TSTP Solution File: SEU275+2 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU275+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 06:38:15 EST 2010

% Result   : Theorem 1.95s
% Output   : CNFRefutation 1.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (  19 unt;   0 def)
%            Number of atoms       :  140 (   0 equ)
%            Maximal formula atoms :   22 (   3 avg)
%            Number of connectives :  165 (  70   ~;  67   |;  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   :   34 (   4 sgn  20   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(68,axiom,
    ! [X1] :
      ( relation(X1)
     => ( well_ordering(X1)
      <=> ( reflexive(X1)
          & transitive(X1)
          & antisymmetric(X1)
          & connected(X1)
          & well_founded_relation(X1) ) ) ),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',d4_wellord1) ).

fof(136,axiom,
    ! [X1] :
      ( ordinal(X1)
     => well_founded_relation(inclusion_relation(X1)) ),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',t6_wellord2) ).

fof(157,axiom,
    ! [X1] : reflexive(inclusion_relation(X1)),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',t2_wellord2) ).

fof(161,conjecture,
    ! [X1] :
      ( ordinal(X1)
     => well_ordering(inclusion_relation(X1)) ),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',t7_wellord2) ).

fof(205,axiom,
    ! [X1] : antisymmetric(inclusion_relation(X1)),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',t5_wellord2) ).

fof(206,axiom,
    ! [X1] : relation(inclusion_relation(X1)),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',dt_k1_wellord2) ).

fof(271,axiom,
    ! [X1] : transitive(inclusion_relation(X1)),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',t3_wellord2) ).

fof(298,axiom,
    ! [X1] :
      ( ordinal(X1)
     => connected(inclusion_relation(X1)) ),
    file('/tmp/tmpw1dS_t/sel_SEU275+2.p_1',t4_wellord2) ).

fof(354,negated_conjecture,
    ~ ! [X1] :
        ( ordinal(X1)
       => well_ordering(inclusion_relation(X1)) ),
    inference(assume_negation,[status(cth)],[161]) ).

fof(740,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)],[68]) ).

fof(741,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)],[740]) ).

fof(742,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)],[741]) ).

cnf(743,plain,
    ( well_ordering(X1)
    | ~ relation(X1)
    | ~ well_founded_relation(X1)
    | ~ connected(X1)
    | ~ antisymmetric(X1)
    | ~ transitive(X1)
    | ~ reflexive(X1) ),
    inference(split_conjunct,[status(thm)],[742]) ).

fof(1034,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | well_founded_relation(inclusion_relation(X1)) ),
    inference(fof_nnf,[status(thm)],[136]) ).

fof(1035,plain,
    ! [X2] :
      ( ~ ordinal(X2)
      | well_founded_relation(inclusion_relation(X2)) ),
    inference(variable_rename,[status(thm)],[1034]) ).

cnf(1036,plain,
    ( well_founded_relation(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[1035]) ).

fof(1109,plain,
    ! [X2] : reflexive(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[157]) ).

cnf(1110,plain,
    reflexive(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[1109]) ).

fof(1126,negated_conjecture,
    ? [X1] :
      ( ordinal(X1)
      & ~ well_ordering(inclusion_relation(X1)) ),
    inference(fof_nnf,[status(thm)],[354]) ).

fof(1127,negated_conjecture,
    ? [X2] :
      ( ordinal(X2)
      & ~ well_ordering(inclusion_relation(X2)) ),
    inference(variable_rename,[status(thm)],[1126]) ).

fof(1128,negated_conjecture,
    ( ordinal(esk70_0)
    & ~ well_ordering(inclusion_relation(esk70_0)) ),
    inference(skolemize,[status(esa)],[1127]) ).

cnf(1129,negated_conjecture,
    ~ well_ordering(inclusion_relation(esk70_0)),
    inference(split_conjunct,[status(thm)],[1128]) ).

cnf(1130,negated_conjecture,
    ordinal(esk70_0),
    inference(split_conjunct,[status(thm)],[1128]) ).

fof(1391,plain,
    ! [X2] : antisymmetric(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[205]) ).

cnf(1392,plain,
    antisymmetric(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[1391]) ).

fof(1393,plain,
    ! [X2] : relation(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[206]) ).

cnf(1394,plain,
    relation(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[1393]) ).

fof(1690,plain,
    ! [X2] : transitive(inclusion_relation(X2)),
    inference(variable_rename,[status(thm)],[271]) ).

cnf(1691,plain,
    transitive(inclusion_relation(X1)),
    inference(split_conjunct,[status(thm)],[1690]) ).

fof(1814,plain,
    ! [X1] :
      ( ~ ordinal(X1)
      | connected(inclusion_relation(X1)) ),
    inference(fof_nnf,[status(thm)],[298]) ).

fof(1815,plain,
    ! [X2] :
      ( ~ ordinal(X2)
      | connected(inclusion_relation(X2)) ),
    inference(variable_rename,[status(thm)],[1814]) ).

cnf(1816,plain,
    ( connected(inclusion_relation(X1))
    | ~ ordinal(X1) ),
    inference(split_conjunct,[status(thm)],[1815]) ).

cnf(3456,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ transitive(inclusion_relation(X1))
    | ~ antisymmetric(inclusion_relation(X1))
    | ~ connected(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1)) ),
    inference(spm,[status(thm)],[743,1110,theory(equality)]) ).

cnf(3459,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | $false
    | ~ antisymmetric(inclusion_relation(X1))
    | ~ connected(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1)) ),
    inference(rw,[status(thm)],[3456,1691,theory(equality)]) ).

cnf(3460,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | $false
    | $false
    | ~ connected(inclusion_relation(X1))
    | ~ relation(inclusion_relation(X1)) ),
    inference(rw,[status(thm)],[3459,1392,theory(equality)]) ).

cnf(3461,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | $false
    | $false
    | ~ connected(inclusion_relation(X1))
    | $false ),
    inference(rw,[status(thm)],[3460,1394,theory(equality)]) ).

cnf(3462,plain,
    ( well_ordering(inclusion_relation(X1))
    | ~ well_founded_relation(inclusion_relation(X1))
    | ~ connected(inclusion_relation(X1)) ),
    inference(cn,[status(thm)],[3461,theory(equality)]) ).

cnf(19365,plain,
    ( ~ well_founded_relation(inclusion_relation(esk70_0))
    | ~ connected(inclusion_relation(esk70_0)) ),
    inference(spm,[status(thm)],[1129,3462,theory(equality)]) ).

cnf(19397,plain,
    ( ~ connected(inclusion_relation(esk70_0))
    | ~ ordinal(esk70_0) ),
    inference(spm,[status(thm)],[19365,1036,theory(equality)]) ).

cnf(19400,plain,
    ( ~ connected(inclusion_relation(esk70_0))
    | $false ),
    inference(rw,[status(thm)],[19397,1130,theory(equality)]) ).

cnf(19401,plain,
    ~ connected(inclusion_relation(esk70_0)),
    inference(cn,[status(thm)],[19400,theory(equality)]) ).

cnf(19402,plain,
    ~ ordinal(esk70_0),
    inference(spm,[status(thm)],[19401,1816,theory(equality)]) ).

cnf(19406,plain,
    $false,
    inference(rw,[status(thm)],[19402,1130,theory(equality)]) ).

cnf(19407,plain,
    $false,
    inference(cn,[status(thm)],[19406,theory(equality)]) ).

cnf(19408,plain,
    $false,
    19407,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU275+2.p
% --creating new selector for []
% -running prover on /tmp/tmpw1dS_t/sel_SEU275+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU275+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU275+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU275+2.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
% 
%------------------------------------------------------------------------------