TSTP Solution File: SET095+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET095+1 : TPTP v5.3.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2800MHz
% Memory   : 2005MB
% OS       : Linux 2.6.32.26-175.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Fri Jun 15 08:06:24 EDT 2012

% Result   : Theorem 0.43s
% Output   : CNFRefutation 0.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (  10 unt;   0 def)
%            Number of atoms       :  102 (   8 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  110 (  40   ~;  42   |;  23   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   60 (   0 sgn  36   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2] :
      ( subclass(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/tmp/tmpKDnLhh/sel_SET095+1.p_4',subclass_defn) ).

fof(6,axiom,
    ! [X1] : equal(singleton(X1),unordered_pair(X1,X1)),
    file('/tmp/tmpKDnLhh/sel_SET095+1.p_4',singleton_set_defn) ).

fof(7,axiom,
    ! [X3,X1,X2] :
      ( member(X3,unordered_pair(X1,X2))
    <=> ( member(X3,universal_class)
        & ( equal(X3,X1)
          | equal(X3,X2) ) ) ),
    file('/tmp/tmpKDnLhh/sel_SET095+1.p_4',unordered_pair_defn) ).

fof(9,conjecture,
    ! [X1,X2] :
      ( member(X1,X2)
     => subclass(singleton(X1),X2) ),
    file('/tmp/tmpKDnLhh/sel_SET095+1.p_4',property_of_singletons2) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( member(X1,X2)
       => subclass(singleton(X1),X2) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(17,plain,
    ! [X1,X2] :
      ( ( ~ subclass(X1,X2)
        | ! [X3] :
            ( ~ member(X3,X1)
            | member(X3,X2) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & ~ member(X3,X2) )
        | subclass(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(18,plain,
    ! [X4,X5] :
      ( ( ~ subclass(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ? [X7] :
            ( member(X7,X4)
            & ~ member(X7,X5) )
        | subclass(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[17]) ).

fof(19,plain,
    ! [X4,X5] :
      ( ( ~ subclass(X4,X5)
        | ! [X6] :
            ( ~ member(X6,X4)
            | member(X6,X5) ) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subclass(X4,X5) ) ),
    inference(skolemize,[status(esa)],[18]) ).

fof(20,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subclass(X4,X5) )
      & ( ( member(esk1_2(X4,X5),X4)
          & ~ member(esk1_2(X4,X5),X5) )
        | subclass(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[19]) ).

fof(21,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,X4)
        | member(X6,X5)
        | ~ subclass(X4,X5) )
      & ( member(esk1_2(X4,X5),X4)
        | subclass(X4,X5) )
      & ( ~ member(esk1_2(X4,X5),X5)
        | subclass(X4,X5) ) ),
    inference(distribute,[status(thm)],[20]) ).

cnf(22,plain,
    ( subclass(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(23,plain,
    ( subclass(X1,X2)
    | member(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(35,plain,
    ! [X2] : equal(singleton(X2),unordered_pair(X2,X2)),
    inference(variable_rename,[status(thm)],[6]) ).

cnf(36,plain,
    singleton(X1) = unordered_pair(X1,X1),
    inference(split_conjunct,[status(thm)],[35]) ).

fof(37,plain,
    ! [X3,X1,X2] :
      ( ( ~ member(X3,unordered_pair(X1,X2))
        | ( member(X3,universal_class)
          & ( equal(X3,X1)
            | equal(X3,X2) ) ) )
      & ( ~ member(X3,universal_class)
        | ( ~ equal(X3,X1)
          & ~ equal(X3,X2) )
        | member(X3,unordered_pair(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(38,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X4,unordered_pair(X5,X6))
        | ( member(X4,universal_class)
          & ( equal(X4,X5)
            | equal(X4,X6) ) ) )
      & ( ~ member(X4,universal_class)
        | ( ~ equal(X4,X5)
          & ~ equal(X4,X6) )
        | member(X4,unordered_pair(X5,X6)) ) ),
    inference(variable_rename,[status(thm)],[37]) ).

fof(39,plain,
    ! [X4,X5,X6] :
      ( ( member(X4,universal_class)
        | ~ member(X4,unordered_pair(X5,X6)) )
      & ( equal(X4,X5)
        | equal(X4,X6)
        | ~ member(X4,unordered_pair(X5,X6)) )
      & ( ~ equal(X4,X5)
        | ~ member(X4,universal_class)
        | member(X4,unordered_pair(X5,X6)) )
      & ( ~ equal(X4,X6)
        | ~ member(X4,universal_class)
        | member(X4,unordered_pair(X5,X6)) ) ),
    inference(distribute,[status(thm)],[38]) ).

cnf(42,plain,
    ( X1 = X3
    | X1 = X2
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(46,negated_conjecture,
    ? [X1,X2] :
      ( member(X1,X2)
      & ~ subclass(singleton(X1),X2) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(47,negated_conjecture,
    ? [X3,X4] :
      ( member(X3,X4)
      & ~ subclass(singleton(X3),X4) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ( member(esk2_0,esk3_0)
    & ~ subclass(singleton(esk2_0),esk3_0) ),
    inference(skolemize,[status(esa)],[47]) ).

cnf(49,negated_conjecture,
    ~ subclass(singleton(esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,negated_conjecture,
    member(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(52,negated_conjecture,
    ~ subclass(unordered_pair(esk2_0,esk2_0),esk3_0),
    inference(rw,[status(thm)],[49,36,theory(equality)]),
    [unfolding] ).

cnf(61,plain,
    ( esk1_2(unordered_pair(X1,X2),X3) = X1
    | esk1_2(unordered_pair(X1,X2),X3) = X2
    | subclass(unordered_pair(X1,X2),X3) ),
    inference(spm,[status(thm)],[42,23,theory(equality)]) ).

cnf(82,plain,
    ( esk1_2(unordered_pair(X4,X5),X6) = X4
    | subclass(unordered_pair(X4,X5),X6)
    | X5 != X4 ),
    inference(ef,[status(thm)],[61,theory(equality)]) ).

cnf(90,plain,
    ( esk1_2(unordered_pair(X1,X1),X2) = X1
    | subclass(unordered_pair(X1,X1),X2) ),
    inference(er,[status(thm)],[82,theory(equality)]) ).

cnf(94,plain,
    ( subclass(unordered_pair(X1,X1),X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[22,90,theory(equality)]) ).

cnf(100,negated_conjecture,
    ~ member(esk2_0,esk3_0),
    inference(spm,[status(thm)],[52,94,theory(equality)]) ).

cnf(103,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[100,50,theory(equality)]) ).

cnf(104,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[103,theory(equality)]) ).

cnf(105,negated_conjecture,
    $false,
    104,
    [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/SET/SET095+1.p
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpKDnLhh/sel_SET095+1.p_1 with time limit 29
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/tmp/tmpKDnLhh/sel_SET095+1.p_1']
% -prover status CounterSatisfiable
% -running prover on /tmp/tmpKDnLhh/sel_SET095+1.p_2 with time limit 89
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=89', '/tmp/tmpKDnLhh/sel_SET095+1.p_2']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpKDnLhh/sel_SET095+1.p_3 with time limit 119
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=119', '/tmp/tmpKDnLhh/sel_SET095+1.p_3']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpKDnLhh/sel_SET095+1.p_4 with time limit 149
% -running prover with command ['/davis/home/graph/tptp/Systems/SInE---0.4/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=149', '/tmp/tmpKDnLhh/sel_SET095+1.p_4']
% -prover status Theorem
% Problem SET095+1.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET095+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET095+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
% 
%------------------------------------------------------------------------------