TSTP Solution File: SEU103+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU103+1 : TPTP v5.0.0. Released v3.2.0.
% 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 @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 04:36:18 EST 2010

% Result   : Theorem 0.18s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   54 (  13 unt;   0 def)
%            Number of atoms       :  204 (  13 equ)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  241 (  91   ~;  94   |;  42   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   87 (   0 sgn  61   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',redefinition_k2_finsub_1) ).

fof(10,axiom,
    ! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
    file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',d6_xboole_0) ).

fof(16,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
    file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',redefinition_k1_finsub_1) ).

fof(36,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_difference(X1,X2,X3),X1) ),
    file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',dt_k2_finsub_1) ).

fof(37,conjecture,
    ! [X1,X2,X3] :
      ( ( ~ empty(X3)
        & preboolean(X3) )
     => ( ( element(X1,X3)
          & element(X2,X3) )
       => element(symmetric_difference(X1,X2),X3) ) ),
    file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',t14_finsub_1) ).

fof(42,axiom,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_union2(X1,X2,X3),X1) ),
    file('/tmp/tmpGRHwd2/sel_SEU103+1.p_1',dt_k1_finsub_1) ).

fof(47,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( ~ empty(X3)
          & preboolean(X3) )
       => ( ( element(X1,X3)
            & element(X2,X3) )
         => element(symmetric_difference(X1,X2),X3) ) ),
    inference(assume_negation,[status(cth)],[37]) ).

fof(49,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
    inference(fof_simplification,[status(thm)],[4,theory(equality)]) ).

fof(54,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
    inference(fof_simplification,[status(thm)],[16,theory(equality)]) ).

fof(61,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_difference(X1,X2,X3),X1) ),
    inference(fof_simplification,[status(thm)],[36,theory(equality)]) ).

fof(62,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( ~ empty(X3)
          & preboolean(X3) )
       => ( ( element(X1,X3)
            & element(X2,X3) )
         => element(symmetric_difference(X1,X2),X3) ) ),
    inference(fof_simplification,[status(thm)],[47,theory(equality)]) ).

fof(64,plain,
    ! [X1,X2,X3] :
      ( ( ~ empty(X1)
        & preboolean(X1)
        & element(X2,X1)
        & element(X3,X1) )
     => element(prebool_union2(X1,X2,X3),X1) ),
    inference(fof_simplification,[status(thm)],[42,theory(equality)]) ).

fof(77,plain,
    ! [X1,X2,X3] :
      ( empty(X1)
      | ~ preboolean(X1)
      | ~ element(X2,X1)
      | ~ element(X3,X1)
      | prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
    inference(fof_nnf,[status(thm)],[49]) ).

fof(78,plain,
    ! [X4,X5,X6] :
      ( empty(X4)
      | ~ preboolean(X4)
      | ~ element(X5,X4)
      | ~ element(X6,X4)
      | prebool_difference(X4,X5,X6) = set_difference(X5,X6) ),
    inference(variable_rename,[status(thm)],[77]) ).

cnf(79,plain,
    ( prebool_difference(X1,X2,X3) = set_difference(X2,X3)
    | empty(X1)
    | ~ element(X3,X1)
    | ~ element(X2,X1)
    | ~ preboolean(X1) ),
    inference(split_conjunct,[status(thm)],[78]) ).

fof(94,plain,
    ! [X3,X4] : symmetric_difference(X3,X4) = set_union2(set_difference(X3,X4),set_difference(X4,X3)),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(95,plain,
    symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
    inference(split_conjunct,[status(thm)],[94]) ).

fof(126,plain,
    ! [X1,X2,X3] :
      ( empty(X1)
      | ~ preboolean(X1)
      | ~ element(X2,X1)
      | ~ element(X3,X1)
      | prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
    inference(fof_nnf,[status(thm)],[54]) ).

fof(127,plain,
    ! [X4,X5,X6] :
      ( empty(X4)
      | ~ preboolean(X4)
      | ~ element(X5,X4)
      | ~ element(X6,X4)
      | prebool_union2(X4,X5,X6) = set_union2(X5,X6) ),
    inference(variable_rename,[status(thm)],[126]) ).

cnf(128,plain,
    ( prebool_union2(X1,X2,X3) = set_union2(X2,X3)
    | empty(X1)
    | ~ element(X3,X1)
    | ~ element(X2,X1)
    | ~ preboolean(X1) ),
    inference(split_conjunct,[status(thm)],[127]) ).

fof(184,plain,
    ! [X1,X2,X3] :
      ( empty(X1)
      | ~ preboolean(X1)
      | ~ element(X2,X1)
      | ~ element(X3,X1)
      | element(prebool_difference(X1,X2,X3),X1) ),
    inference(fof_nnf,[status(thm)],[61]) ).

fof(185,plain,
    ! [X4,X5,X6] :
      ( empty(X4)
      | ~ preboolean(X4)
      | ~ element(X5,X4)
      | ~ element(X6,X4)
      | element(prebool_difference(X4,X5,X6),X4) ),
    inference(variable_rename,[status(thm)],[184]) ).

cnf(186,plain,
    ( element(prebool_difference(X1,X2,X3),X1)
    | empty(X1)
    | ~ element(X3,X1)
    | ~ element(X2,X1)
    | ~ preboolean(X1) ),
    inference(split_conjunct,[status(thm)],[185]) ).

fof(187,negated_conjecture,
    ? [X1,X2,X3] :
      ( ~ empty(X3)
      & preboolean(X3)
      & element(X1,X3)
      & element(X2,X3)
      & ~ element(symmetric_difference(X1,X2),X3) ),
    inference(fof_nnf,[status(thm)],[62]) ).

fof(188,negated_conjecture,
    ? [X4,X5,X6] :
      ( ~ empty(X6)
      & preboolean(X6)
      & element(X4,X6)
      & element(X5,X6)
      & ~ element(symmetric_difference(X4,X5),X6) ),
    inference(variable_rename,[status(thm)],[187]) ).

fof(189,negated_conjecture,
    ( ~ empty(esk9_0)
    & preboolean(esk9_0)
    & element(esk7_0,esk9_0)
    & element(esk8_0,esk9_0)
    & ~ element(symmetric_difference(esk7_0,esk8_0),esk9_0) ),
    inference(skolemize,[status(esa)],[188]) ).

cnf(190,negated_conjecture,
    ~ element(symmetric_difference(esk7_0,esk8_0),esk9_0),
    inference(split_conjunct,[status(thm)],[189]) ).

cnf(191,negated_conjecture,
    element(esk8_0,esk9_0),
    inference(split_conjunct,[status(thm)],[189]) ).

cnf(192,negated_conjecture,
    element(esk7_0,esk9_0),
    inference(split_conjunct,[status(thm)],[189]) ).

cnf(193,negated_conjecture,
    preboolean(esk9_0),
    inference(split_conjunct,[status(thm)],[189]) ).

cnf(194,negated_conjecture,
    ~ empty(esk9_0),
    inference(split_conjunct,[status(thm)],[189]) ).

fof(210,plain,
    ! [X1,X2,X3] :
      ( empty(X1)
      | ~ preboolean(X1)
      | ~ element(X2,X1)
      | ~ element(X3,X1)
      | element(prebool_union2(X1,X2,X3),X1) ),
    inference(fof_nnf,[status(thm)],[64]) ).

fof(211,plain,
    ! [X4,X5,X6] :
      ( empty(X4)
      | ~ preboolean(X4)
      | ~ element(X5,X4)
      | ~ element(X6,X4)
      | element(prebool_union2(X4,X5,X6),X4) ),
    inference(variable_rename,[status(thm)],[210]) ).

cnf(212,plain,
    ( element(prebool_union2(X1,X2,X3),X1)
    | empty(X1)
    | ~ element(X3,X1)
    | ~ element(X2,X1)
    | ~ preboolean(X1) ),
    inference(split_conjunct,[status(thm)],[211]) ).

cnf(229,negated_conjecture,
    ~ element(set_union2(set_difference(esk7_0,esk8_0),set_difference(esk8_0,esk7_0)),esk9_0),
    inference(rw,[status(thm)],[190,95,theory(equality)]),
    [unfolding] ).

cnf(332,plain,
    ( element(set_difference(X2,X3),X1)
    | empty(X1)
    | ~ preboolean(X1)
    | ~ element(X3,X1)
    | ~ element(X2,X1) ),
    inference(spm,[status(thm)],[186,79,theory(equality)]) ).

cnf(333,plain,
    ( element(set_union2(X2,X3),X1)
    | empty(X1)
    | ~ preboolean(X1)
    | ~ element(X3,X1)
    | ~ element(X2,X1) ),
    inference(spm,[status(thm)],[212,128,theory(equality)]) ).

cnf(461,negated_conjecture,
    ( empty(esk9_0)
    | ~ preboolean(esk9_0)
    | ~ element(set_difference(esk8_0,esk7_0),esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
    inference(spm,[status(thm)],[229,333,theory(equality)]) ).

cnf(468,negated_conjecture,
    ( empty(esk9_0)
    | $false
    | ~ element(set_difference(esk8_0,esk7_0),esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
    inference(rw,[status(thm)],[461,193,theory(equality)]) ).

cnf(469,negated_conjecture,
    ( empty(esk9_0)
    | ~ element(set_difference(esk8_0,esk7_0),esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
    inference(cn,[status(thm)],[468,theory(equality)]) ).

cnf(470,negated_conjecture,
    ( ~ element(set_difference(esk8_0,esk7_0),esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
    inference(sr,[status(thm)],[469,194,theory(equality)]) ).

cnf(475,negated_conjecture,
    ( empty(esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0)
    | ~ preboolean(esk9_0)
    | ~ element(esk7_0,esk9_0)
    | ~ element(esk8_0,esk9_0) ),
    inference(spm,[status(thm)],[470,332,theory(equality)]) ).

cnf(476,negated_conjecture,
    ( empty(esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0)
    | $false
    | ~ element(esk7_0,esk9_0)
    | ~ element(esk8_0,esk9_0) ),
    inference(rw,[status(thm)],[475,193,theory(equality)]) ).

cnf(477,negated_conjecture,
    ( empty(esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0)
    | $false
    | $false
    | ~ element(esk8_0,esk9_0) ),
    inference(rw,[status(thm)],[476,192,theory(equality)]) ).

cnf(478,negated_conjecture,
    ( empty(esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[477,191,theory(equality)]) ).

cnf(479,negated_conjecture,
    ( empty(esk9_0)
    | ~ element(set_difference(esk7_0,esk8_0),esk9_0) ),
    inference(cn,[status(thm)],[478,theory(equality)]) ).

cnf(480,negated_conjecture,
    ~ element(set_difference(esk7_0,esk8_0),esk9_0),
    inference(sr,[status(thm)],[479,194,theory(equality)]) ).

cnf(481,negated_conjecture,
    ( empty(esk9_0)
    | ~ preboolean(esk9_0)
    | ~ element(esk8_0,esk9_0)
    | ~ element(esk7_0,esk9_0) ),
    inference(spm,[status(thm)],[480,332,theory(equality)]) ).

cnf(482,negated_conjecture,
    ( empty(esk9_0)
    | $false
    | ~ element(esk8_0,esk9_0)
    | ~ element(esk7_0,esk9_0) ),
    inference(rw,[status(thm)],[481,193,theory(equality)]) ).

cnf(483,negated_conjecture,
    ( empty(esk9_0)
    | $false
    | $false
    | ~ element(esk7_0,esk9_0) ),
    inference(rw,[status(thm)],[482,191,theory(equality)]) ).

cnf(484,negated_conjecture,
    ( empty(esk9_0)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[483,192,theory(equality)]) ).

cnf(485,negated_conjecture,
    empty(esk9_0),
    inference(cn,[status(thm)],[484,theory(equality)]) ).

cnf(486,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[485,194,theory(equality)]) ).

cnf(487,negated_conjecture,
    $false,
    486,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU103+1.p
% --creating new selector for []
% -running prover on /tmp/tmpGRHwd2/sel_SEU103+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU103+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU103+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU103+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
% 
%------------------------------------------------------------------------------