TSTP Solution File: SET355+4 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET355+4 : 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 02:55:41 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   27 (   5 unt;   0 def)
%            Number of atoms       :   94 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  108 (  41   ~;  38   |;  24   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (   0 sgn  39   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpi2gjG6/sel_SET355+4.p_1',subset) ).

fof(2,axiom,
    ! [X3,X1] :
      ( member(X3,sum(X1))
    <=> ? [X4] :
          ( member(X4,X1)
          & member(X3,X4) ) ),
    file('/tmp/tmpi2gjG6/sel_SET355+4.p_1',sum) ).

fof(3,conjecture,
    ! [X1,X3] :
      ( member(X3,X1)
     => subset(X3,sum(X1)) ),
    file('/tmp/tmpi2gjG6/sel_SET355+4.p_1',thI43) ).

fof(4,negated_conjecture,
    ~ ! [X1,X3] :
        ( member(X3,X1)
       => subset(X3,sum(X1)) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(5,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(6,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)],[5]) ).

fof(7,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)],[6]) ).

fof(8,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)],[7]) ).

fof(9,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)],[8]) ).

cnf(10,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[9]) ).

cnf(11,plain,
    ( subset(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[9]) ).

fof(13,plain,
    ! [X3,X1] :
      ( ( ~ member(X3,sum(X1))
        | ? [X4] :
            ( member(X4,X1)
            & member(X3,X4) ) )
      & ( ! [X4] :
            ( ~ member(X4,X1)
            | ~ member(X3,X4) )
        | member(X3,sum(X1)) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(14,plain,
    ! [X5,X6] :
      ( ( ~ member(X5,sum(X6))
        | ? [X7] :
            ( member(X7,X6)
            & member(X5,X7) ) )
      & ( ! [X8] :
            ( ~ member(X8,X6)
            | ~ member(X5,X8) )
        | member(X5,sum(X6)) ) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,plain,
    ! [X5,X6] :
      ( ( ~ member(X5,sum(X6))
        | ( member(esk2_2(X5,X6),X6)
          & member(X5,esk2_2(X5,X6)) ) )
      & ( ! [X8] :
            ( ~ member(X8,X6)
            | ~ member(X5,X8) )
        | member(X5,sum(X6)) ) ),
    inference(skolemize,[status(esa)],[14]) ).

fof(16,plain,
    ! [X5,X6,X8] :
      ( ( ~ member(X8,X6)
        | ~ member(X5,X8)
        | member(X5,sum(X6)) )
      & ( ~ member(X5,sum(X6))
        | ( member(esk2_2(X5,X6),X6)
          & member(X5,esk2_2(X5,X6)) ) ) ),
    inference(shift_quantors,[status(thm)],[15]) ).

fof(17,plain,
    ! [X5,X6,X8] :
      ( ( ~ member(X8,X6)
        | ~ member(X5,X8)
        | member(X5,sum(X6)) )
      & ( member(esk2_2(X5,X6),X6)
        | ~ member(X5,sum(X6)) )
      & ( member(X5,esk2_2(X5,X6))
        | ~ member(X5,sum(X6)) ) ),
    inference(distribute,[status(thm)],[16]) ).

cnf(20,plain,
    ( member(X1,sum(X2))
    | ~ member(X1,X3)
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(21,negated_conjecture,
    ? [X1,X3] :
      ( member(X3,X1)
      & ~ subset(X3,sum(X1)) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(22,negated_conjecture,
    ? [X4,X5] :
      ( member(X5,X4)
      & ~ subset(X5,sum(X4)) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,negated_conjecture,
    ( member(esk4_0,esk3_0)
    & ~ subset(esk4_0,sum(esk3_0)) ),
    inference(skolemize,[status(esa)],[22]) ).

cnf(24,negated_conjecture,
    ~ subset(esk4_0,sum(esk3_0)),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(25,negated_conjecture,
    member(esk4_0,esk3_0),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(26,negated_conjecture,
    ( member(X1,sum(esk3_0))
    | ~ member(X1,esk4_0) ),
    inference(spm,[status(thm)],[20,25,theory(equality)]) ).

cnf(32,negated_conjecture,
    ( subset(X1,sum(esk3_0))
    | ~ member(esk1_2(X1,sum(esk3_0)),esk4_0) ),
    inference(spm,[status(thm)],[10,26,theory(equality)]) ).

cnf(34,negated_conjecture,
    subset(esk4_0,sum(esk3_0)),
    inference(spm,[status(thm)],[32,11,theory(equality)]) ).

cnf(35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[34,24,theory(equality)]) ).

cnf(36,negated_conjecture,
    $false,
    35,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET355+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpi2gjG6/sel_SET355+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET355+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET355+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET355+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
% 
%------------------------------------------------------------------------------