TSTP Solution File: SET162+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET162+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 02:53:00 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   40 (  16 unt;   0 def)
%            Number of atoms       :  117 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  130 (  53   ~;  50   |;  23   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   71 (   3 sgn  43   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpp6RlQk/sel_SET162+4.p_1',subset) ).

fof(2,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpp6RlQk/sel_SET162+4.p_1',equal_set) ).

fof(3,axiom,
    ! [X3,X1,X2] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmpp6RlQk/sel_SET162+4.p_1',union) ).

fof(4,axiom,
    ! [X3] : ~ member(X3,empty_set),
    file('/tmp/tmpp6RlQk/sel_SET162+4.p_1',empty_set) ).

fof(5,conjecture,
    ! [X1] : equal_set(union(X1,empty_set),X1),
    file('/tmp/tmpp6RlQk/sel_SET162+4.p_1',thI18) ).

fof(6,negated_conjecture,
    ~ ! [X1] : equal_set(union(X1,empty_set),X1),
    inference(assume_negation,[status(cth)],[5]) ).

fof(7,plain,
    ! [X3] : ~ member(X3,empty_set),
    inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).

fof(8,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(9,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[8]) ).

fof(10,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[9]) ).

fof(11,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[10]) ).

fof(12,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subset(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[11]) ).

cnf(13,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[12]) ).

cnf(14,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(16,plain,
    ! [X1,X2] :
      ( ( ~ equal_set(X1,X2)
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | equal_set(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(17,plain,
    ! [X3,X4] :
      ( ( ~ equal_set(X3,X4)
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(distribute,[status(thm)],[17]) ).

cnf(19,plain,
    ( equal_set(X1,X2)
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(22,plain,
    ! [X3,X1,X2] :
      ( ( ~ member(X3,union(X1,X2))
        | member(X3,X1)
        | member(X3,X2) )
      & ( ( ~ member(X3,X1)
          & ~ member(X3,X2) )
        | member(X3,union(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,union(X5,X6))
        | member(X4,X5)
        | member(X4,X6) )
      & ( ( ~ member(X4,X5)
          & ~ member(X4,X6) )
        | member(X4,union(X5,X6)) ) ),
    inference(variable_rename,[status(thm)],[22]) ).

fof(24,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,union(X5,X6))
        | member(X4,X5)
        | member(X4,X6) )
      & ( ~ member(X4,X5)
        | member(X4,union(X5,X6)) )
      & ( ~ member(X4,X6)
        | member(X4,union(X5,X6)) ) ),
    inference(distribute,[status(thm)],[23]) ).

cnf(26,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[24]) ).

cnf(27,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(28,plain,
    ! [X4] : ~ member(X4,empty_set),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(29,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(30,negated_conjecture,
    ? [X1] : ~ equal_set(union(X1,empty_set),X1),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(31,negated_conjecture,
    ? [X2] : ~ equal_set(union(X2,empty_set),X2),
    inference(variable_rename,[status(thm)],[30]) ).

fof(32,negated_conjecture,
    ~ equal_set(union(esk2_0,empty_set),esk2_0),
    inference(skolemize,[status(esa)],[31]) ).

cnf(33,negated_conjecture,
    ~ equal_set(union(esk2_0,empty_set),esk2_0),
    inference(split_conjunct,[status(thm)],[32]) ).

cnf(34,negated_conjecture,
    ( ~ subset(esk2_0,union(esk2_0,empty_set))
    | ~ subset(union(esk2_0,empty_set),esk2_0) ),
    inference(spm,[status(thm)],[33,19,theory(equality)]) ).

cnf(39,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[13,26,theory(equality)]) ).

cnf(43,plain,
    ( member(esk1_2(union(X1,X2),X3),X2)
    | member(esk1_2(union(X1,X2),X3),X1)
    | subset(union(X1,X2),X3) ),
    inference(spm,[status(thm)],[27,14,theory(equality)]) ).

cnf(52,plain,
    subset(X1,union(X1,X2)),
    inference(spm,[status(thm)],[39,14,theory(equality)]) ).

cnf(54,negated_conjecture,
    ( $false
    | ~ subset(union(esk2_0,empty_set),esk2_0) ),
    inference(rw,[status(thm)],[34,52,theory(equality)]) ).

cnf(55,negated_conjecture,
    ~ subset(union(esk2_0,empty_set),esk2_0),
    inference(cn,[status(thm)],[54,theory(equality)]) ).

cnf(69,plain,
    ( member(esk1_2(union(X1,empty_set),X2),X1)
    | subset(union(X1,empty_set),X2) ),
    inference(spm,[status(thm)],[29,43,theory(equality)]) ).

cnf(406,plain,
    subset(union(X1,empty_set),X1),
    inference(spm,[status(thm)],[13,69,theory(equality)]) ).

cnf(427,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[55,406,theory(equality)]) ).

cnf(428,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[427,theory(equality)]) ).

cnf(429,negated_conjecture,
    $false,
    428,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET162+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpp6RlQk/sel_SET162+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET162+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET162+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET162+4.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
% 
%------------------------------------------------------------------------------