X3) ) )
      & ( ~ in(X1,X3)
        | ~ in(X2,X3)
        | subset(unordered_pair(X1,X2),X3) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(25,plain,
    ! [X4,X5,X6] :
      ( ( ~ subset(unordered_pair(X4,X5),X6)
        | ( in(X4,X6)
          & in(X5,X6) ) )
      & ( ~ in(X4,X6)
        | ~ in(X5,X6)
        | subset(unordered_pair(X4,X5),X6) ) ),
    inference(variable_rename,[status(thm)],[24]) ).

fof(26,plain,
    ! [X4,X5,X6] :
      ( ( in(X4,X6)
        | ~ subset(unordered_pair(X4,X5),X6) )
      & ( in(X5,X6)
        | ~ subset(unordered_pair(X4,X5),X6) )
      & ( ~ in(X4,X6)
        | ~ in(X5,X6)
        | subset(unordered_pair(X4,X5),X6) ) ),
    inference(distribute,[status(thm)],[25]) ).

cnf(27,plain,
    ( subset(unordered_pair(X1,X2),X3)
    | ~ in(X2,X3)
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(30,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(31,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[30]) ).

fof(38,negated_conjecture,
    ? [X1,X2,X3] :
      ( in(X1,X2)
      & in(X3,X2)
      & set_intersection2(unordered_pair(X1,X3),X2) != unordered_pair(X1,X3) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(39,negated_conjecture,
    ? [X4,X5,X6] :
      ( in(X4,X5)
      & in(X6,X5)
      & set_intersection2(unordered_pair(X4,X6),X5) != unordered_pair(X4,X6) ),
    inference(variable_rename,[status(thm)],[38]) ).

fof(40,negated_conjecture,
    ( in(esk3_0,esk4_0)
    & in(esk5_0,esk4_0)
    & set_intersection2(unordered_pair(esk3_0,esk5_0),esk4_0) != unordered_pair(esk3_0,esk5_0) ),
    inference(skolemize,[status(esa)],[39]) ).

cnf(41,negated_conjecture,
    set_intersection2(unordered_pair(esk3_0,esk5_0),esk4_0) != unordered_pair(esk3_0,esk5_0),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(42,negated_conjecture,
    in(esk5_0,esk4_0),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(43,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[40]) ).

cnf(54,negated_conjecture,
    set_intersection2(esk4_0,unordered_pair(esk3_0,esk5_0)) != unordered_pair(esk3_0,esk5_0),
    inference(rw,[status(thm)],[41,15,theory(equality)]) ).

cnf(61,negated_conjecture,
    ( subset(unordered_pair(X1,esk3_0),esk4_0)
    | ~ in(X1,esk4_0) ),
    inference(spm,[status(thm)],[27,43,theory(equality)]) ).

cnf(80,negated_conjecture,
    subset(unordered_pair(esk5_0,esk3_0),esk4_0),
    inference(spm,[status(thm)],[61,42,theory(equality)]) ).

cnf(81,negated_conjecture,
    subset(unordered_pair(esk3_0,esk5_0),esk4_0),
    inference(rw,[status(thm)],[80,31,theory(equality)]) ).

cnf(92,negated_conjecture,
    set_intersection2(unordered_pair(esk3_0,esk5_0),esk4_0) = unordered_pair(esk3_0,esk5_0),
    inference(spm,[status(thm)],[20,81,theory(equality)]) ).

cnf(95,negated_conjecture,
    set_intersection2(esk4_0,unordered_pair(esk3_0,esk5_0)) = unordered_pair(esk3_0,esk5_0),
    inference(rw,[status(thm)],[92,15,theory(equality)]) ).

cnf(96,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[95,54,theory(equality)]) ).

cnf(97,negated_conjecture,
    $false,
    96,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET912+1.p
% --creating new selector for []
% -running prover on /tmp/tmpPG0Y3Z/sel_SET912+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET912+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET912+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET912+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
% 
%------------------------------------------------------------------------------