TSTP Solution File: SET813+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET813+4 : TPTP v5.0.0. Released v3.2.0.
% 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 03:41:31 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (   7 unt;   0 def)
%            Number of atoms       :   65 (   6 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   65 (  25   ~;  22   |;  13   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   2 sgn  26   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X3,X1] :
      ( member(X3,singleton(X1))
    <=> X3 = X1 ),
    file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',singleton) ).

fof(4,axiom,
    ! [X3,X1,X2] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',union) ).

fof(10,axiom,
    ! [X1,X3] :
      ( member(X3,suc(X1))
    <=> member(X3,union(X1,singleton(X1))) ),
    file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',successor) ).

fof(11,conjecture,
    ! [X1] :
      ( member(X1,on)
     => member(X1,suc(X1)) ),
    file('/tmp/tmpcq0ZOy/sel_SET813+4.p_1',thV12) ).

fof(12,negated_conjecture,
    ~ ! [X1] :
        ( member(X1,on)
       => member(X1,suc(X1)) ),
    inference(assume_negation,[status(cth)],[11]) ).

fof(21,plain,
    ! [X3,X1] :
      ( ( ~ member(X3,singleton(X1))
        | X3 = X1 )
      & ( X3 != X1
        | member(X3,singleton(X1)) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(22,plain,
    ! [X4,X5] :
      ( ( ~ member(X4,singleton(X5))
        | X4 = X5 )
      & ( X4 != X5
        | member(X4,singleton(X5)) ) ),
    inference(variable_rename,[status(thm)],[21]) ).

cnf(23,plain,
    ( member(X1,singleton(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[22]) ).

fof(35,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)],[4]) ).

fof(36,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)],[35]) ).

fof(37,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)],[36]) ).

cnf(38,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(100,plain,
    ! [X1,X3] :
      ( ( ~ member(X3,suc(X1))
        | member(X3,union(X1,singleton(X1))) )
      & ( ~ member(X3,union(X1,singleton(X1)))
        | member(X3,suc(X1)) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(101,plain,
    ! [X4,X5] :
      ( ( ~ member(X5,suc(X4))
        | member(X5,union(X4,singleton(X4))) )
      & ( ~ member(X5,union(X4,singleton(X4)))
        | member(X5,suc(X4)) ) ),
    inference(variable_rename,[status(thm)],[100]) ).

cnf(102,plain,
    ( member(X1,suc(X2))
    | ~ member(X1,union(X2,singleton(X2))) ),
    inference(split_conjunct,[status(thm)],[101]) ).

fof(104,negated_conjecture,
    ? [X1] :
      ( member(X1,on)
      & ~ member(X1,suc(X1)) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(105,negated_conjecture,
    ? [X2] :
      ( member(X2,on)
      & ~ member(X2,suc(X2)) ),
    inference(variable_rename,[status(thm)],[104]) ).

fof(106,negated_conjecture,
    ( member(esk12_0,on)
    & ~ member(esk12_0,suc(esk12_0)) ),
    inference(skolemize,[status(esa)],[105]) ).

cnf(107,negated_conjecture,
    ~ member(esk12_0,suc(esk12_0)),
    inference(split_conjunct,[status(thm)],[106]) ).

cnf(110,plain,
    member(X1,singleton(X1)),
    inference(er,[status(thm)],[23,theory(equality)]) ).

cnf(320,plain,
    member(X1,union(X2,singleton(X1))),
    inference(spm,[status(thm)],[38,110,theory(equality)]) ).

cnf(484,plain,
    member(X1,suc(X1)),
    inference(spm,[status(thm)],[102,320,theory(equality)]) ).

cnf(494,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[107,484,theory(equality)]) ).

cnf(495,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[494,theory(equality)]) ).

cnf(496,negated_conjecture,
    $false,
    495,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET813+4.p
% --creating new selector for [SET006+0.ax, SET006+4.ax]
% -running prover on /tmp/tmpcq0ZOy/sel_SET813+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET813+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET813+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET813+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
% 
%------------------------------------------------------------------------------