TSTP Solution File: SET847-2 by Faust---1.0

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%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET847-2 : TPTP v3.4.2. Released v3.2.0.
% 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 15:39:21 EDT 2009

% Result   : Unsatisfiable 0.8s
% Output   : Refutation 0.8s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   20 (   9 unt;   0 def)
%            Number of atoms       :   33 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   27 (  14   ~;  13   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   2 con; 0-3 aty)
%            Number of variables   :   47 (   2 sgn  18   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(cls_conjecture_0,plain,
    ! [A] : ~ c_in(A,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164170488,plain,
    ~ c_in(A,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

fof(cls_Zorn_Oequal__succ__Union_1,plain,
    ! [A,B] :
      ( ~ c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B)))
      | $equal(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B))) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164143008,plain,
    ( ~ c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B)))
    | $equal(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B))) ),
    inference(rewrite,[status(thm)],[cls_Zorn_Oequal__succ__Union_1]),
    [] ).

fof(cls_Zorn_OTFin__UnionI_0,plain,
    ! [A,B,C] :
      ( ~ c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))
      | c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C))) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164126888,plain,
    ( ~ c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))
    | c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C))) ),
    inference(rewrite,[status(thm)],[cls_Zorn_OTFin__UnionI_0]),
    [] ).

fof(cls_Set_Osubset__refl_0,plain,
    ! [A,B] : c_lessequals(A,A,tc_set(B)),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164099952,plain,
    c_lessequals(A,A,tc_set(B)),
    inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),
    [] ).

cnf(173965464,plain,
    c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B))),
    inference(resolution,[status(thm)],[164126888,164099952]),
    [] ).

cnf(190296672,plain,
    $equal(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B))),
    inference(resolution,[status(thm)],[164143008,173965464]),
    [] ).

fof(cls_Zorn_Osucc__not__equals_0,plain,
    ! [A,B,C] :
      ( ~ c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))
      | ~ $equal(c_zorn_osucc(B,A,C),A) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164162200,plain,
    ( ~ c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))
    | ~ $equal(c_zorn_osucc(B,A,C),A) ),
    inference(rewrite,[status(thm)],[cls_Zorn_Osucc__not__equals_0]),
    [] ).

fof(cls_Zorn_OTFin__chain__lemma4_0,plain,
    ! [A,B,C] :
      ( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
      | c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C))) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164132840,plain,
    ( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
    | c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C))) ),
    inference(rewrite,[status(thm)],[cls_Zorn_OTFin__chain__lemma4_0]),
    [] ).

cnf(174411096,plain,
    c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_ochain(A,B),tc_set(tc_set(B))),
    inference(resolution,[status(thm)],[173965464,164132840]),
    [] ).

fof(cls_Set_ODiffI_0,plain,
    ! [A,B,C,D] :
      ( ~ c_in(A,B,C)
      | c_in(A,D,C)
      | c_in(A,c_minus(B,D,tc_set(C)),C) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),
    [] ).

cnf(164067016,plain,
    ( ~ c_in(A,B,C)
    | c_in(A,D,C)
    | c_in(A,c_minus(B,D,tc_set(C)),C) ),
    inference(rewrite,[status(thm)],[cls_Set_ODiffI_0]),
    [] ).

cnf(174625088,plain,
    ( c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),C,tc_set(tc_set(B)))
    | c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_minus(c_zorn_ochain(A,B),C,tc_set(tc_set(tc_set(B)))),tc_set(tc_set(B))) ),
    inference(resolution,[status(thm)],[174411096,164067016]),
    [] ).

cnf(196568088,plain,
    c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_omaxchain(A,B),tc_set(tc_set(B))),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[190296672,164162200,174625088]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(resolution,[status(thm)],[164170488,196568088]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(cls_conjecture_0,plain,(~c_in(A,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164170488,plain,(~c_in(A,c_zorn_omaxchain(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% fof(cls_Zorn_Oequal__succ__Union_1,plain,(~c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B)))|$equal(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164143008,plain,(~c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B)))|$equal(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B)))),inference(rewrite,[status(thm)],[cls_Zorn_Oequal__succ__Union_1]),[]).
% 
% fof(cls_Zorn_OTFin__UnionI_0,plain,(~c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))|c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164126888,plain,(~c_lessequals(A,c_zorn_otfin(B,C),tc_set(tc_set(tc_set(C))))|c_in(c_union(A,tc_set(C)),c_zorn_otfin(B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OTFin__UnionI_0]),[]).
% 
% fof(cls_Set_Osubset__refl_0,plain,(c_lessequals(A,A,tc_set(B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164099952,plain,(c_lessequals(A,A,tc_set(B))),inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),[]).
% 
% cnf(173965464,plain,(c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_otfin(A,B),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[164126888,164099952]),[]).
% 
% cnf(190296672,plain,($equal(c_zorn_osucc(A,c_union(c_zorn_otfin(A,B),tc_set(B)),B),c_union(c_zorn_otfin(A,B),tc_set(B)))),inference(resolution,[status(thm)],[164143008,173965464]),[]).
% 
% fof(cls_Zorn_Osucc__not__equals_0,plain,(~c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))|~$equal(c_zorn_osucc(B,A,C),A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164162200,plain,(~c_in(A,c_minus(c_zorn_ochain(B,C),c_zorn_omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C)))|~$equal(c_zorn_osucc(B,A,C),A)),inference(rewrite,[status(thm)],[cls_Zorn_Osucc__not__equals_0]),[]).
% 
% fof(cls_Zorn_OTFin__chain__lemma4_0,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164132840,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|c_in(A,c_zorn_ochain(B,C),tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_OTFin__chain__lemma4_0]),[]).
% 
% cnf(174411096,plain,(c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_ochain(A,B),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[173965464,164132840]),[]).
% 
% fof(cls_Set_ODiffI_0,plain,(~c_in(A,B,C)|c_in(A,D,C)|c_in(A,c_minus(B,D,tc_set(C)),C)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET847-2.tptp',unknown),[]).
% 
% cnf(164067016,plain,(~c_in(A,B,C)|c_in(A,D,C)|c_in(A,c_minus(B,D,tc_set(C)),C)),inference(rewrite,[status(thm)],[cls_Set_ODiffI_0]),[]).
% 
% cnf(174625088,plain,(c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),C,tc_set(tc_set(B)))|c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_minus(c_zorn_ochain(A,B),C,tc_set(tc_set(tc_set(B)))),tc_set(tc_set(B)))),inference(resolution,[status(thm)],[174411096,164067016]),[]).
% 
% cnf(196568088,plain,(c_in(c_union(c_zorn_otfin(A,B),tc_set(B)),c_zorn_omaxchain(A,B),tc_set(tc_set(B)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[190296672,164162200,174625088]),[]).
% 
% cnf(contradiction,plain,$false,inference(resolution,[status(thm)],[164170488,196568088]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------