TSTP Solution File: SET635+3 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET635+3 : TPTP v5.0.0. Released v2.2.0.
% 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 : Sun Dec 26 03:06:16 EST 2010

% Result   : Theorem 0.65s
% Output   : CNFRefutation 0.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   38 (  34 unt;   0 def)
%            Number of atoms       :   46 (  34 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (  11   ~;   5   |;   2   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   72 (   0 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',commutativity_of_intersection) ).

fof(5,conjecture,
    ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',prove_th117) ).

fof(6,axiom,
    ! [X1] : subset(X1,X1),
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',reflexivity_of_subset) ).

fof(7,axiom,
    ! [X1,X2,X3] : difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',difference_and_intersection_and_union) ).

fof(10,axiom,
    ! [X1,X2] :
      ( difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',difference_empty_set) ).

fof(12,axiom,
    ! [X1] : union(X1,empty_set) = X1,
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',union_empty_set) ).

fof(14,axiom,
    ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
    file('/tmp/tmpZHsWoR/sel_SET635+3.p_1',difference_and_intersection) ).

fof(17,negated_conjecture,
    ~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),intersection(X1,X3)),
    inference(assume_negation,[status(cth)],[5]) ).

fof(21,plain,
    ! [X3,X4] : intersection(X3,X4) = intersection(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(22,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(33,negated_conjecture,
    ? [X1,X2,X3] : intersection(X1,difference(X2,X3)) != difference(intersection(X1,X2),intersection(X1,X3)),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(34,negated_conjecture,
    ? [X4,X5,X6] : intersection(X4,difference(X5,X6)) != difference(intersection(X4,X5),intersection(X4,X6)),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,negated_conjecture,
    intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),intersection(esk1_0,esk3_0)),
    inference(skolemize,[status(esa)],[34]) ).

cnf(36,negated_conjecture,
    intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),intersection(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(37,plain,
    ! [X2] : subset(X2,X2),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(38,plain,
    subset(X1,X1),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(39,plain,
    ! [X4,X5,X6] : difference(X4,intersection(X5,X6)) = union(difference(X4,X5),difference(X4,X6)),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(40,plain,
    difference(X1,intersection(X2,X3)) = union(difference(X1,X2),difference(X1,X3)),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(58,plain,
    ! [X1,X2] :
      ( ( difference(X1,X2) != empty_set
        | subset(X1,X2) )
      & ( ~ subset(X1,X2)
        | difference(X1,X2) = empty_set ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(59,plain,
    ! [X3,X4] :
      ( ( difference(X3,X4) != empty_set
        | subset(X3,X4) )
      & ( ~ subset(X3,X4)
        | difference(X3,X4) = empty_set ) ),
    inference(variable_rename,[status(thm)],[58]) ).

cnf(60,plain,
    ( difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[59]) ).

fof(68,plain,
    ! [X2] : union(X2,empty_set) = X2,
    inference(variable_rename,[status(thm)],[12]) ).

cnf(69,plain,
    union(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[68]) ).

fof(76,plain,
    ! [X4,X5,X6] : intersection(X4,difference(X5,X6)) = difference(intersection(X4,X5),X6),
    inference(variable_rename,[status(thm)],[14]) ).

cnf(77,plain,
    intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[76]) ).

cnf(100,plain,
    difference(X1,X1) = empty_set,
    inference(spm,[status(thm)],[60,38,theory(equality)]) ).

cnf(126,negated_conjecture,
    intersection(esk1_0,difference(esk2_0,intersection(esk1_0,esk3_0))) != intersection(esk1_0,difference(esk2_0,esk3_0)),
    inference(rw,[status(thm)],[36,77,theory(equality)]) ).

cnf(182,plain,
    union(difference(X1,X2),empty_set) = difference(X1,intersection(X2,X1)),
    inference(spm,[status(thm)],[40,100,theory(equality)]) ).

cnf(186,plain,
    difference(X1,X2) = difference(X1,intersection(X2,X1)),
    inference(rw,[status(thm)],[182,69,theory(equality)]) ).

cnf(480,plain,
    union(difference(X1,X2),difference(X1,X3)) = difference(X1,intersection(intersection(X2,X1),X3)),
    inference(spm,[status(thm)],[40,186,theory(equality)]) ).

cnf(495,plain,
    difference(X1,intersection(X1,X2)) = difference(X1,X2),
    inference(spm,[status(thm)],[186,22,theory(equality)]) ).

cnf(505,plain,
    difference(X1,intersection(X2,X3)) = difference(X1,intersection(intersection(X2,X1),X3)),
    inference(rw,[status(thm)],[480,40,theory(equality)]) ).

cnf(513,plain,
    difference(intersection(X1,X2),X3) = intersection(X1,difference(X2,intersection(intersection(X1,X2),X3))),
    inference(spm,[status(thm)],[77,495,theory(equality)]) ).

cnf(538,plain,
    intersection(X1,difference(X2,X3)) = intersection(X1,difference(X2,intersection(intersection(X1,X2),X3))),
    inference(rw,[status(thm)],[513,77,theory(equality)]) ).

cnf(18884,plain,
    intersection(X1,difference(X2,intersection(X1,X3))) = intersection(X1,difference(X2,X3)),
    inference(rw,[status(thm)],[538,505,theory(equality)]) ).

cnf(19046,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[126,18884,theory(equality)]) ).

cnf(19047,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[19046,theory(equality)]) ).

cnf(19048,negated_conjecture,
    $false,
    19047,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET635+3.p
% --creating new selector for []
% -running prover on /tmp/tmpZHsWoR/sel_SET635+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET635+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET635+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET635+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
% 
%------------------------------------------------------------------------------