%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET027+3 : TPTP v3.4.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art01.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 15:24:44 EDT 2009

% Result   : Theorem 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   15 (   8 unt;   0 def)
%            Number of atoms       :   29 (   0 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   25 (  11   ~;  10   |;   4   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :   18 (   6 sgn   3   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(subset_defn,plain,
    ! [A,B,C] :
      ( ( ~ subset(A,B)
        | ~ member(C,A)
        | member(C,B) )
      & ( ~ member(d(A,B,C),B)
        | subset(A,B) )
      & ( member(d(A,B,C),A)
        | subset(A,B) ) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET027+3.tptp',unknown),
    [] ).

cnf(173514768,plain,
    ( ~ subset(A,B)
    | ~ member(C,A)
    | member(C,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

fof(prove_transitivity_of_subset,plain,
    ( subset(b,c)
    & subset(c,d)
    & ~ subset(b,d) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET027+3.tptp',unknown),
    [] ).

cnf(173588440,plain,
    subset(b,c),
    inference(rewrite,[status(thm)],[prove_transitivity_of_subset]),
    [] ).

cnf(186694232,plain,
    ( ~ member(A,b)
    | member(A,c) ),
    inference(resolution,[status(thm)],[173514768,173588440]),
    [] ).

cnf(173492904,plain,
    ( member(d(A,B,C),A)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

cnf(173570152,plain,
    ~ subset(b,d),
    inference(rewrite,[status(thm)],[prove_transitivity_of_subset]),
    [] ).

cnf(186614008,plain,
    member(d(b,d,A),b),
    inference(resolution,[status(thm)],[173492904,173570152]),
    [] ).

cnf(186859296,plain,
    member(d(b,d,A),c),
    inference(resolution,[status(thm)],[186694232,186614008]),
    [] ).

cnf(173581416,plain,
    subset(c,d),
    inference(rewrite,[status(thm)],[prove_transitivity_of_subset]),
    [] ).

cnf(186674848,plain,
    ( ~ member(A,c)
    | member(A,d) ),
    inference(resolution,[status(thm)],[173514768,173581416]),
    [] ).

cnf(186943344,plain,
    member(d(b,d,A),d),
    inference(resolution,[status(thm)],[186859296,186674848]),
    [] ).

cnf(173499480,plain,
    ( ~ member(d(A,B,C),B)
    | subset(A,B) ),
    inference(rewrite,[status(thm)],[subset_defn]),
    [] ).

cnf(186627616,plain,
    ~ member(d(b,d,A),d),
    inference(resolution,[status(thm)],[173499480,173570152]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[186943344,186627616]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(subset_defn,plain,(((~subset(A,B)|~member(C,A)|member(C,B))&(~member(d(A,B,C),B)|subset(A,B))&(member(d(A,B,C),A)|subset(A,B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET027+3.tptp',unknown),[]).
% 
% cnf(173514768,plain,(~subset(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% fof(prove_transitivity_of_subset,plain,((subset(b,c)&subset(c,d)&~subset(b,d))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET027+3.tptp',unknown),[]).
% 
% cnf(173588440,plain,(subset(b,c)),inference(rewrite,[status(thm)],[prove_transitivity_of_subset]),[]).
% 
% cnf(186694232,plain,(~member(A,b)|member(A,c)),inference(resolution,[status(thm)],[173514768,173588440]),[]).
% 
% cnf(173492904,plain,(member(d(A,B,C),A)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% cnf(173570152,plain,(~subset(b,d)),inference(rewrite,[status(thm)],[prove_transitivity_of_subset]),[]).
% 
% cnf(186614008,plain,(member(d(b,d,A),b)),inference(resolution,[status(thm)],[173492904,173570152]),[]).
% 
% cnf(186859296,plain,(member(d(b,d,A),c)),inference(resolution,[status(thm)],[186694232,186614008]),[]).
% 
% cnf(173581416,plain,(subset(c,d)),inference(rewrite,[status(thm)],[prove_transitivity_of_subset]),[]).
% 
% cnf(186674848,plain,(~member(A,c)|member(A,d)),inference(resolution,[status(thm)],[173514768,173581416]),[]).
% 
% cnf(186943344,plain,(member(d(b,d,A),d)),inference(resolution,[status(thm)],[186859296,186674848]),[]).
% 
% cnf(173499480,plain,(~member(d(A,B,C),B)|subset(A,B)),inference(rewrite,[status(thm)],[subset_defn]),[]).
% 
% cnf(186627616,plain,(~member(d(b,d,A),d)),inference(resolution,[status(thm)],[173499480,173570152]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[186943344,186627616]),[]).
% 
% END OF PROOF SEQUENCE
% faust: ../JJParser/Signature.c:39: void FreeSignatureList(SymbolNodeType**): Assertion `(*Symbols)->NumberOfUses == 0' failed.
% 
%------------------------------------------------------------------------------