TSTP Solution File: SET928+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET928+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 03:48:06 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   39 (   9 unt;   0 def)
%            Number of atoms       :  100 (  25 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  114 (  53   ~;  39   |;  18   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   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   :   61 (   2 sgn  40   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2,X3] :
      ~ ( ~ in(X1,X2)
        & ~ in(X3,X2)
        & ~ disjoint(unordered_pair(X1,X3),X2) ),
    file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t57_zfmisc_1) ).

fof(3,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',commutativity_k2_tarski) ).

fof(4,conjecture,
    ! [X1,X2,X3] :
      ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
    <=> ( ~ in(X1,X3)
        & ~ in(X2,X3) ) ),
    file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t72_zfmisc_1) ).

fof(8,axiom,
    ! [X1,X2,X3] :
      ~ ( disjoint(unordered_pair(X1,X2),X3)
        & in(X1,X3) ),
    file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t55_zfmisc_1) ).

fof(9,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_difference(X1,X2) = X1 ),
    file('/tmp/tmp8rE5Ti/sel_SET928+1.p_1',t83_xboole_1) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
      <=> ( ~ in(X1,X3)
          & ~ in(X2,X3) ) ),
    inference(assume_negation,[status(cth)],[4]) ).

fof(12,plain,
    ! [X1,X2,X3] :
      ~ ( ~ in(X1,X2)
        & ~ in(X3,X2)
        & ~ disjoint(unordered_pair(X1,X3),X2) ),
    inference(fof_simplification,[status(thm)],[2,theory(equality)]) ).

fof(13,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
      <=> ( ~ in(X1,X3)
          & ~ in(X2,X3) ) ),
    inference(fof_simplification,[status(thm)],[10,theory(equality)]) ).

fof(18,plain,
    ! [X1,X2,X3] :
      ( in(X1,X2)
      | in(X3,X2)
      | disjoint(unordered_pair(X1,X3),X2) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(19,plain,
    ! [X4,X5,X6] :
      ( in(X4,X5)
      | in(X6,X5)
      | disjoint(unordered_pair(X4,X6),X5) ),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(20,plain,
    ( disjoint(unordered_pair(X1,X2),X3)
    | in(X2,X3)
    | in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(21,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = unordered_pair(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(22,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(23,negated_conjecture,
    ? [X1,X2,X3] :
      ( ( set_difference(unordered_pair(X1,X2),X3) != unordered_pair(X1,X2)
        | in(X1,X3)
        | in(X2,X3) )
      & ( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
        | ( ~ in(X1,X3)
          & ~ in(X2,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(24,negated_conjecture,
    ? [X4,X5,X6] :
      ( ( set_difference(unordered_pair(X4,X5),X6) != unordered_pair(X4,X5)
        | in(X4,X6)
        | in(X5,X6) )
      & ( set_difference(unordered_pair(X4,X5),X6) = unordered_pair(X4,X5)
        | ( ~ in(X4,X6)
          & ~ in(X5,X6) ) ) ),
    inference(variable_rename,[status(thm)],[23]) ).

fof(25,negated_conjecture,
    ( ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0)
      | in(esk2_0,esk4_0)
      | in(esk3_0,esk4_0) )
    & ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0)
      | ( ~ in(esk2_0,esk4_0)
        & ~ in(esk3_0,esk4_0) ) ) ),
    inference(skolemize,[status(esa)],[24]) ).

fof(26,negated_conjecture,
    ( ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0)
      | in(esk2_0,esk4_0)
      | in(esk3_0,esk4_0) )
    & ( ~ in(esk2_0,esk4_0)
      | set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0) )
    & ( ~ in(esk3_0,esk4_0)
      | set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0) ) ),
    inference(distribute,[status(thm)],[25]) ).

cnf(27,negated_conjecture,
    ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0)
    | ~ in(esk3_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(28,negated_conjecture,
    ( set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) = unordered_pair(esk2_0,esk3_0)
    | ~ in(esk2_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[26]) ).

cnf(29,negated_conjecture,
    ( in(esk3_0,esk4_0)
    | in(esk2_0,esk4_0)
    | set_difference(unordered_pair(esk2_0,esk3_0),esk4_0) != unordered_pair(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(39,plain,
    ! [X1,X2,X3] :
      ( ~ disjoint(unordered_pair(X1,X2),X3)
      | ~ in(X1,X3) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(40,plain,
    ! [X4,X5,X6] :
      ( ~ disjoint(unordered_pair(X4,X5),X6)
      | ~ in(X4,X6) ),
    inference(variable_rename,[status(thm)],[39]) ).

cnf(41,plain,
    ( ~ in(X1,X2)
    | ~ disjoint(unordered_pair(X1,X3),X2) ),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(42,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | set_difference(X1,X2) = X1 )
      & ( set_difference(X1,X2) != X1
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(43,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_difference(X3,X4) = X3 )
      & ( set_difference(X3,X4) != X3
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[42]) ).

cnf(44,plain,
    ( disjoint(X1,X2)
    | set_difference(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(45,plain,
    ( set_difference(X1,X2) = X1
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(48,negated_conjecture,
    ( in(esk3_0,esk4_0)
    | in(esk2_0,esk4_0)
    | ~ disjoint(unordered_pair(esk2_0,esk3_0),esk4_0) ),
    inference(spm,[status(thm)],[29,45,theory(equality)]) ).

cnf(49,negated_conjecture,
    ( disjoint(unordered_pair(esk2_0,esk3_0),esk4_0)
    | ~ in(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[44,28,theory(equality)]) ).

cnf(50,negated_conjecture,
    ( disjoint(unordered_pair(esk2_0,esk3_0),esk4_0)
    | ~ in(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[44,27,theory(equality)]) ).

cnf(52,plain,
    ( ~ disjoint(unordered_pair(X2,X1),X3)
    | ~ in(X1,X3) ),
    inference(spm,[status(thm)],[41,22,theory(equality)]) ).

cnf(61,negated_conjecture,
    ~ in(esk2_0,esk4_0),
    inference(csr,[status(thm)],[49,41]) ).

cnf(62,negated_conjecture,
    ~ in(esk3_0,esk4_0),
    inference(csr,[status(thm)],[50,52]) ).

cnf(63,negated_conjecture,
    ( in(esk2_0,esk4_0)
    | ~ disjoint(unordered_pair(esk2_0,esk3_0),esk4_0) ),
    inference(sr,[status(thm)],[48,62,theory(equality)]) ).

cnf(64,negated_conjecture,
    ~ disjoint(unordered_pair(esk2_0,esk3_0),esk4_0),
    inference(sr,[status(thm)],[63,61,theory(equality)]) ).

cnf(65,negated_conjecture,
    ( in(esk2_0,esk4_0)
    | in(esk3_0,esk4_0) ),
    inference(spm,[status(thm)],[64,20,theory(equality)]) ).

cnf(66,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(sr,[status(thm)],[65,61,theory(equality)]) ).

cnf(67,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[66,62,theory(equality)]) ).

cnf(68,negated_conjecture,
    $false,
    67,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET928+1.p
% --creating new selector for []
% -running prover on /tmp/tmp8rE5Ti/sel_SET928+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET928+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET928+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET928+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
% 
%------------------------------------------------------------------------------