TSTP Solution File: SET074-7 by Faust---1.0

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%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET074-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% 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 15:27:12 EDT 2009

% Result   : Unsatisfiable 0.3s
% Output   : Refutation 0.3s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   15 (   9 unt;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   19 (  11   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   17 (   3 sgn   8   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_corollary_to_unordered_pair_axiom2_1,plain,
    member(y,universal_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),
    [] ).

cnf(170110392,plain,
    member(y,universal_class),
    inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom2_1]),
    [] ).

fof(unordered_pair3,plain,
    ! [A,B] :
      ( ~ member(A,universal_class)
      | member(A,unordered_pair(B,A)) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),
    [] ).

cnf(169065256,plain,
    ( ~ member(A,universal_class)
    | member(A,unordered_pair(B,A)) ),
    inference(rewrite,[status(thm)],[unordered_pair3]),
    [] ).

fof(existence_of_null_class,plain,
    ! [A] : ~ member(A,null_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),
    [] ).

cnf(169987896,plain,
    ~ member(A,null_class),
    inference(rewrite,[status(thm)],[existence_of_null_class]),
    [] ).

fof(subclass_members,plain,
    ! [A,B,C] :
      ( ~ subclass(A,B)
      | ~ member(C,A)
      | member(C,B) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),
    [] ).

cnf(168973480,plain,
    ( ~ subclass(A,B)
    | ~ member(C,A)
    | member(C,B) ),
    inference(rewrite,[status(thm)],[subclass_members]),
    [] ).

fof(equal_implies_subclass2,plain,
    ! [B,A] :
      ( ~ $equal(B,A)
      | subclass(B,A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),
    [] ).

cnf(169025488,plain,
    ( ~ $equal(B,A)
    | subclass(B,A) ),
    inference(rewrite,[status(thm)],[equal_implies_subclass2]),
    [] ).

fof(prove_corollary_to_unordered_pair_axiom2_2,plain,
    $equal(unordered_pair(x,y),null_class),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),
    [] ).

cnf(170114128,plain,
    $equal(unordered_pair(x,y),null_class),
    inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom2_2]),
    [] ).

cnf(182136160,plain,
    subclass(unordered_pair(x,y),null_class),
    inference(resolution,[status(thm)],[169025488,170114128]),
    [] ).

cnf(185364896,plain,
    ~ member(A,unordered_pair(x,y)),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[169987896,168973480,182136160]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[170110392,169065256,185364896]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_corollary_to_unordered_pair_axiom2_1,plain,(member(y,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),[]).
% 
% cnf(170110392,plain,(member(y,universal_class)),inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom2_1]),[]).
% 
% fof(unordered_pair3,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),[]).
% 
% cnf(169065256,plain,(~member(A,universal_class)|member(A,unordered_pair(B,A))),inference(rewrite,[status(thm)],[unordered_pair3]),[]).
% 
% fof(existence_of_null_class,plain,(~member(A,null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),[]).
% 
% cnf(169987896,plain,(~member(A,null_class)),inference(rewrite,[status(thm)],[existence_of_null_class]),[]).
% 
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),[]).
% 
% cnf(168973480,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
% 
% fof(equal_implies_subclass2,plain,(~$equal(B,A)|subclass(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),[]).
% 
% cnf(169025488,plain,(~$equal(B,A)|subclass(B,A)),inference(rewrite,[status(thm)],[equal_implies_subclass2]),[]).
% 
% fof(prove_corollary_to_unordered_pair_axiom2_2,plain,($equal(unordered_pair(x,y),null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET074-7.tptp',unknown),[]).
% 
% cnf(170114128,plain,($equal(unordered_pair(x,y),null_class)),inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom2_2]),[]).
% 
% cnf(182136160,plain,(subclass(unordered_pair(x,y),null_class)),inference(resolution,[status(thm)],[169025488,170114128]),[]).
% 
% cnf(185364896,plain,(~member(A,unordered_pair(x,y))),inference(forward_subsumption_resolution__resolution,[status(thm)],[169987896,168973480,182136160]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[170110392,169065256,185364896]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------