TSTP Solution File: SET654+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET654+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 03:07:47 EST 2010

% Result   : Theorem 0.30s
% Output   : CNFRefutation 0.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   45 (  11 unt;   0 def)
%            Number of atoms       :  189 (   0 equ)
%            Maximal formula atoms :    8 (   4 avg)
%            Number of connectives :  235 (  91   ~; 101   |;  21   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  112 (   6 sgn  53   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] : ilf_type(X1,set_type),
    file('/tmp/tmp-LLv0m/sel_SET654+3.p_1',p22) ).

fof(14,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,relation_type(X1,X2))
             => ( subset(domain_of(X3),X1)
                & subset(range_of(X3),X2) ) ) ) ),
    file('/tmp/tmp-LLv0m/sel_SET654+3.p_1',p2) ).

fof(15,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X3,X1))
                 => ( subset(range_of(X4),X2)
                   => ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
    file('/tmp/tmp-LLv0m/sel_SET654+3.p_1',p3) ).

fof(16,axiom,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ( ( subset(X1,X2)
                  & subset(X2,X3) )
               => subset(X1,X3) ) ) ) ),
    file('/tmp/tmp-LLv0m/sel_SET654+3.p_1',p1) ).

fof(23,conjecture,
    ! [X1] :
      ( ilf_type(X1,set_type)
     => ! [X2] :
          ( ilf_type(X2,set_type)
         => ! [X3] :
              ( ilf_type(X3,set_type)
             => ! [X4] :
                  ( ilf_type(X4,relation_type(X3,X1))
                 => ( subset(X1,X2)
                   => ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
    file('/tmp/tmp-LLv0m/sel_SET654+3.p_1',prove_relset_1_16) ).

fof(24,negated_conjecture,
    ~ ! [X1] :
        ( ilf_type(X1,set_type)
       => ! [X2] :
            ( ilf_type(X2,set_type)
           => ! [X3] :
                ( ilf_type(X3,set_type)
               => ! [X4] :
                    ( ilf_type(X4,relation_type(X3,X1))
                   => ( subset(X1,X2)
                     => ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[23]) ).

fof(37,plain,
    ! [X2] : ilf_type(X2,set_type),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(38,plain,
    ilf_type(X1,set_type),
    inference(split_conjunct,[status(thm)],[37]) ).

fof(98,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,relation_type(X1,X2))
              | ( subset(domain_of(X3),X1)
                & subset(range_of(X3),X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(99,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,set_type)
          | ! [X6] :
              ( ~ ilf_type(X6,relation_type(X4,X5))
              | ( subset(domain_of(X6),X4)
                & subset(range_of(X6),X5) ) ) ) ),
    inference(variable_rename,[status(thm)],[98]) ).

fof(100,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X6,relation_type(X4,X5))
      | ( subset(domain_of(X6),X4)
        & subset(range_of(X6),X5) )
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X4,set_type) ),
    inference(shift_quantors,[status(thm)],[99]) ).

fof(101,plain,
    ! [X4,X5,X6] :
      ( ( subset(domain_of(X6),X4)
        | ~ ilf_type(X6,relation_type(X4,X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) )
      & ( subset(range_of(X6),X5)
        | ~ ilf_type(X6,relation_type(X4,X5))
        | ~ ilf_type(X5,set_type)
        | ~ ilf_type(X4,set_type) ) ),
    inference(distribute,[status(thm)],[100]) ).

cnf(102,plain,
    ( subset(range_of(X3),X2)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[101]) ).

fof(104,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,set_type)
              | ! [X4] :
                  ( ~ ilf_type(X4,relation_type(X3,X1))
                  | ~ subset(range_of(X4),X2)
                  | ilf_type(X4,relation_type(X3,X2)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(105,plain,
    ! [X5] :
      ( ~ ilf_type(X5,set_type)
      | ! [X6] :
          ( ~ ilf_type(X6,set_type)
          | ! [X7] :
              ( ~ ilf_type(X7,set_type)
              | ! [X8] :
                  ( ~ ilf_type(X8,relation_type(X7,X5))
                  | ~ subset(range_of(X8),X6)
                  | ilf_type(X8,relation_type(X7,X6)) ) ) ) ),
    inference(variable_rename,[status(thm)],[104]) ).

fof(106,plain,
    ! [X5,X6,X7,X8] :
      ( ~ ilf_type(X8,relation_type(X7,X5))
      | ~ subset(range_of(X8),X6)
      | ilf_type(X8,relation_type(X7,X6))
      | ~ ilf_type(X7,set_type)
      | ~ ilf_type(X6,set_type)
      | ~ ilf_type(X5,set_type) ),
    inference(shift_quantors,[status(thm)],[105]) ).

cnf(107,plain,
    ( ilf_type(X4,relation_type(X3,X2))
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X3,set_type)
    | ~ subset(range_of(X4),X2)
    | ~ ilf_type(X4,relation_type(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[106]) ).

fof(108,plain,
    ! [X1] :
      ( ~ ilf_type(X1,set_type)
      | ! [X2] :
          ( ~ ilf_type(X2,set_type)
          | ! [X3] :
              ( ~ ilf_type(X3,set_type)
              | ~ subset(X1,X2)
              | ~ subset(X2,X3)
              | subset(X1,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(109,plain,
    ! [X4] :
      ( ~ ilf_type(X4,set_type)
      | ! [X5] :
          ( ~ ilf_type(X5,set_type)
          | ! [X6] :
              ( ~ ilf_type(X6,set_type)
              | ~ subset(X4,X5)
              | ~ subset(X5,X6)
              | subset(X4,X6) ) ) ),
    inference(variable_rename,[status(thm)],[108]) ).

fof(110,plain,
    ! [X4,X5,X6] :
      ( ~ ilf_type(X6,set_type)
      | ~ subset(X4,X5)
      | ~ subset(X5,X6)
      | subset(X4,X6)
      | ~ ilf_type(X5,set_type)
      | ~ ilf_type(X4,set_type) ),
    inference(shift_quantors,[status(thm)],[109]) ).

cnf(111,plain,
    ( subset(X1,X3)
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X2,set_type)
    | ~ subset(X2,X3)
    | ~ subset(X1,X2)
    | ~ ilf_type(X3,set_type) ),
    inference(split_conjunct,[status(thm)],[110]) ).

fof(142,negated_conjecture,
    ? [X1] :
      ( ilf_type(X1,set_type)
      & ? [X2] :
          ( ilf_type(X2,set_type)
          & ? [X3] :
              ( ilf_type(X3,set_type)
              & ? [X4] :
                  ( ilf_type(X4,relation_type(X3,X1))
                  & subset(X1,X2)
                  & ~ ilf_type(X4,relation_type(X3,X2)) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(143,negated_conjecture,
    ? [X5] :
      ( ilf_type(X5,set_type)
      & ? [X6] :
          ( ilf_type(X6,set_type)
          & ? [X7] :
              ( ilf_type(X7,set_type)
              & ? [X8] :
                  ( ilf_type(X8,relation_type(X7,X5))
                  & subset(X5,X6)
                  & ~ ilf_type(X8,relation_type(X7,X6)) ) ) ) ),
    inference(variable_rename,[status(thm)],[142]) ).

fof(144,negated_conjecture,
    ( ilf_type(esk10_0,set_type)
    & ilf_type(esk11_0,set_type)
    & ilf_type(esk12_0,set_type)
    & ilf_type(esk13_0,relation_type(esk12_0,esk10_0))
    & subset(esk10_0,esk11_0)
    & ~ ilf_type(esk13_0,relation_type(esk12_0,esk11_0)) ),
    inference(skolemize,[status(esa)],[143]) ).

cnf(145,negated_conjecture,
    ~ ilf_type(esk13_0,relation_type(esk12_0,esk11_0)),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(146,negated_conjecture,
    subset(esk10_0,esk11_0),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(147,negated_conjecture,
    ilf_type(esk13_0,relation_type(esk12_0,esk10_0)),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(215,plain,
    ( subset(range_of(X3),X2)
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[102,38,theory(equality)]) ).

cnf(216,plain,
    ( subset(range_of(X3),X2)
    | $false
    | $false
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(rw,[status(thm)],[215,38,theory(equality)]) ).

cnf(217,plain,
    ( subset(range_of(X3),X2)
    | ~ ilf_type(X3,relation_type(X1,X2)) ),
    inference(cn,[status(thm)],[216,theory(equality)]) ).

cnf(218,negated_conjecture,
    subset(range_of(esk13_0),esk10_0),
    inference(spm,[status(thm)],[217,147,theory(equality)]) ).

cnf(225,plain,
    ( subset(X1,X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X2)
    | $false
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[111,38,theory(equality)]) ).

cnf(226,plain,
    ( subset(X1,X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X2)
    | $false
    | $false
    | ~ ilf_type(X1,set_type) ),
    inference(rw,[status(thm)],[225,38,theory(equality)]) ).

cnf(227,plain,
    ( subset(X1,X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X2)
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[226,38,theory(equality)]) ).

cnf(228,plain,
    ( subset(X1,X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X2) ),
    inference(cn,[status(thm)],[227,theory(equality)]) ).

cnf(229,negated_conjecture,
    ( subset(X1,esk11_0)
    | ~ subset(X1,esk10_0) ),
    inference(spm,[status(thm)],[228,146,theory(equality)]) ).

cnf(279,plain,
    ( ilf_type(X4,relation_type(X3,X2))
    | $false
    | ~ ilf_type(X2,set_type)
    | ~ ilf_type(X1,set_type)
    | ~ subset(range_of(X4),X2)
    | ~ ilf_type(X4,relation_type(X3,X1)) ),
    inference(rw,[status(thm)],[107,38,theory(equality)]) ).

cnf(280,plain,
    ( ilf_type(X4,relation_type(X3,X2))
    | $false
    | $false
    | ~ ilf_type(X1,set_type)
    | ~ subset(range_of(X4),X2)
    | ~ ilf_type(X4,relation_type(X3,X1)) ),
    inference(rw,[status(thm)],[279,38,theory(equality)]) ).

cnf(281,plain,
    ( ilf_type(X4,relation_type(X3,X2))
    | $false
    | $false
    | $false
    | ~ subset(range_of(X4),X2)
    | ~ ilf_type(X4,relation_type(X3,X1)) ),
    inference(rw,[status(thm)],[280,38,theory(equality)]) ).

cnf(282,plain,
    ( ilf_type(X4,relation_type(X3,X2))
    | ~ subset(range_of(X4),X2)
    | ~ ilf_type(X4,relation_type(X3,X1)) ),
    inference(cn,[status(thm)],[281,theory(equality)]) ).

cnf(321,negated_conjecture,
    subset(range_of(esk13_0),esk11_0),
    inference(spm,[status(thm)],[229,218,theory(equality)]) ).

cnf(343,negated_conjecture,
    ( ilf_type(esk13_0,relation_type(X1,esk11_0))
    | ~ ilf_type(esk13_0,relation_type(X1,X2)) ),
    inference(spm,[status(thm)],[282,321,theory(equality)]) ).

cnf(601,negated_conjecture,
    ilf_type(esk13_0,relation_type(esk12_0,esk11_0)),
    inference(spm,[status(thm)],[343,147,theory(equality)]) ).

cnf(603,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[601,145,theory(equality)]) ).

cnf(604,negated_conjecture,
    $false,
    603,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET654+3.p
% --creating new selector for []
% -running prover on /tmp/tmp-LLv0m/sel_SET654+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET654+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET654+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET654+3.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
% 
%------------------------------------------------------------------------------