TSTP Solution File: SEU128+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU128+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 04:48:44 EST 2010

% Result   : Theorem 3.05s
% Output   : CNFRefutation 3.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   50 (  13 unt;   0 def)
%            Number of atoms       :  193 (  26 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  226 (  83   ~;  93   |;  44   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  114 (   5 sgn  52   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/tmp/tmpKLRTYH/sel_SEU128+1.p_1',commutativity_k3_xboole_0) ).

fof(9,conjecture,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X1,X3) )
     => subset(X1,set_intersection2(X2,X3)) ),
    file('/tmp/tmpKLRTYH/sel_SEU128+1.p_1',t19_xboole_1) ).

fof(12,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_intersection2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & in(X4,X2) ) ) ),
    file('/tmp/tmpKLRTYH/sel_SEU128+1.p_1',d3_xboole_0) ).

fof(14,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmpKLRTYH/sel_SEU128+1.p_1',d3_tarski) ).

fof(17,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( subset(X1,X2)
          & subset(X1,X3) )
       => subset(X1,set_intersection2(X2,X3)) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(20,plain,
    ! [X3,X4] : set_intersection2(X3,X4) = set_intersection2(X4,X3),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(21,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(37,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & subset(X1,X3)
      & ~ subset(X1,set_intersection2(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(38,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & subset(X4,X6)
      & ~ subset(X4,set_intersection2(X5,X6)) ),
    inference(variable_rename,[status(thm)],[37]) ).

fof(39,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    & subset(esk2_0,esk4_0)
    & ~ subset(esk2_0,set_intersection2(esk3_0,esk4_0)) ),
    inference(skolemize,[status(esa)],[38]) ).

cnf(40,negated_conjecture,
    ~ subset(esk2_0,set_intersection2(esk3_0,esk4_0)),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(41,negated_conjecture,
    subset(esk2_0,esk4_0),
    inference(split_conjunct,[status(thm)],[39]) ).

cnf(42,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[39]) ).

fof(49,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_intersection2(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | ~ in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & in(X4,X2) ) ) )
        | X3 = set_intersection2(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(50,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | ~ in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & in(X9,X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[49]) ).

fof(51,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_intersection2(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | ~ in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
            | ~ in(esk6_3(X5,X6,X7),X5)
            | ~ in(esk6_3(X5,X6,X7),X6) )
          & ( in(esk6_3(X5,X6,X7),X7)
            | ( in(esk6_3(X5,X6,X7),X5)
              & in(esk6_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(skolemize,[status(esa)],[50]) ).

fof(52,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | ~ in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_intersection2(X5,X6) )
      & ( ( ( ~ in(esk6_3(X5,X6,X7),X7)
            | ~ in(esk6_3(X5,X6,X7),X5)
            | ~ in(esk6_3(X5,X6,X7),X6) )
          & ( in(esk6_3(X5,X6,X7),X7)
            | ( in(esk6_3(X5,X6,X7),X5)
              & in(esk6_3(X5,X6,X7),X6) ) ) )
        | X7 = set_intersection2(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[51]) ).

fof(53,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(X8,X5)
        | ~ in(X8,X6)
        | in(X8,X7)
        | X7 != set_intersection2(X5,X6) )
      & ( ~ in(esk6_3(X5,X6,X7),X7)
        | ~ in(esk6_3(X5,X6,X7),X5)
        | ~ in(esk6_3(X5,X6,X7),X6)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X5)
        | in(esk6_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) )
      & ( in(esk6_3(X5,X6,X7),X6)
        | in(esk6_3(X5,X6,X7),X7)
        | X7 = set_intersection2(X5,X6) ) ),
    inference(distribute,[status(thm)],[52]) ).

cnf(55,plain,
    ( X1 = set_intersection2(X2,X3)
    | in(esk6_3(X2,X3,X1),X1)
    | in(esk6_3(X2,X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(56,plain,
    ( X1 = set_intersection2(X2,X3)
    | ~ in(esk6_3(X2,X3,X1),X3)
    | ~ in(esk6_3(X2,X3,X1),X2)
    | ~ in(esk6_3(X2,X3,X1),X1) ),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(57,plain,
    ( in(X4,X1)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[53]) ).

cnf(58,plain,
    ( in(X4,X3)
    | X1 != set_intersection2(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[53]) ).

fof(63,plain,
    ! [X1,X2] :
      ( ( ~ subset(X1,X2)
        | ! [X3] :
            ( ~ in(X3,X1)
            | in(X3,X2) ) )
      & ( ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X2) )
        | subset(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(64,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ? [X7] :
            ( in(X7,X4)
            & ~ in(X7,X5) )
        | subset(X4,X5) ) ),
    inference(variable_rename,[status(thm)],[63]) ).

fof(65,plain,
    ! [X4,X5] :
      ( ( ~ subset(X4,X5)
        | ! [X6] :
            ( ~ in(X6,X4)
            | in(X6,X5) ) )
      & ( ( in(esk7_2(X4,X5),X4)
          & ~ in(esk7_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(skolemize,[status(esa)],[64]) ).

fof(66,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( ( in(esk7_2(X4,X5),X4)
          & ~ in(esk7_2(X4,X5),X5) )
        | subset(X4,X5) ) ),
    inference(shift_quantors,[status(thm)],[65]) ).

fof(67,plain,
    ! [X4,X5,X6] :
      ( ( ~ in(X6,X4)
        | in(X6,X5)
        | ~ subset(X4,X5) )
      & ( in(esk7_2(X4,X5),X4)
        | subset(X4,X5) )
      & ( ~ in(esk7_2(X4,X5),X5)
        | subset(X4,X5) ) ),
    inference(distribute,[status(thm)],[66]) ).

cnf(68,plain,
    ( subset(X1,X2)
    | ~ in(esk7_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(69,plain,
    ( subset(X1,X2)
    | in(esk7_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(70,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[67]) ).

cnf(86,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,esk2_0) ),
    inference(spm,[status(thm)],[70,42,theory(equality)]) ).

cnf(87,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk2_0) ),
    inference(spm,[status(thm)],[70,41,theory(equality)]) ).

cnf(90,plain,
    ( in(X1,X2)
    | ~ in(X1,set_intersection2(X3,X2)) ),
    inference(er,[status(thm)],[58,theory(equality)]) ).

cnf(102,plain,
    ( in(X1,set_intersection2(X2,X3))
    | ~ in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[57,theory(equality)]) ).

cnf(114,plain,
    ( set_intersection2(X4,X5) = X4
    | in(esk6_3(X4,X5,X4),X4) ),
    inference(ef,[status(thm)],[55,theory(equality)]) ).

cnf(138,negated_conjecture,
    ( subset(X1,esk3_0)
    | ~ in(esk7_2(X1,esk3_0),esk2_0) ),
    inference(spm,[status(thm)],[68,86,theory(equality)]) ).

cnf(144,negated_conjecture,
    ( set_intersection2(X1,esk4_0) = X2
    | ~ in(esk6_3(X1,esk4_0,X2),X1)
    | ~ in(esk6_3(X1,esk4_0,X2),X2)
    | ~ in(esk6_3(X1,esk4_0,X2),esk2_0) ),
    inference(spm,[status(thm)],[56,87,theory(equality)]) ).

cnf(152,plain,
    ( in(esk7_2(set_intersection2(X1,X2),X3),X2)
    | subset(set_intersection2(X1,X2),X3) ),
    inference(spm,[status(thm)],[90,69,theory(equality)]) ).

cnf(194,negated_conjecture,
    subset(set_intersection2(X1,esk2_0),esk3_0),
    inference(spm,[status(thm)],[138,152,theory(equality)]) ).

cnf(204,negated_conjecture,
    subset(set_intersection2(esk2_0,X1),esk3_0),
    inference(spm,[status(thm)],[194,21,theory(equality)]) ).

cnf(249,negated_conjecture,
    ( in(X1,esk3_0)
    | ~ in(X1,set_intersection2(esk2_0,X2)) ),
    inference(spm,[status(thm)],[70,204,theory(equality)]) ).

cnf(391,plain,
    ( subset(X1,set_intersection2(X2,X3))
    | ~ in(esk7_2(X1,set_intersection2(X2,X3)),X3)
    | ~ in(esk7_2(X1,set_intersection2(X2,X3)),X2) ),
    inference(spm,[status(thm)],[68,102,theory(equality)]) ).

cnf(450,negated_conjecture,
    ( in(esk7_2(set_intersection2(esk2_0,X1),X2),esk3_0)
    | subset(set_intersection2(esk2_0,X1),X2) ),
    inference(spm,[status(thm)],[249,69,theory(equality)]) ).

cnf(987,negated_conjecture,
    ( set_intersection2(esk2_0,esk4_0) = esk2_0
    | ~ in(esk6_3(esk2_0,esk4_0,esk2_0),esk2_0) ),
    inference(spm,[status(thm)],[144,114,theory(equality)]) ).

cnf(1724,negated_conjecture,
    set_intersection2(esk2_0,esk4_0) = esk2_0,
    inference(csr,[status(thm)],[987,114]) ).

cnf(3338,plain,
    ( subset(set_intersection2(X1,X2),set_intersection2(X3,X2))
    | ~ in(esk7_2(set_intersection2(X1,X2),set_intersection2(X3,X2)),X3) ),
    inference(spm,[status(thm)],[391,152,theory(equality)]) ).

cnf(71358,negated_conjecture,
    subset(set_intersection2(esk2_0,X1),set_intersection2(esk3_0,X1)),
    inference(spm,[status(thm)],[3338,450,theory(equality)]) ).

cnf(71512,negated_conjecture,
    subset(esk2_0,set_intersection2(esk3_0,esk4_0)),
    inference(spm,[status(thm)],[71358,1724,theory(equality)]) ).

cnf(71585,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[71512,40,theory(equality)]) ).

cnf(71586,negated_conjecture,
    $false,
    71585,
    [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/SEU128+1.p
% --creating new selector for []
% -running prover on /tmp/tmpKLRTYH/sel_SEU128+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU128+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU128+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU128+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
% 
%------------------------------------------------------------------------------