TSTP Solution File: SET676+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET676+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 03:10:15 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   30 (   9 unt;   0 def)
%            Number of atoms       :   84 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   93 (  39   ~;  40   |;   7   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (   1 sgn  22   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
    file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',p1) ).

fof(6,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ( ilf_type(X2,identity_relation_of_type(X1))
          <=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
    file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',p4) ).

fof(8,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) ),
    file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',prove_relset_1_41) ).

fof(20,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/tmp/tmpVuwnwk/sel_SET676+3.p_1',p19) ).

fof(21,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(41,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ilf_type(cross_product(X1,X2),relation_type(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(42,plain,
    ! [X3] :
      ( ~ ilf_type(X3,set_type)
      | ! [X4] :
          ( ~ ilf_type(X4,set_type)
          | ilf_type(cross_product(X3,X4),relation_type(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[41]) ).

fof(43,plain,
    ! [X3,X4] :
      ( ~ ilf_type(X4,set_type)
      | ilf_type(cross_product(X3,X4),relation_type(X3,X4))
      | ~ ilf_type(X3,set_type) ),
    inference(shift_quantors,[status(thm)],[42]) ).

cnf(44,plain,
    ( ilf_type(cross_product(X1,X2),relation_type(X1,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(55,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ( ( ~ ilf_type(X2,identity_relation_of_type(X1))
              | ilf_type(X2,relation_type(X1,X1)) )
            & ( ~ ilf_type(X2,relation_type(X1,X1))
              | ilf_type(X2,identity_relation_of_type(X1)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(56,plain,
    ! [X3] :
      ( ~ ilf_type(X3,set_type)
      | ! [X4] :
          ( ~ ilf_type(X4,set_type)
          | ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
              | ilf_type(X4,relation_type(X3,X3)) )
            & ( ~ ilf_type(X4,relation_type(X3,X3))
              | ilf_type(X4,identity_relation_of_type(X3)) ) ) ) ),
    inference(variable_rename,[status(thm)],[55]) ).

fof(57,plain,
    ! [X3,X4] :
      ( ~ ilf_type(X4,set_type)
      | ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
          | ilf_type(X4,relation_type(X3,X3)) )
        & ( ~ ilf_type(X4,relation_type(X3,X3))
          | ilf_type(X4,identity_relation_of_type(X3)) ) )
      | ~ ilf_type(X3,set_type) ),
    inference(shift_quantors,[status(thm)],[56]) ).

fof(58,plain,
    ! [X3,X4] :
      ( ( ~ ilf_type(X4,identity_relation_of_type(X3))
        | ilf_type(X4,relation_type(X3,X3))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) )
      & ( ~ ilf_type(X4,relation_type(X3,X3))
        | ilf_type(X4,identity_relation_of_type(X3))
        | ~ ilf_type(X4,set_type)
        | ~ ilf_type(X3,set_type) ) ),
    inference(distribute,[status(thm)],[57]) ).

cnf(59,plain,
    ( ilf_type(X2,identity_relation_of_type(X1))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X2,relation_type(X1,X1)) ),
    inference(split_conjunct,[status(thm)],[58]) ).

fof(65,negated_conjecture,
    ? [X1] :
      ( ilf_type(X1,set_type)
      & ~ ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(66,negated_conjecture,
    ? [X2] :
      ( ilf_type(X2,set_type)
      & ~ ilf_type(cross_product(X2,X2),identity_relation_of_type(X2)) ),
    inference(variable_rename,[status(thm)],[65]) ).

fof(67,negated_conjecture,
    ( ilf_type(esk4_0,set_type)
    & ~ ilf_type(cross_product(esk4_0,esk4_0),identity_relation_of_type(esk4_0)) ),
    inference(skolemize,[status(esa)],[66]) ).

cnf(68,negated_conjecture,
    ~ ilf_type(cross_product(esk4_0,esk4_0),identity_relation_of_type(esk4_0)),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(135,plain,
    ! [X2] : ilf_type(X2,set_type),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(136,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(165,plain,
    ( ilf_type(cross_product(X1,X2),relation_type(X1,X2))
    | $false
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[44,136,theory(equality)]) ).

cnf(166,plain,
    ( ilf_type(cross_product(X1,X2),relation_type(X1,X2))
    | $false
    | $false ),
    inference(rw,[status(thm)],[165,136,theory(equality)]) ).

cnf(167,plain,
    ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
    inference(cn,[status(thm)],[166,theory(equality)]) ).

cnf(188,plain,
    ( ilf_type(X2,identity_relation_of_type(X1))
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,relation_type(X1,X1)) ),
    inference(rw,[status(thm)],[59,136,theory(equality)]) ).

cnf(189,plain,
    ( ilf_type(X2,identity_relation_of_type(X1))
    | $false
    | $false
    | ~ ilf_type(X2,relation_type(X1,X1)) ),
    inference(rw,[status(thm)],[188,136,theory(equality)]) ).

cnf(190,plain,
    ( ilf_type(X2,identity_relation_of_type(X1))
    | ~ ilf_type(X2,relation_type(X1,X1)) ),
    inference(cn,[status(thm)],[189,theory(equality)]) ).

cnf(191,plain,
    ilf_type(cross_product(X1,X1),identity_relation_of_type(X1)),
    inference(spm,[status(thm)],[190,167,theory(equality)]) ).

cnf(298,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[68,191,theory(equality)]) ).

cnf(299,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[298,theory(equality)]) ).

cnf(300,negated_conjecture,
    $false,
    299,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET676+3.p
% --creating new selector for []
% -running prover on /tmp/tmpVuwnwk/sel_SET676+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET676+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET676+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET676+3.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
% 
%------------------------------------------------------------------------------