TSTP Solution File: SEU148+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU148+3 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 04:52:47 EST 2010

% Result   : Theorem 0.20s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (   9 unt;   0 def)
%            Number of atoms       :  116 (  75 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  137 (  53   ~;  55   |;  24   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   55 (   1 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,conjecture,
    ! [X1,X2] :
      ( subset(singleton(X1),singleton(X2))
     => X1 = X2 ),
    file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',t6_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2] :
      ( subset(X1,singleton(X2))
    <=> ( X1 = empty_set
        | X1 = singleton(X2) ) ),
    file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',l4_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',d1_tarski) ).

fof(5,axiom,
    ! [X1] : singleton(X1) != empty_set,
    file('/tmp/tmpKZarHh/sel_SEU148+3.p_1',l1_zfmisc_1) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( subset(singleton(X1),singleton(X2))
       => X1 = X2 ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(16,negated_conjecture,
    ? [X1,X2] :
      ( subset(singleton(X1),singleton(X2))
      & X1 != X2 ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(17,negated_conjecture,
    ? [X3,X4] :
      ( subset(singleton(X3),singleton(X4))
      & X3 != X4 ),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,negated_conjecture,
    ( subset(singleton(esk2_0),singleton(esk3_0))
    & esk2_0 != esk3_0 ),
    inference(skolemize,[status(esa)],[17]) ).

cnf(19,negated_conjecture,
    esk2_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[18]) ).

cnf(20,negated_conjecture,
    subset(singleton(esk2_0),singleton(esk3_0)),
    inference(split_conjunct,[status(thm)],[18]) ).

fof(21,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,singleton(X2))
        | X1 = empty_set
        | X1 = singleton(X2) )
      & ( ( X1 != empty_set
          & X1 != singleton(X2) )
        | subset(X1,singleton(X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(22,plain,
    ! [X3,X4] :
      ( ( ~ subset(X3,singleton(X4))
        | X3 = empty_set
        | X3 = singleton(X4) )
      & ( ( X3 != empty_set
          & X3 != singleton(X4) )
        | subset(X3,singleton(X4)) ) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,plain,
    ! [X3,X4] :
      ( ( ~ subset(X3,singleton(X4))
        | X3 = empty_set
        | X3 = singleton(X4) )
      & ( X3 != empty_set
        | subset(X3,singleton(X4)) )
      & ( X3 != singleton(X4)
        | subset(X3,singleton(X4)) ) ),
    inference(distribute,[status(thm)],[22]) ).

cnf(26,plain,
    ( X1 = singleton(X2)
    | X1 = empty_set
    | ~ subset(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(27,plain,
    ! [X1,X2] :
      ( ( X2 != singleton(X1)
        | ! [X3] :
            ( ( ~ in(X3,X2)
              | X3 = X1 )
            & ( X3 != X1
              | in(X3,X2) ) ) )
      & ( ? [X3] :
            ( ( ~ in(X3,X2)
              | X3 != X1 )
            & ( in(X3,X2)
              | X3 = X1 ) )
        | X2 = singleton(X1) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(28,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ? [X7] :
            ( ( ~ in(X7,X5)
              | X7 != X4 )
            & ( in(X7,X5)
              | X7 = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(variable_rename,[status(thm)],[27]) ).

fof(29,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) != X4 )
          & ( in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(skolemize,[status(esa)],[28]) ).

fof(30,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | X6 = X4 )
          & ( X6 != X4
            | in(X6,X5) ) )
        | X5 != singleton(X4) )
      & ( ( ( ~ in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) != X4 )
          & ( in(esk4_2(X4,X5),X5)
            | esk4_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(shift_quantors,[status(thm)],[29]) ).

fof(31,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk4_2(X4,X5),X5)
        | esk4_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk4_2(X4,X5),X5)
        | esk4_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    inference(distribute,[status(thm)],[30]) ).

cnf(34,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(35,plain,
    ( X3 = X2
    | X1 != singleton(X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(36,plain,
    ! [X2] : singleton(X2) != empty_set,
    inference(variable_rename,[status(thm)],[5]) ).

cnf(37,plain,
    singleton(X1) != empty_set,
    inference(split_conjunct,[status(thm)],[36]) ).

cnf(47,plain,
    ( in(X1,X2)
    | singleton(X1) != X2 ),
    inference(er,[status(thm)],[34,theory(equality)]) ).

cnf(48,negated_conjecture,
    ( singleton(esk3_0) = singleton(esk2_0)
    | empty_set = singleton(esk2_0) ),
    inference(spm,[status(thm)],[26,20,theory(equality)]) ).

cnf(51,negated_conjecture,
    singleton(esk3_0) = singleton(esk2_0),
    inference(sr,[status(thm)],[48,37,theory(equality)]) ).

cnf(61,plain,
    ( X1 = X2
    | singleton(X1) != X3
    | singleton(X2) != X3 ),
    inference(spm,[status(thm)],[35,47,theory(equality)]) ).

cnf(67,plain,
    ( X1 = X2
    | singleton(X2) != singleton(X1) ),
    inference(er,[status(thm)],[61,theory(equality)]) ).

cnf(70,negated_conjecture,
    ( X1 = esk3_0
    | singleton(esk2_0) != singleton(X1) ),
    inference(spm,[status(thm)],[67,51,theory(equality)]) ).

cnf(74,negated_conjecture,
    esk2_0 = esk3_0,
    inference(er,[status(thm)],[70,theory(equality)]) ).

cnf(75,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[74,19,theory(equality)]) ).

cnf(76,negated_conjecture,
    $false,
    75,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU148+3.p
% --creating new selector for []
% -running prover on /tmp/tmpKZarHh/sel_SEU148+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU148+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU148+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU148+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
% 
%------------------------------------------------------------------------------