TSTP Solution File: SET081+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET081+1 : TPTP v5.3.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : appomattox.cs.miami.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Core(TM)2 CPU          6600  @ 2.40GHz @ 2400MHz
% Memory   : 1003MB
% OS       : Linux 2.6.32.26-175.fc12.x86_64
% CPULimit : 300s
% DateTime : Fri Jun 15 08:05:27 EDT 2012

% Result   : Theorem 0.13s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   9 unt;   0 def)
%            Number of atoms       :   53 (   5 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :   54 (  20   ~;  18   |;  13   &)
%                                         (   1 <=>;   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   :   26 (   0 sgn  18   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] :
      ( member(X1,unordered_pair(X2,X3))
    <=> ( member(X1,universal_class)
        & ( equal(X1,X2)
          | equal(X1,X3) ) ) ),
    file('/tmp/tmpDRzgX4/sel_SET081+1.p_4',unordered_pair_defn) ).

fof(3,axiom,
    ! [X2] : equal(singleton(X2),unordered_pair(X2,X2)),
    file('/tmp/tmpDRzgX4/sel_SET081+1.p_4',singleton_set_defn) ).

fof(6,conjecture,
    ! [X2,X3] :
      ( member(X3,singleton(X2))
     => equal(X3,X2) ),
    file('/tmp/tmpDRzgX4/sel_SET081+1.p_4',only_member_in_singleton) ).

fof(7,negated_conjecture,
    ~ ! [X2,X3] :
        ( member(X3,singleton(X2))
       => equal(X3,X2) ),
    inference(assume_negation,[status(cth)],[6]) ).

fof(8,plain,
    ! [X1,X2,X3] :
      ( ( ~ member(X1,unordered_pair(X2,X3))
        | ( member(X1,universal_class)
          & ( equal(X1,X2)
            | equal(X1,X3) ) ) )
      & ( ~ member(X1,universal_class)
        | ( ~ equal(X1,X2)
          & ~ equal(X1,X3) )
        | member(X1,unordered_pair(X2,X3)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(9,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)],[8]) ).

fof(10,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)],[9]) ).

cnf(13,plain,
    ( X1 = X3
    | X1 = X2
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[10]) ).

fof(17,plain,
    ! [X3] : equal(singleton(X3),unordered_pair(X3,X3)),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(18,plain,
    singleton(X1) = unordered_pair(X1,X1),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(27,negated_conjecture,
    ? [X2,X3] :
      ( member(X3,singleton(X2))
      & ~ equal(X3,X2) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(28,negated_conjecture,
    ? [X4,X5] :
      ( member(X5,singleton(X4))
      & ~ equal(X5,X4) ),
    inference(variable_rename,[status(thm)],[27]) ).

fof(29,negated_conjecture,
    ( member(esk2_0,singleton(esk1_0))
    & ~ equal(esk2_0,esk1_0) ),
    inference(skolemize,[status(esa)],[28]) ).

cnf(30,negated_conjecture,
    esk2_0 != esk1_0,
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(31,negated_conjecture,
    member(esk2_0,singleton(esk1_0)),
    inference(split_conjunct,[status(thm)],[29]) ).

cnf(32,negated_conjecture,
    member(esk2_0,unordered_pair(esk1_0,esk1_0)),
    inference(rw,[status(thm)],[31,18,theory(equality)]),
    [unfolding] ).

cnf(38,negated_conjecture,
    esk2_0 = esk1_0,
    inference(spm,[status(thm)],[13,32,theory(equality)]) ).

cnf(39,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[38,30,theory(equality)]) ).

cnf(40,negated_conjecture,
    $false,
    39,
    [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/SET081+1.p
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpDRzgX4/sel_SET081+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/tmpDRzgX4/sel_SET081+1.p_1']
% -prover status CounterSatisfiable
% -running prover on /tmp/tmpDRzgX4/sel_SET081+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/tmpDRzgX4/sel_SET081+1.p_2']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpDRzgX4/sel_SET081+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/tmpDRzgX4/sel_SET081+1.p_3']
% -prover status CounterSatisfiable
% --creating new selector for [SET005+0.ax]
% -running prover on /tmp/tmpDRzgX4/sel_SET081+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/tmpDRzgX4/sel_SET081+1.p_4']
% -prover status Theorem
% Problem SET081+1.p solved in phase 3.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET081+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET081+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
% 
%------------------------------------------------------------------------------