TSTP Solution File: SET628+3 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET628+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art08.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 1003MB
% OS       : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May  6 15:33:37 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   32 (  11 unt;   0 def)
%            Number of atoms       :   86 (   0 equ)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives :   94 (  40   ~;  42   |;  12   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   34 (   7 sgn  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersect_defn,plain,
    ! [A,B,D] :
      ( ( member(d_nn_1(A,B),B)
        | ~ intersect(A,B) )
      & ( member(d_nn_1(A,B),A)
        | ~ intersect(A,B) )
      & ( intersect(A,B)
        | ~ member(D,A)
        | ~ member(D,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
    [] ).

cnf(169824616,plain,
    ( intersect(A,B)
    | ~ member(D,A)
    | ~ member(D,B) ),
    inference(rewrite,[status(thm)],[intersect_defn]),
    [] ).

fof(equal_member_defn,plain,
    ! [C,A,B] :
      ( ( member(C,A)
        | ~ member(C,B)
        | ~ $equal(B,A) )
      & ( ~ member(C,A)
        | member(C,B)
        | ~ $equal(B,A) )
      & ( member(d(A,B,C),B)
        | ~ member(d(A,B,C),B)
        | $equal(B,A) )
      & ( ~ member(d(A,B,C),A)
        | ~ member(d(A,B,C),B)
        | $equal(B,A) )
      & ( member(d(A,B,C),B)
        | member(d(A,B,C),A)
        | $equal(B,A) )
      & ( ~ member(d(A,B,C),A)
        | member(d(A,B,C),A)
        | $equal(B,A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
    [] ).

cnf(169856440,plain,
    ( member(d(A,B,C),B)
    | member(d(A,B,C),A)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[equal_member_defn]),
    [] ).

fof(empty_set_defn,plain,
    ! [A] : ~ member(A,empty_set),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
    [] ).

cnf(169841448,plain,
    ~ member(A,empty_set),
    inference(rewrite,[status(thm)],[empty_set_defn]),
    [] ).

cnf(180502392,plain,
    ( member(d(A,empty_set,B),A)
    | $equal(empty_set,A) ),
    inference(resolution,[status(thm)],[169856440,169841448]),
    [] ).

fof(prove_th110,plain,
    ( ( not_equal(b,empty_set)
      | intersect(b,b) )
    & ( ~ intersect(b,b)
      | intersect(b,b) )
    & ( not_equal(b,empty_set)
      | ~ not_equal(b,empty_set) )
    & ( ~ intersect(b,b)
      | ~ not_equal(b,empty_set) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
    [] ).

cnf(169978224,plain,
    ( ~ intersect(b,b)
    | ~ not_equal(b,empty_set) ),
    inference(rewrite,[status(thm)],[prove_th110]),
    [] ).

fof(not_equal_defn,plain,
    ! [A,B] :
      ( ( ~ not_equal(A,B)
        | ~ $equal(B,A) )
      & ( not_equal(A,B)
        | $equal(B,A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
    [] ).

cnf(169888880,plain,
    ( not_equal(A,B)
    | $equal(B,A) ),
    inference(rewrite,[status(thm)],[not_equal_defn]),
    [] ).

cnf(180623296,plain,
    ( ~ intersect(b,b)
    | $equal(empty_set,b) ),
    inference(resolution,[status(thm)],[169978224,169888880]),
    [] ).

fof(empty_defn,plain,
    ! [A,B] :
      ( ( ~ empty(A)
        | ~ member(B,A) )
      & ( empty(A)
        | member(c(A,B),A) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),
    [] ).

cnf(169912360,plain,
    ( empty(A)
    | member(c(A,B),A) ),
    inference(rewrite,[status(thm)],[empty_defn]),
    [] ).

cnf(180429240,plain,
    empty(empty_set),
    inference(resolution,[status(thm)],[169912360,169841448]),
    [] ).

cnf(180643288,plain,
    ( ~ intersect(b,b)
    | empty(b) ),
    inference(paramodulation,[status(thm)],[180623296,180429240,theory(equality)]),
    [] ).

cnf(169811488,plain,
    ( ~ not_equal(A,B)
    | ~ $equal(B,A) ),
    inference(rewrite,[status(thm)],[not_equal_defn]),
    [] ).

cnf(169988264,plain,
    ( not_equal(b,empty_set)
    | intersect(b,b) ),
    inference(rewrite,[status(thm)],[prove_th110]),
    [] ).

cnf(180580456,plain,
    ( ~ $equal(empty_set,b)
    | intersect(b,b) ),
    inference(resolution,[status(thm)],[169811488,169988264]),
    [] ).

cnf(180674544,plain,
    ( empty(b)
    | ~ $equal(empty_set,b) ),
    inference(resolution,[status(thm)],[180643288,180580456]),
    [] ).

cnf(169831296,plain,
    ( member(d_nn_1(A,B),A)
    | ~ intersect(A,B) ),
    inference(rewrite,[status(thm)],[intersect_defn]),
    [] ).

cnf(169918944,plain,
    ( ~ empty(A)
    | ~ member(B,A) ),
    inference(rewrite,[status(thm)],[empty_defn]),
    [] ).

cnf(180787248,plain,
    ( ~ intersect(A,B)
    | ~ empty(A) ),
    inference(resolution,[status(thm)],[169831296,169918944]),
    [] ).

cnf(180849536,plain,
    ~ $equal(empty_set,b),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[180674544,180787248,180580456]),
    [] ).

cnf(181081184,plain,
    member(d(b,empty_set,A),b),
    inference(resolution,[status(thm)],[180502392,180849536]),
    [] ).

cnf(181142888,plain,
    ~ empty(b),
    inference(resolution,[status(thm)],[181081184,169918944]),
    [] ).

cnf(181164560,plain,
    member(c(b,A),b),
    inference(resolution,[status(thm)],[181142888,169912360]),
    [] ).

cnf(181624320,plain,
    intersect(b,b),
    inference(resolution,[status(thm)],[169824616,181164560]),
    [] ).

cnf(180667392,plain,
    ( empty(b)
    | not_equal(b,empty_set) ),
    inference(resolution,[status(thm)],[180643288,169988264]),
    [] ).

cnf(180828408,plain,
    not_equal(b,empty_set),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[180667392,180787248,169988264]),
    [] ).

cnf(180856696,plain,
    ~ intersect(b,b),
    inference(resolution,[status(thm)],[180828408,169978224]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[181624320,180856696]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(intersect_defn,plain,(((member(d_nn_1(A,B),B)|~intersect(A,B))&(member(d_nn_1(A,B),A)|~intersect(A,B))&(intersect(A,B)|~member(D,A)|~member(D,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
% 
% cnf(169824616,plain,(intersect(A,B)|~member(D,A)|~member(D,B)),inference(rewrite,[status(thm)],[intersect_defn]),[]).
% 
% fof(equal_member_defn,plain,(((member(C,A)|~member(C,B)|~$equal(B,A))&(~member(C,A)|member(C,B)|~$equal(B,A))&(member(d(A,B,C),B)|~member(d(A,B,C),B)|$equal(B,A))&(~member(d(A,B,C),A)|~member(d(A,B,C),B)|$equal(B,A))&(member(d(A,B,C),B)|member(d(A,B,C),A)|$equal(B,A))&(~member(d(A,B,C),A)|member(d(A,B,C),A)|$equal(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
% 
% cnf(169856440,plain,(member(d(A,B,C),B)|member(d(A,B,C),A)|$equal(B,A)),inference(rewrite,[status(thm)],[equal_member_defn]),[]).
% 
% fof(empty_set_defn,plain,(~member(A,empty_set)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
% 
% cnf(169841448,plain,(~member(A,empty_set)),inference(rewrite,[status(thm)],[empty_set_defn]),[]).
% 
% cnf(180502392,plain,(member(d(A,empty_set,B),A)|$equal(empty_set,A)),inference(resolution,[status(thm)],[169856440,169841448]),[]).
% 
% fof(prove_th110,plain,(((not_equal(b,empty_set)|intersect(b,b))&(~intersect(b,b)|intersect(b,b))&(not_equal(b,empty_set)|~not_equal(b,empty_set))&(~intersect(b,b)|~not_equal(b,empty_set)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
% 
% cnf(169978224,plain,(~intersect(b,b)|~not_equal(b,empty_set)),inference(rewrite,[status(thm)],[prove_th110]),[]).
% 
% fof(not_equal_defn,plain,(((~not_equal(A,B)|~$equal(B,A))&(not_equal(A,B)|$equal(B,A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
% 
% cnf(169888880,plain,(not_equal(A,B)|$equal(B,A)),inference(rewrite,[status(thm)],[not_equal_defn]),[]).
% 
% cnf(180623296,plain,(~intersect(b,b)|$equal(empty_set,b)),inference(resolution,[status(thm)],[169978224,169888880]),[]).
% 
% fof(empty_defn,plain,(((~empty(A)|~member(B,A))&(empty(A)|member(c(A,B),A)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET628+3.tptp',unknown),[]).
% 
% cnf(169912360,plain,(empty(A)|member(c(A,B),A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
% 
% cnf(180429240,plain,(empty(empty_set)),inference(resolution,[status(thm)],[169912360,169841448]),[]).
% 
% cnf(180643288,plain,(~intersect(b,b)|empty(b)),inference(paramodulation,[status(thm)],[180623296,180429240,theory(equality)]),[]).
% 
% cnf(169811488,plain,(~not_equal(A,B)|~$equal(B,A)),inference(rewrite,[status(thm)],[not_equal_defn]),[]).
% 
% cnf(169988264,plain,(not_equal(b,empty_set)|intersect(b,b)),inference(rewrite,[status(thm)],[prove_th110]),[]).
% 
% cnf(180580456,plain,(~$equal(empty_set,b)|intersect(b,b)),inference(resolution,[status(thm)],[169811488,169988264]),[]).
% 
% cnf(180674544,plain,(empty(b)|~$equal(empty_set,b)),inference(resolution,[status(thm)],[180643288,180580456]),[]).
% 
% cnf(169831296,plain,(member(d_nn_1(A,B),A)|~intersect(A,B)),inference(rewrite,[status(thm)],[intersect_defn]),[]).
% 
% cnf(169918944,plain,(~empty(A)|~member(B,A)),inference(rewrite,[status(thm)],[empty_defn]),[]).
% 
% cnf(180787248,plain,(~intersect(A,B)|~empty(A)),inference(resolution,[status(thm)],[169831296,169918944]),[]).
% 
% cnf(180849536,plain,(~$equal(empty_set,b)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180674544,180787248,180580456]),[]).
% 
% cnf(181081184,plain,(member(d(b,empty_set,A),b)),inference(resolution,[status(thm)],[180502392,180849536]),[]).
% 
% cnf(181142888,plain,(~empty(b)),inference(resolution,[status(thm)],[181081184,169918944]),[]).
% 
% cnf(181164560,plain,(member(c(b,A),b)),inference(resolution,[status(thm)],[181142888,169912360]),[]).
% 
% cnf(181624320,plain,(intersect(b,b)),inference(resolution,[status(thm)],[169824616,181164560]),[]).
% 
% cnf(180667392,plain,(empty(b)|not_equal(b,empty_set)),inference(resolution,[status(thm)],[180643288,169988264]),[]).
% 
% cnf(180828408,plain,(not_equal(b,empty_set)),inference(forward_subsumption_resolution__resolution,[status(thm)],[180667392,180787248,169988264]),[]).
% 
% cnf(180856696,plain,(~intersect(b,b)),inference(resolution,[status(thm)],[180828408,169978224]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[181624320,180856696]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------