TSTP Solution File: SET884+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET884+1 : 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 03:43:24 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    :   38 (   8 unt;   0 def)
%            Number of atoms       :  211 ( 114 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  276 ( 103   ~; 107   |;  60   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   95 (   0 sgn  66   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2,X3] :
      ~ ( subset(singleton(X1),unordered_pair(X2,X3))
        & X1 != X2
        & X1 != X3 ),
    file('/tmp/tmpF-5BRC/sel_SET884+1.p_1',t25_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] :
      ( X2 = singleton(X1)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> X3 = X1 ) ),
    file('/tmp/tmpF-5BRC/sel_SET884+1.p_1',d1_tarski) ).

fof(7,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmpF-5BRC/sel_SET884+1.p_1',d3_tarski) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ( X3 = unordered_pair(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( X4 = X1
            | X4 = X2 ) ) ),
    file('/tmp/tmpF-5BRC/sel_SET884+1.p_1',d2_tarski) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ~ ( subset(singleton(X1),unordered_pair(X2,X3))
          & X1 != X2
          & X1 != X3 ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(13,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(singleton(X1),unordered_pair(X2,X3))
      & X1 != X2
      & X1 != X3 ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(14,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(singleton(X4),unordered_pair(X5,X6))
      & X4 != X5
      & X4 != X6 ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ( subset(singleton(esk1_0),unordered_pair(esk2_0,esk3_0))
    & esk1_0 != esk2_0
    & esk1_0 != esk3_0 ),
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    esk1_0 != esk3_0,
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    esk1_0 != esk2_0,
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(18,negated_conjecture,
    subset(singleton(esk1_0),unordered_pair(esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(24,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(25,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)],[24]) ).

fof(26,plain,
    ! [X4,X5] :
      ( ( X5 != singleton(X4)
        | ! [X6] :
            ( ( ~ in(X6,X5)
              | X6 = X4 )
            & ( X6 != X4
              | in(X6,X5) ) ) )
      & ( ( ( ~ in(esk5_2(X4,X5),X5)
            | esk5_2(X4,X5) != X4 )
          & ( in(esk5_2(X4,X5),X5)
            | esk5_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(skolemize,[status(esa)],[25]) ).

fof(27,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ in(X6,X5)
            | X6 = X4 )
          & ( X6 != X4
            | in(X6,X5) ) )
        | X5 != singleton(X4) )
      & ( ( ( ~ in(esk5_2(X4,X5),X5)
            | esk5_2(X4,X5) != X4 )
          & ( in(esk5_2(X4,X5),X5)
            | esk5_2(X4,X5) = X4 ) )
        | X5 = singleton(X4) ) ),
    inference(shift_quantors,[status(thm)],[26]) ).

fof(28,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X5)
        | X6 = X4
        | X5 != singleton(X4) )
      & ( X6 != X4
        | in(X6,X5)
        | X5 != singleton(X4) )
      & ( ~ in(esk5_2(X4,X5),X5)
        | esk5_2(X4,X5) != X4
        | X5 = singleton(X4) )
      & ( in(esk5_2(X4,X5),X5)
        | esk5_2(X4,X5) = X4
        | X5 = singleton(X4) ) ),
    inference(distribute,[status(thm)],[27]) ).

cnf(31,plain,
    ( in(X3,X1)
    | X1 != singleton(X2)
    | X3 != X2 ),
    inference(split_conjunct,[status(thm)],[28]) ).

fof(39,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X2) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(40,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ? [X7] :
            ( in(X7,X4)
            & ~ in(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ( in(esk7_2(X4,X5),X4)
          & ~ in(esk7_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[40]) ).

fof(42,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( in(esk7_2(X4,X5),X4)
          & ~ in(esk7_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[41]) ).

fof(43,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( in(esk7_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk7_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[42]) ).

cnf(46,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(47,plain,
    ! [X1,X2,X3] :
      ( ( X3 != unordered_pair(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | X4 = X1
              | X4 = X2 )
            & ( ( X4 != X1
                & X4 != X2 )
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ( X4 != X1
                & X4 != X2 ) )
            & ( in(X4,X3)
              | X4 = X1
              | X4 = X2 ) )
        | X3 = unordered_pair(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(48,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ( X9 != X5
                & X9 != X6 ) )
            & ( in(X9,X7)
              | X9 = X5
              | X9 = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[47]) ).

fof(49,plain,
    ! [X5,X6,X7] :
      ( ( X7 != unordered_pair(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | X8 = X5
              | X8 = X6 )
            & ( ( X8 != X5
                & X8 != X6 )
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
            | ( esk8_3(X5,X6,X7) != X5
              & esk8_3(X5,X6,X7) != X6 ) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | esk8_3(X5,X6,X7) = X5
            | esk8_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(skolemize,[status(esa)],[48]) ).

fof(50,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | X8 = X5
            | X8 = X6 )
          & ( ( X8 != X5
              & X8 != X6 )
            | in(X8,X7) ) )
        | X7 != unordered_pair(X5,X6) )
      & ( ( ( ~ in(esk8_3(X5,X6,X7),X7)
            | ( esk8_3(X5,X6,X7) != X5
              & esk8_3(X5,X6,X7) != X6 ) )
          & ( in(esk8_3(X5,X6,X7),X7)
            | esk8_3(X5,X6,X7) = X5
            | esk8_3(X5,X6,X7) = X6 ) )
        | X7 = unordered_pair(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[49]) ).

fof(51,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(X8,X7)
        | X8 = X5
        | X8 = X6
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X5
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( X8 != X6
        | in(X8,X7)
        | X7 != unordered_pair(X5,X6) )
      & ( esk8_3(X5,X6,X7) != X5
        | ~ in(esk8_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( esk8_3(X5,X6,X7) != X6
        | ~ in(esk8_3(X5,X6,X7),X7)
        | X7 = unordered_pair(X5,X6) )
      & ( in(esk8_3(X5,X6,X7),X7)
        | esk8_3(X5,X6,X7) = X5
        | esk8_3(X5,X6,X7) = X6
        | X7 = unordered_pair(X5,X6) ) ),
    inference(distribute,[status(thm)],[50]) ).

cnf(57,plain,
    ( X4 = X3
    | X4 = X2
    | X1 != unordered_pair(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[51]) ).

cnf(60,plain,
    ( in(X1,X2)
    | singleton(X1) != X2 ),
    inference(er,[status(thm)],[31,theory(equality)]) ).

cnf(68,negated_conjecture,
    ( in(X1,unordered_pair(esk2_0,esk3_0))
    | ~ in(X1,singleton(esk1_0)) ),
    inference(spm,[status(thm)],[46,18,theory(equality)]) ).

cnf(69,plain,
    ( X1 = X2
    | X3 = X2
    | ~ in(X2,unordered_pair(X1,X3)) ),
    inference(er,[status(thm)],[57,theory(equality)]) ).

cnf(79,plain,
    in(X1,singleton(X1)),
    inference(er,[status(thm)],[60,theory(equality)]) ).

cnf(89,negated_conjecture,
    in(esk1_0,unordered_pair(esk2_0,esk3_0)),
    inference(spm,[status(thm)],[68,79,theory(equality)]) ).

cnf(121,negated_conjecture,
    ( esk3_0 = esk1_0
    | esk2_0 = esk1_0 ),
    inference(spm,[status(thm)],[69,89,theory(equality)]) ).

cnf(127,negated_conjecture,
    esk2_0 = esk1_0,
    inference(sr,[status(thm)],[121,16,theory(equality)]) ).

cnf(128,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[127,17,theory(equality)]) ).

cnf(129,negated_conjecture,
    $false,
    128,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET884+1.p
% --creating new selector for []
% -running prover on /tmp/tmpF-5BRC/sel_SET884+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET884+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET884+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET884+1.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
% 
%------------------------------------------------------------------------------