TSTP Solution File: SEU275+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU275+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 06:42:26 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   43 (  18 unt;   0 def)
%            Number of atoms       :  146 (   0 equ)
%            Maximal formula atoms :   22 (   3 avg)
%            Number of connectives :  174 (  71   ~;  75   |;  22   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   36 (   4 sgn  20   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] : relation(inclusion_relation(X1)),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',dt_k1_wellord2) ).

fof(2,axiom,
    ! [X1] :
      ( ordinal(X1)
     => well_founded_relation(inclusion_relation(X1)) ),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',t6_wellord2) ).

fof(4,axiom,
    ! [X1] :
      ( relation(X1)
     => ( well_ordering(X1)
      <=> ( reflexive(X1)
          & transitive(X1)
          & antisymmetric(X1)
          & connected(X1)
          & well_founded_relation(X1) ) ) ),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',d4_wellord1) ).

fof(5,axiom,
    ! [X1] : reflexive(inclusion_relation(X1)),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',t2_wellord2) ).

fof(6,axiom,
    ! [X1] : transitive(inclusion_relation(X1)),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',t3_wellord2) ).

fof(8,conjecture,
    ! [X1] :
      ( ordinal(X1)
     => well_ordering(inclusion_relation(X1)) ),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',t7_wellord2) ).

fof(9,axiom,
    ! [X1] :
      ( ordinal(X1)
     => connected(inclusion_relation(X1)) ),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',t4_wellord2) ).

fof(11,axiom,
    ! [X1] : antisymmetric(inclusion_relation(X1)),
    file('/tmp/tmpvSTDBQ/sel_SEU275+1.p_1',t5_wellord2) ).

fof(12,negated_conjecture,
    ~ ! [X1] :
        ( ordinal(X1)
       => well_ordering(inclusion_relation(X1)) ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(13,plain,
    ! [X2] : relation(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(14,plain,
    relation(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(15,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | well_founded_relation(inclusion_relation(X1)) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(16,plain,
    ! [X2] :
      ( ~ ordinal(X2)
      | well_founded_relation(inclusion_relation(X2)) ),
    inference(variable_rename,[status(thm)],[15]) ).

cnf(17,plain,
    ( well_founded_relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(23,plain,
    ! [X1] :
      ( ~ relation(X1)
      | ( ( ~ well_ordering(X1)
          | ( reflexive(X1)
            & transitive(X1)
            & antisymmetric(X1)
            & connected(X1)
            & well_founded_relation(X1) ) )
        & ( ~ reflexive(X1)
          | ~ transitive(X1)
          | ~ antisymmetric(X1)
          | ~ connected(X1)
          | ~ well_founded_relation(X1)
          | well_ordering(X1) ) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(24,plain,
    ! [X2] :
      ( ~ relation(X2)
      | ( ( ~ well_ordering(X2)
          | ( reflexive(X2)
            & transitive(X2)
            & antisymmetric(X2)
            & connected(X2)
            & well_founded_relation(X2) ) )
        & ( ~ reflexive(X2)
          | ~ transitive(X2)
          | ~ antisymmetric(X2)
          | ~ connected(X2)
          | ~ well_founded_relation(X2)
          | well_ordering(X2) ) ) ),
    inference(variable_rename,[status(thm)],[23]) ).

fof(25,plain,
    ! [X2] :
      ( ( reflexive(X2)
        | ~ well_ordering(X2)
        | ~ relation(X2) )
      & ( transitive(X2)
        | ~ well_ordering(X2)
        | ~ relation(X2) )
      & ( antisymmetric(X2)
        | ~ well_ordering(X2)
        | ~ relation(X2) )
      & ( connected(X2)
        | ~ well_ordering(X2)
        | ~ relation(X2) )
      & ( well_founded_relation(X2)
        | ~ well_ordering(X2)
        | ~ relation(X2) )
      & ( ~ reflexive(X2)
        | ~ transitive(X2)
        | ~ antisymmetric(X2)
        | ~ connected(X2)
        | ~ well_founded_relation(X2)
        | well_ordering(X2)
        | ~ relation(X2) ) ),
    inference(distribute,[status(thm)],[24]) ).

cnf(26,plain,
    ( well_ordering(X1)
    | ~ relation(X1)
    | ~ well_founded_relation(X1)
    | ~ connected(X1)
    | ~ antisymmetric(X1)
    | ~ transitive(X1)
    | ~ reflexive(X1) ),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(32,plain,
    ! [X2] : reflexive(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[5]) ).

cnf(33,plain,
    reflexive(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(34,plain,
    ! [X2] : transitive(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(35,plain,
    transitive(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(39,negated_conjecture,
    ? [X1] :
      ( ordinal(X1)
      & ~ well_ordering(inclusion_relation(X1)) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(40,negated_conjecture,
    ? [X2] :
      ( ordinal(X2)
      & ~ well_ordering(inclusion_relation(X2)) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,negated_conjecture,
    ( ordinal(esk2_0)
    & ~ well_ordering(inclusion_relation(esk2_0)) ),
    inference(skolemize,[status(esa)],[40]) ).

cnf(42,negated_conjecture,
    ~ well_ordering(inclusion_relation(esk2_0)),
    inference(split_conjunct,[status(thm)],[41]) ).

cnf(43,negated_conjecture,
    ordinal(esk2_0),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(44,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | connected(inclusion_relation(X1)) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(45,plain,
    ! [X2] :
      ( ~ ordinal(X2)
      | connected(inclusion_relation(X2)) ),
    inference(variable_rename,[status(thm)],[44]) ).

cnf(46,plain,
    ( connected(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(52,plain,
    ! [X2] : antisymmetric(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[11]) ).

cnf(53,plain,
    antisymmetric(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[52]) ).

cnf(59,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ antisymmetric(inclusion_relation(X1))
    | ~ transitive(inclusion_relation(X1))
    | ~ reflexive(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(spm,[status(thm)],[26,46,theory(equality)]) ).

cnf(61,plain,
    ( well_ordering(inclusion_relation(X1))
    | $false
    | ~ transitive(inclusion_relation(X1))
    | ~ reflexive(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(rw,[status(thm)],[59,53,theory(equality)]) ).

cnf(62,plain,
    ( well_ordering(inclusion_relation(X1))
    | $false
    | $false
    | ~ reflexive(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(rw,[status(thm)],[61,35,theory(equality)]) ).

cnf(63,plain,
    ( well_ordering(inclusion_relation(X1))
    | $false
    | $false
    | $false
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(rw,[status(thm)],[62,33,theory(equality)]) ).

cnf(64,plain,
    ( well_ordering(inclusion_relation(X1))
    | $false
    | $false
    | $false
    | ~ well_founded_relation(inclusion_relation(X1))
    | $false
    | ~ ordinal(X1) ),
    inference(rw,[status(thm)],[63,14,theory(equality)]) ).

cnf(65,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(cn,[status(thm)],[64,theory(equality)]) ).

cnf(66,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(csr,[status(thm)],[65,17]) ).

cnf(67,negated_conjecture,
    ~ ordinal(esk2_0),
    inference(spm,[status(thm)],[42,66,theory(equality)]) ).

cnf(68,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[67,43,theory(equality)]) ).

cnf(69,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[68,theory(equality)]) ).

cnf(70,negated_conjecture,
    $false,
    69,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU275+1.p
% --creating new selector for []
% -running prover on /tmp/tmpvSTDBQ/sel_SEU275+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU275+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU275+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU275+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
% 
%------------------------------------------------------------------------------