TSTP Solution File: SEU263+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU263+1 : TPTP v5.0.0. Released v3.3.0.
% 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 : Sun Dec 26 06:27:47 EST 2010

% Result   : Theorem 0.92s
% Output   : CNFRefutation 0.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   54 (   9 unt;   0 def)
%            Number of atoms       :  131 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  130 (  53   ~;  49   |;  16   &)
%                                         (   2 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  128 (   5 sgn  80   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => element(X3,powerset(cartesian_product2(X1,X2))) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',dt_m2_relset_1) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
    <=> relation_of2(X3,X1,X2) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',redefinition_m2_relset_1) ).

fof(4,axiom,
    ! [X1,X2,X3,X4] :
      ( ( subset(X1,X2)
        & subset(X3,X4) )
     => subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t119_zfmisc_1) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( element(X3,powerset(cartesian_product2(X1,X2)))
     => relation(X3) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',cc1_relset_1) ).

fof(7,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t1_xboole_1) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( relation_of2(X3,X1,X2)
    <=> subset(X3,cartesian_product2(X1,X2)) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',d1_relset_1) ).

fof(9,axiom,
    ! [X1] :
      ( relation(X1)
     => subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t21_relat_1) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( relation_of2_as_subset(X3,X1,X2)
     => ( subset(relation_dom(X3),X1)
        & subset(relation_rng(X3),X2) ) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t12_relset_1) ).

fof(19,conjecture,
    ! [X1,X2,X3,X4] :
      ( relation_of2_as_subset(X4,X3,X1)
     => ( subset(relation_rng(X4),X2)
       => relation_of2_as_subset(X4,X3,X2) ) ),
    file('/tmp/tmpPO6-YU/sel_SEU263+1.p_1',t14_relset_1) ).

fof(21,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( relation_of2_as_subset(X4,X3,X1)
       => ( subset(relation_rng(X4),X2)
         => relation_of2_as_subset(X4,X3,X2) ) ),
    inference(assume_negation,[status(cth)],[19]) ).

fof(22,plain,
    ! [X1,X2,X3] :
      ( ~ relation_of2_as_subset(X3,X1,X2)
      | element(X3,powerset(cartesian_product2(X1,X2))) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ~ relation_of2_as_subset(X6,X4,X5)
      | element(X6,powerset(cartesian_product2(X4,X5))) ),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(24,plain,
    ( element(X1,powerset(cartesian_product2(X2,X3)))
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(25,plain,
    ! [X1,X2,X3] :
      ( ( ~ relation_of2_as_subset(X3,X1,X2)
        | relation_of2(X3,X1,X2) )
      & ( ~ relation_of2(X3,X1,X2)
        | relation_of2_as_subset(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(26,plain,
    ! [X4,X5,X6] :
      ( ( ~ relation_of2_as_subset(X6,X4,X5)
        | relation_of2(X6,X4,X5) )
      & ( ~ relation_of2(X6,X4,X5)
        | relation_of2_as_subset(X6,X4,X5) ) ),
    inference(variable_rename,[status(thm)],[25]) ).

cnf(27,plain,
    ( relation_of2_as_subset(X1,X2,X3)
    | ~ relation_of2(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(32,plain,
    ! [X1,X2,X3,X4] :
      ( ~ subset(X1,X2)
      | ~ subset(X3,X4)
      | subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(33,plain,
    ! [X5,X6,X7,X8] :
      ( ~ subset(X5,X6)
      | ~ subset(X7,X8)
      | subset(cartesian_product2(X5,X7),cartesian_product2(X6,X8)) ),
    inference(variable_rename,[status(thm)],[32]) ).

cnf(34,plain,
    ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
    | ~ subset(X2,X4)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[33]) ).

fof(38,plain,
    ! [X1,X2,X3] :
      ( ~ element(X3,powerset(cartesian_product2(X1,X2)))
      | relation(X3) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(39,plain,
    ! [X4,X5,X6] :
      ( ~ element(X6,powerset(cartesian_product2(X4,X5)))
      | relation(X6) ),
    inference(variable_rename,[status(thm)],[38]) ).

cnf(40,plain,
    ( relation(X1)
    | ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(41,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X2,X3)
      | subset(X1,X3) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(42,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6) ),
    inference(variable_rename,[status(thm)],[41]) ).

cnf(43,plain,
    ( subset(X1,X2)
    | ~ subset(X3,X2)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[42]) ).

fof(44,plain,
    ! [X1,X2,X3] :
      ( ( ~ relation_of2(X3,X1,X2)
        | subset(X3,cartesian_product2(X1,X2)) )
      & ( ~ subset(X3,cartesian_product2(X1,X2))
        | relation_of2(X3,X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(45,plain,
    ! [X4,X5,X6] :
      ( ( ~ relation_of2(X6,X4,X5)
        | subset(X6,cartesian_product2(X4,X5)) )
      & ( ~ subset(X6,cartesian_product2(X4,X5))
        | relation_of2(X6,X4,X5) ) ),
    inference(variable_rename,[status(thm)],[44]) ).

cnf(46,plain,
    ( relation_of2(X1,X2,X3)
    | ~ subset(X1,cartesian_product2(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(48,plain,
    ! [X1] :
      ( ~ relation(X1)
      | subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1))) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(49,plain,
    ! [X2] :
      ( ~ relation(X2)
      | subset(X2,cartesian_product2(relation_dom(X2),relation_rng(X2))) ),
    inference(variable_rename,[status(thm)],[48]) ).

cnf(50,plain,
    ( subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[49]) ).

fof(56,plain,
    ! [X1,X2,X3] :
      ( ~ relation_of2_as_subset(X3,X1,X2)
      | ( subset(relation_dom(X3),X1)
        & subset(relation_rng(X3),X2) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(57,plain,
    ! [X4,X5,X6] :
      ( ~ relation_of2_as_subset(X6,X4,X5)
      | ( subset(relation_dom(X6),X4)
        & subset(relation_rng(X6),X5) ) ),
    inference(variable_rename,[status(thm)],[56]) ).

fof(58,plain,
    ! [X4,X5,X6] :
      ( ( subset(relation_dom(X6),X4)
        | ~ relation_of2_as_subset(X6,X4,X5) )
      & ( subset(relation_rng(X6),X5)
        | ~ relation_of2_as_subset(X6,X4,X5) ) ),
    inference(distribute,[status(thm)],[57]) ).

cnf(60,plain,
    ( subset(relation_dom(X1),X2)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[58]) ).

fof(70,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( relation_of2_as_subset(X4,X3,X1)
      & subset(relation_rng(X4),X2)
      & ~ relation_of2_as_subset(X4,X3,X2) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(71,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( relation_of2_as_subset(X8,X7,X5)
      & subset(relation_rng(X8),X6)
      & ~ relation_of2_as_subset(X8,X7,X6) ),
    inference(variable_rename,[status(thm)],[70]) ).

fof(72,negated_conjecture,
    ( relation_of2_as_subset(esk7_0,esk6_0,esk4_0)
    & subset(relation_rng(esk7_0),esk5_0)
    & ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0) ),
    inference(skolemize,[status(esa)],[71]) ).

cnf(73,negated_conjecture,
    ~ relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(74,negated_conjecture,
    subset(relation_rng(esk7_0),esk5_0),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(75,negated_conjecture,
    relation_of2_as_subset(esk7_0,esk6_0,esk4_0),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(81,negated_conjecture,
    subset(relation_dom(esk7_0),esk6_0),
    inference(spm,[status(thm)],[60,75,theory(equality)]) ).

cnf(94,plain,
    ( relation_of2_as_subset(X1,X2,X3)
    | ~ subset(X1,cartesian_product2(X2,X3)) ),
    inference(spm,[status(thm)],[27,46,theory(equality)]) ).

cnf(102,plain,
    ( subset(X1,cartesian_product2(X2,X3))
    | ~ subset(X1,cartesian_product2(X4,X5))
    | ~ subset(X5,X3)
    | ~ subset(X4,X2) ),
    inference(spm,[status(thm)],[43,34,theory(equality)]) ).

cnf(104,plain,
    ( relation(X1)
    | ~ relation_of2_as_subset(X1,X2,X3) ),
    inference(spm,[status(thm)],[40,24,theory(equality)]) ).

cnf(117,negated_conjecture,
    relation(esk7_0),
    inference(spm,[status(thm)],[104,75,theory(equality)]) ).

cnf(397,plain,
    ( subset(X1,cartesian_product2(X2,X3))
    | ~ subset(relation_rng(X1),X3)
    | ~ subset(relation_dom(X1),X2)
    | ~ relation(X1) ),
    inference(spm,[status(thm)],[102,50,theory(equality)]) ).

cnf(10246,negated_conjecture,
    ( subset(esk7_0,cartesian_product2(X1,esk5_0))
    | ~ relation(esk7_0)
    | ~ subset(relation_dom(esk7_0),X1) ),
    inference(spm,[status(thm)],[397,74,theory(equality)]) ).

cnf(10578,negated_conjecture,
    ( subset(esk7_0,cartesian_product2(X1,esk5_0))
    | $false
    | ~ subset(relation_dom(esk7_0),X1) ),
    inference(rw,[status(thm)],[10246,117,theory(equality)]) ).

cnf(10579,negated_conjecture,
    ( subset(esk7_0,cartesian_product2(X1,esk5_0))
    | ~ subset(relation_dom(esk7_0),X1) ),
    inference(cn,[status(thm)],[10578,theory(equality)]) ).

cnf(11231,negated_conjecture,
    subset(esk7_0,cartesian_product2(esk6_0,esk5_0)),
    inference(spm,[status(thm)],[10579,81,theory(equality)]) ).

cnf(11241,negated_conjecture,
    relation_of2_as_subset(esk7_0,esk6_0,esk5_0),
    inference(spm,[status(thm)],[94,11231,theory(equality)]) ).

cnf(11246,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[11241,73,theory(equality)]) ).

cnf(11247,negated_conjecture,
    $false,
    11246,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU263+1.p
% --creating new selector for []
% -running prover on /tmp/tmpPO6-YU/sel_SEU263+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU263+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU263+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU263+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
% 
%------------------------------------------------------------------------------