%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET008-1 : TPTP v3.4.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art03.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 15:22:56 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (   9 unt;   0 def)
%            Number of atoms       :   33 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   27 (  12   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   27 (   2 sgn  11   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(intersection_axiom2,plain,
    ! [A,B,C] :
      ( member(h(A,B,C),C)
      | intersection(A,B,C)
      | member(h(A,B,C),B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
    [] ).

cnf(161774536,plain,
    ( member(h(A,B,C),C)
    | intersection(A,B,C)
    | member(h(A,B,C),B) ),
    inference(rewrite,[status(thm)],[intersection_axiom2]),
    [] ).

fof(prove_aI_bDa_is_empty,plain,
    ! [A] : ~ member(A,ai_bda),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
    [] ).

cnf(161855992,plain,
    ~ member(A,ai_bda),
    inference(rewrite,[status(thm)],[prove_aI_bDa_is_empty]),
    [] ).

cnf(172547944,plain,
    ( intersection(A,B,ai_bda)
    | member(h(A,B,ai_bda),B) ),
    inference(resolution,[status(thm)],[161774536,161855992]),
    [] ).

fof(a_intersection_bDa,plain,
    ~ intersection(a,bda,ai_bda),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
    [] ).

cnf(161847792,plain,
    ~ intersection(a,bda,ai_bda),
    inference(rewrite,[status(thm)],[a_intersection_bDa]),
    [] ).

cnf(172725448,plain,
    member(h(a,bda,ai_bda),bda),
    inference(resolution,[status(thm)],[172547944,161847792]),
    [] ).

fof(not_member_of_difference,plain,
    ! [A,B,C,D] :
      ( ~ member(A,B)
      | ~ member(A,C)
      | ~ difference(D,B,C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
    [] ).

cnf(161802456,plain,
    ( ~ member(A,B)
    | ~ member(A,C)
    | ~ difference(D,B,C) ),
    inference(rewrite,[status(thm)],[not_member_of_difference]),
    [] ).

fof(b_minus_a,plain,
    difference(b,a,bda),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
    [] ).

cnf(161843672,plain,
    difference(b,a,bda),
    inference(rewrite,[status(thm)],[b_minus_a]),
    [] ).

cnf(172340664,plain,
    ( ~ member(A,a)
    | ~ member(A,bda) ),
    inference(resolution,[status(thm)],[161802456,161843672]),
    [] ).

fof(intersection_axiom1,plain,
    ! [A,B,C] :
      ( member(h(A,B,C),C)
      | intersection(A,B,C)
      | member(h(A,B,C),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),
    [] ).

cnf(161770208,plain,
    ( member(h(A,B,C),C)
    | intersection(A,B,C)
    | member(h(A,B,C),A) ),
    inference(rewrite,[status(thm)],[intersection_axiom1]),
    [] ).

cnf(172514984,plain,
    ( intersection(A,B,ai_bda)
    | member(h(A,B,ai_bda),A) ),
    inference(resolution,[status(thm)],[161770208,161855992]),
    [] ).

cnf(172711768,plain,
    member(h(a,bda,ai_bda),a),
    inference(resolution,[status(thm)],[172514984,161847792]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[172725448,172340664,172711768]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% fof(intersection_axiom2,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
% 
% cnf(161774536,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B)),inference(rewrite,[status(thm)],[intersection_axiom2]),[]).
% 
% fof(prove_aI_bDa_is_empty,plain,(~member(A,ai_bda)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
% 
% cnf(161855992,plain,(~member(A,ai_bda)),inference(rewrite,[status(thm)],[prove_aI_bDa_is_empty]),[]).
% 
% cnf(172547944,plain,(intersection(A,B,ai_bda)|member(h(A,B,ai_bda),B)),inference(resolution,[status(thm)],[161774536,161855992]),[]).
% 
% fof(a_intersection_bDa,plain,(~intersection(a,bda,ai_bda)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
% 
% cnf(161847792,plain,(~intersection(a,bda,ai_bda)),inference(rewrite,[status(thm)],[a_intersection_bDa]),[]).
% 
% cnf(172725448,plain,(member(h(a,bda,ai_bda),bda)),inference(resolution,[status(thm)],[172547944,161847792]),[]).
% 
% fof(not_member_of_difference,plain,(~member(A,B)|~member(A,C)|~difference(D,B,C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
% 
% cnf(161802456,plain,(~member(A,B)|~member(A,C)|~difference(D,B,C)),inference(rewrite,[status(thm)],[not_member_of_difference]),[]).
% 
% fof(b_minus_a,plain,(difference(b,a,bda)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
% 
% cnf(161843672,plain,(difference(b,a,bda)),inference(rewrite,[status(thm)],[b_minus_a]),[]).
% 
% cnf(172340664,plain,(~member(A,a)|~member(A,bda)),inference(resolution,[status(thm)],[161802456,161843672]),[]).
% 
% fof(intersection_axiom1,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET008-1.tptp',unknown),[]).
% 
% cnf(161770208,plain,(member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A)),inference(rewrite,[status(thm)],[intersection_axiom1]),[]).
% 
% cnf(172514984,plain,(intersection(A,B,ai_bda)|member(h(A,B,ai_bda),A)),inference(resolution,[status(thm)],[161770208,161855992]),[]).
% 
% cnf(172711768,plain,(member(h(a,bda,ai_bda),a)),inference(resolution,[status(thm)],[172514984,161847792]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[172725448,172340664,172711768]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------