TSTP Solution File: SET844-2 by Faust---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Faust---1.0
% Problem  : SET844-2 : TPTP v3.4.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : faust %s

% Computer : art10.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 15:39:14 EDT 2009

% Result   : Unsatisfiable 0.1s
% Output   : Refutation 0.1s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   15 (  10 unt;   0 def)
%            Number of atoms       :   24 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (  11   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   21 (   1 sgn   9   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
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/SET844-2.tptp',unknown),
    [] ).

cnf(165863024,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/SET844-2.tptp',unknown),
    [] ).

cnf(165834776,plain,
    c_lessequals(A,A,tc_set(B)),
    inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),
    [] ).

cnf(178989496,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)],[165863024,165834776]),
    [] ).

fof(cls_conjecture_0,plain,
    c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),
    [] ).

cnf(165907648,plain,
    c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_0]),
    [] ).

fof(cls_Zorn_Oeq__succ__upper_0,plain,
    ! [A,B,C,D] :
      ( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
      | ~ c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))
      | ~ $equal(c_zorn_osucc(B,A,C),A)
      | c_lessequals(D,A,tc_set(tc_set(C))) ),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),
    [] ).

cnf(165898792,plain,
    ( ~ c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))
    | ~ c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))
    | ~ $equal(c_zorn_osucc(B,A,C),A)
    | c_lessequals(D,A,tc_set(tc_set(C))) ),
    inference(rewrite,[status(thm)],[cls_Zorn_Oeq__succ__upper_0]),
    [] ).

fof(cls_conjecture_1,plain,
    $equal(c_zorn_osucc(v_s,v_m,t_a),v_m),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),
    [] ).

cnf(165912608,plain,
    $equal(c_zorn_osucc(v_s,v_m,t_a),v_m),
    inference(rewrite,[status(thm)],[cls_conjecture_1]),
    [] ).

cnf(179012248,plain,
    ( ~ c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))
    | c_lessequals(A,v_m,tc_set(tc_set(t_a))) ),
    inference(forward_subsumption_resolution__resolution,[status(thm)],[165907648,165898792,165912608]),
    [] ).

fof(cls_conjecture_2,plain,
    ~ c_lessequals(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),
    [] ).

cnf(165920896,plain,
    ~ c_lessequals(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
    inference(rewrite,[status(thm)],[cls_conjecture_2]),
    [] ).

cnf(contradiction,plain,
    $false,
    inference(forward_subsumption_resolution__resolution,[status(thm)],[178989496,179012248,165920896]),
    [] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 0 seconds
% START OF PROOF SEQUENCE
% 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/SET844-2.tptp',unknown),[]).
% 
% cnf(165863024,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/SET844-2.tptp',unknown),[]).
% 
% cnf(165834776,plain,(c_lessequals(A,A,tc_set(B))),inference(rewrite,[status(thm)],[cls_Set_Osubset__refl_0]),[]).
% 
% cnf(178989496,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)],[165863024,165834776]),[]).
% 
% fof(cls_conjecture_0,plain,(c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),[]).
% 
% cnf(165907648,plain,(c_in(v_m,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_0]),[]).
% 
% fof(cls_Zorn_Oeq__succ__upper_0,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~$equal(c_zorn_osucc(B,A,C),A)|c_lessequals(D,A,tc_set(tc_set(C)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),[]).
% 
% cnf(165898792,plain,(~c_in(A,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~c_in(D,c_zorn_otfin(B,C),tc_set(tc_set(C)))|~$equal(c_zorn_osucc(B,A,C),A)|c_lessequals(D,A,tc_set(tc_set(C)))),inference(rewrite,[status(thm)],[cls_Zorn_Oeq__succ__upper_0]),[]).
% 
% fof(cls_conjecture_1,plain,($equal(c_zorn_osucc(v_s,v_m,t_a),v_m)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),[]).
% 
% cnf(165912608,plain,($equal(c_zorn_osucc(v_s,v_m,t_a),v_m)),inference(rewrite,[status(thm)],[cls_conjecture_1]),[]).
% 
% cnf(179012248,plain,(~c_in(A,c_zorn_otfin(v_s,t_a),tc_set(tc_set(t_a)))|c_lessequals(A,v_m,tc_set(tc_set(t_a)))),inference(forward_subsumption_resolution__resolution,[status(thm)],[165907648,165898792,165912608]),[]).
% 
% fof(cls_conjecture_2,plain,(~c_lessequals(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET844-2.tptp',unknown),[]).
% 
% cnf(165920896,plain,(~c_lessequals(c_union(c_zorn_otfin(v_s,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a)))),inference(rewrite,[status(thm)],[cls_conjecture_2]),[]).
% 
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[178989496,179012248,165920896]),[]).
% 
% END OF PROOF SEQUENCE
% 
%------------------------------------------------------------------------------