TSTP Solution File: SEU132+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU132+1 : 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 04:45:16 EST 2010

% Result   : Theorem 0.81s
% Output   : CNFRefutation 0.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   42 (   7 unt;   0 def)
%            Number of atoms       :  176 (  19 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  213 (  79   ~;  86   |;  40   &)
%                                         (   5 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   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   :  109 (   6 sgn  52   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(7,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/tmp/tmpjOP1E-/sel_SEU132+1.p_1',d4_xboole_0) ).

fof(9,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => subset(set_difference(X1,X3),set_difference(X2,X3)) ),
    file('/tmp/tmpjOP1E-/sel_SEU132+1.p_1',t33_xboole_1) ).

fof(13,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/tmp/tmpjOP1E-/sel_SEU132+1.p_1',d3_tarski) ).

fof(16,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,X2)
       => subset(set_difference(X1,X3),set_difference(X2,X3)) ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(18,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[7,theory(equality)]) ).

fof(33,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_difference(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_difference(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(34,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(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_difference(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
            | ~ in(esk2_3(X5,X6,X7),X5)
            | in(esk2_3(X5,X6,X7),X6) )
          & ( in(esk2_3(X5,X6,X7),X7)
            | ( in(esk2_3(X5,X6,X7),X5)
              & ~ in(esk2_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(skolemize,[status(esa)],[34]) ).

fof(36,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_difference(X5,X6) )
      & ( ( ( ~ in(esk2_3(X5,X6,X7),X7)
            | ~ in(esk2_3(X5,X6,X7),X5)
            | in(esk2_3(X5,X6,X7),X6) )
          & ( in(esk2_3(X5,X6,X7),X7)
            | ( in(esk2_3(X5,X6,X7),X5)
              & ~ in(esk2_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[35]) ).

fof(37,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X6)
        | in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(esk2_3(X5,X6,X7),X7)
        | ~ in(esk2_3(X5,X6,X7),X5)
        | in(esk2_3(X5,X6,X7),X6)
        | X7 = set_difference(X5,X6) )
      & ( in(esk2_3(X5,X6,X7),X5)
        | in(esk2_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) )
      & ( ~ in(esk2_3(X5,X6,X7),X6)
        | in(esk2_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) ) ),
    inference(distribute,[status(thm)],[36]) ).

cnf(41,plain,
    ( in(X4,X1)
    | in(X4,X3)
    | X1 != set_difference(X2,X3)
    | ~ in(X4,X2) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(42,plain,
    ( X1 != set_difference(X2,X3)
    | ~ in(X4,X1)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(43,plain,
    ( in(X4,X2)
    | X1 != set_difference(X2,X3)
    | ~ in(X4,X1) ),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(46,negated_conjecture,
    ? [X1,X2,X3] :
      ( subset(X1,X2)
      & ~ subset(set_difference(X1,X3),set_difference(X2,X3)) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(47,negated_conjecture,
    ? [X4,X5,X6] :
      ( subset(X4,X5)
      & ~ subset(set_difference(X4,X6),set_difference(X5,X6)) ),
    inference(variable_rename,[status(thm)],[46]) ).

fof(48,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & ~ subset(set_difference(esk3_0,esk5_0),set_difference(esk4_0,esk5_0)) ),
    inference(skolemize,[status(esa)],[47]) ).

cnf(49,negated_conjecture,
    ~ subset(set_difference(esk3_0,esk5_0),set_difference(esk4_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[48]) ).

cnf(50,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(60,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)],[13]) ).

fof(61,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)],[60]) ).

fof(62,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)],[61]) ).

fof(63,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)],[62]) ).

fof(64,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)],[63]) ).

cnf(65,plain,
    ( subset(X1,X2)
    | ~ in(esk7_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(66,plain,
    ( subset(X1,X2)
    | in(esk7_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(67,plain,
    ( in(X3,X2)
    | ~ subset(X1,X2)
    | ~ in(X3,X1) ),
    inference(split_conjunct,[status(thm)],[64]) ).

cnf(78,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,esk3_0) ),
    inference(spm,[status(thm)],[67,50,theory(equality)]) ).

cnf(80,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X2,X3)) ),
    inference(er,[status(thm)],[43,theory(equality)]) ).

cnf(84,plain,
    ( ~ in(X1,X2)
    | ~ in(X1,set_difference(X3,X2)) ),
    inference(er,[status(thm)],[42,theory(equality)]) ).

cnf(88,plain,
    ( in(X1,set_difference(X2,X3))
    | in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[41,theory(equality)]) ).

cnf(107,negated_conjecture,
    ( subset(X1,esk4_0)
    | ~ in(esk7_2(X1,esk4_0),esk3_0) ),
    inference(spm,[status(thm)],[65,78,theory(equality)]) ).

cnf(113,plain,
    ( subset(set_difference(X1,X2),X3)
    | ~ in(esk7_2(set_difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[84,66,theory(equality)]) ).

cnf(137,plain,
    ( in(esk7_2(set_difference(X1,X2),X3),X1)
    | subset(set_difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[80,66,theory(equality)]) ).

cnf(225,plain,
    ( subset(X1,set_difference(X2,X3))
    | in(esk7_2(X1,set_difference(X2,X3)),X3)
    | ~ in(esk7_2(X1,set_difference(X2,X3)),X2) ),
    inference(spm,[status(thm)],[65,88,theory(equality)]) ).

cnf(245,negated_conjecture,
    subset(set_difference(esk3_0,X1),esk4_0),
    inference(spm,[status(thm)],[107,137,theory(equality)]) ).

cnf(261,negated_conjecture,
    ( in(X1,esk4_0)
    | ~ in(X1,set_difference(esk3_0,X2)) ),
    inference(spm,[status(thm)],[67,245,theory(equality)]) ).

cnf(307,negated_conjecture,
    ( in(esk7_2(set_difference(esk3_0,X1),X2),esk4_0)
    | subset(set_difference(esk3_0,X1),X2) ),
    inference(spm,[status(thm)],[261,66,theory(equality)]) ).

cnf(1788,negated_conjecture,
    ( subset(set_difference(esk3_0,X1),set_difference(esk4_0,X2))
    | in(esk7_2(set_difference(esk3_0,X1),set_difference(esk4_0,X2)),X2) ),
    inference(spm,[status(thm)],[225,307,theory(equality)]) ).

cnf(16457,negated_conjecture,
    subset(set_difference(esk3_0,X1),set_difference(esk4_0,X1)),
    inference(spm,[status(thm)],[113,1788,theory(equality)]) ).

cnf(16531,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[49,16457,theory(equality)]) ).

cnf(16532,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[16531,theory(equality)]) ).

cnf(16533,negated_conjecture,
    $false,
    16532,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU132+1.p
% --creating new selector for []
% -running prover on /tmp/tmpjOP1E-/sel_SEU132+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU132+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU132+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU132+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
% 
%------------------------------------------------------------------------------