SET007 Axioms: SET007+880.ax
%------------------------------------------------------------------------------
% File : SET007+880 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Construction of Gr"obner Bases: Avoiding S-Polynomials
% Version : [Urb08] axioms.
% English : Buchberger's First Criterium
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : groeb_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 78 ( 0 unt; 0 def)
% Number of atoms : 1737 ( 53 equ)
% Maximal formula atoms : 52 ( 22 avg)
% Number of connectives : 1747 ( 88 ~; 7 |;1257 &)
% ( 4 <=>; 391 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 16 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 55 ( 54 usr; 0 prp; 1-6 aty)
% Number of functors : 46 ( 46 usr; 5 con; 0-5 aty)
% Number of variables : 393 ( 392 !; 1 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_groeb_3,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> v1_finset_1(k12_polynom1(k14_polynom1(A),B,C)) ) ).
fof(fc2_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& l2_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A))) )
=> ( v1_relat_1(k2_groeb_3(A,B,C,D))
& v1_funct_1(k2_groeb_3(A,B,C,D))
& v1_funct_2(k2_groeb_3(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k2_groeb_3(A,B,C,D),k14_polynom1(A),B) ) ) ).
fof(fc3_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_relat_1(k5_groeb_3(A,B,C,D,np__0))
& v1_funct_1(k5_groeb_3(A,B,C,D,np__0))
& v1_funct_2(k5_groeb_3(A,B,C,D,np__0),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k5_groeb_3(A,B,C,D,np__0),k14_polynom1(A),C)
& v3_polynom7(k5_groeb_3(A,B,C,D,np__0),A,C) ) ) ).
fof(fc4_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_relat_1(k5_groeb_3(A,B,C,D,np__1))
& v1_funct_1(k5_groeb_3(A,B,C,D,np__1))
& v1_funct_2(k5_groeb_3(A,B,C,D,np__1),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k5_groeb_3(A,B,C,D,np__1),k14_polynom1(A),C)
& v1_polynom7(k5_groeb_3(A,B,C,D,np__1),A,C)
& v3_polynom7(k5_groeb_3(A,B,C,D,np__1),A,C) ) ) ).
fof(fc5_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_relat_1(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))))
& v1_funct_1(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))))
& v1_funct_2(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))),k14_polynom1(A),C)
& v3_polynom7(k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))),A,C) ) ) ).
fof(t1_groeb_3,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> k1_groeb_2(A,k9_polynom1(A,B,C),C) = B ) ) ).
fof(t2_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r1_termord(A,B,C,D)
=> r1_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,E)) ) ) ) ) ) ) ).
fof(t3_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( ( r1_termord(A,B,C,D)
& r2_termord(A,B,D,E) )
=> r2_termord(A,B,C,E) ) ) ) ) ) ) ).
fof(t4_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_termord(A,B,C,D)
=> r2_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,E)) ) ) ) ) ) ) ).
fof(t5_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( ( r2_termord(A,B,C,D)
& r1_termord(A,B,E,F) )
=> r2_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,F)) ) ) ) ) ) ) ) ).
fof(t6_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( ( r1_termord(A,B,C,D)
& r2_termord(A,B,E,F) )
=> r2_termord(A,B,k9_polynom1(A,C,E),k9_polynom1(A,D,F)) ) ) ) ) ) ) ) ).
fof(t7_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& v2_vectsp_2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v1_polynom7(C,A,B)
& v3_polynom7(C,A,B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v1_polynom7(D,A,B)
& v3_polynom7(D,A,B)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k2_polynom7(A,B,k28_polynom1(A,B,C,D)) = k9_polynom1(A,k2_polynom7(A,B,C),k2_polynom7(A,B,D)) ) ) ) ) ).
fof(t8_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& v2_vectsp_2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v1_polynom7(D,A,B)
& v3_polynom7(D,A,B)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(E,k12_polynom1(k14_polynom1(A),B,C))
<=> r2_hidden(k9_polynom1(A,k2_polynom7(A,B,D),E),k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,D,C))) ) ) ) ) ) ) ).
fof(t10_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& v1_algstr_1(B)
& v2_vectsp_2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v1_polynom7(D,A,B)
& v3_polynom7(D,A,B)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k4_card_1(k12_polynom1(k14_polynom1(A),B,C)) = k4_card_1(k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,D,C))) ) ) ) ) ).
fof(t11_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> k6_termord(A,B,C,k26_polynom1(A,C)) = k26_polynom1(A,C) ) ) ) ).
fof(t12_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(D,k14_polynom1(A),B)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( k25_polynom1(A,B,C,D) = k26_polynom1(A,B)
=> C = D ) ) ) ) ) ).
fof(t13_groeb_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> k24_polynom1(A,B,k26_polynom1(A,B)) = k26_polynom1(A,B) ) ).
fof(t14_groeb_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> k25_polynom1(A,B,k26_polynom1(A,B),C) = k24_polynom1(A,B,C) ) ) ).
fof(t15_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k25_polynom1(A,C,D,k6_termord(A,B,C,D)) = k5_termord(A,B,C,D) ) ) ) ) ).
fof(d1_groeb_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
=> k2_groeb_3(A,B,C,D) = k1_funct_4(C,k2_pre_circ(k4_xboole_0(k12_polynom1(k14_polynom1(A),B,C),D),k1_rlvect_1(B))) ) ) ) ).
fof(t16_groeb_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
=> ( k12_polynom1(k14_polynom1(A),B,k2_groeb_3(A,B,C,D)) = k3_xboole_0(k12_polynom1(k14_polynom1(A),B,C),D)
& ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(E,k12_polynom1(k14_polynom1(A),B,k2_groeb_3(A,B,C,D)))
=> k15_polynom1(A,B,k2_groeb_3(A,B,C,D),E) = k15_polynom1(A,B,C,E) ) ) ) ) ) ) ).
fof(t17_groeb_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
=> r1_tarski(k12_polynom1(k14_polynom1(A),B,k2_groeb_3(A,B,C,D)),k12_polynom1(k14_polynom1(A),B,C)) ) ) ) ).
fof(t18_groeb_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ( k2_groeb_3(A,B,C,k12_polynom1(k14_polynom1(A),B,C)) = C
& k2_groeb_3(A,B,C,k1_subset_1(k14_polynom1(A))) = k26_polynom1(A,B) ) ) ) ).
fof(d2_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [F] :
( ( v1_finset_1(F)
& m1_subset_1(F,k1_zfmisc_1(k14_polynom1(A))) )
=> ( F = k3_groeb_3(A,B,C,D,E)
<=> ( r1_tarski(F,k12_polynom1(k14_polynom1(A),C,D))
& k4_card_1(F) = E
& ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ! [H] :
( ( v7_seqm_3(H)
& v1_polynom1(H)
& m1_pboole(H,A) )
=> ( ( r2_hidden(G,F)
& r2_hidden(H,k12_polynom1(k14_polynom1(A),C,D))
& r1_termord(A,B,G,H) )
=> r2_hidden(H,F) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k4_groeb_3(A,B,C,D,E) = k4_xboole_0(k12_polynom1(k14_polynom1(A),C,D),k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) ).
fof(t19_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ( k2_xboole_0(k3_groeb_3(A,B,C,D,E),k4_groeb_3(A,B,C,D,E)) = k12_polynom1(k14_polynom1(A),C,D)
& k3_xboole_0(k3_groeb_3(A,B,C,D,E),k4_groeb_3(A,B,C,D,E)) = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t20_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( ( r2_hidden(F,k3_groeb_3(A,B,C,D,E))
& r2_hidden(G,k4_groeb_3(A,B,C,D,E)) )
=> r2_termord(A,B,G,F) ) ) ) ) ) ) ) ) ) ).
fof(t21_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k3_groeb_3(A,B,C,D,np__0) = k1_xboole_0
& k4_groeb_3(A,B,C,D,np__0) = k12_polynom1(k14_polynom1(A),C,D) ) ) ) ) ) ).
fof(t22_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k3_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = k12_polynom1(k14_polynom1(A),C,D)
& k4_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = k1_xboole_0 ) ) ) ) ) ).
fof(t23_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) )
=> r2_hidden(k3_termord(A,B,C,D),k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(t24_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ( r1_tarski(k4_groeb_3(A,B,C,D,E),k12_polynom1(k14_polynom1(A),C,D))
& k4_card_1(k4_groeb_3(A,B,C,D,E)) = k5_real_1(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
& ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( ( r2_hidden(F,k4_groeb_3(A,B,C,D,E))
& r2_hidden(G,k12_polynom1(k14_polynom1(A),C,D))
& r1_termord(A,B,G,F) )
=> r2_hidden(G,k4_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k5_groeb_3(A,B,C,D,E) = k2_groeb_3(A,C,D,k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) ).
fof(d5_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k6_groeb_3(A,B,C,D,E) = k2_groeb_3(A,C,D,k4_groeb_3(A,B,C,D,E)) ) ) ) ) ) ).
fof(t25_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ( k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)) = k3_groeb_3(A,B,C,D,E)
& k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)) = k4_groeb_3(A,B,C,D,E) ) ) ) ) ) ) ) ).
fof(t26_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ( r1_tarski(k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,D))
& r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ) ) ) ).
fof(t27_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D))) ) ) ) ) ) ) ).
fof(t28_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D))
=> ( ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)))
| r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E))) )
& ~ r2_hidden(F,k3_xboole_0(k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)))) ) ) ) ) ) ) ) ) ) ).
fof(t29_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)))
& r2_hidden(G,k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E))) )
=> r2_termord(A,B,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t30_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) )
=> r2_hidden(k3_termord(A,B,C,D),k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) ).
fof(t31_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)))
=> ( k15_polynom1(A,C,k6_groeb_3(A,B,C,D,E),F) = k15_polynom1(A,C,D,F)
& k15_polynom1(A,C,k5_groeb_3(A,B,C,D,E),F) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) ).
fof(t32_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k5_groeb_3(A,B,C,D,E)))
=> ( k15_polynom1(A,C,k5_groeb_3(A,B,C,D,E),F) = k15_polynom1(A,C,D,F)
& k15_polynom1(A,C,k6_groeb_3(A,B,C,D,E),F) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) ).
fof(t33_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(E,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> k22_polynom1(A,C,k5_groeb_3(A,B,C,D,E),k6_groeb_3(A,B,C,D,E)) = D ) ) ) ) ) ) ).
fof(t34_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k5_groeb_3(A,B,C,D,np__0) = k26_polynom1(A,C)
& k6_groeb_3(A,B,C,D,np__0) = D ) ) ) ) ) ).
fof(t35_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k5_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = D
& k6_groeb_3(A,B,C,D,k4_card_1(k12_polynom1(k14_polynom1(A),C,D))) = k26_polynom1(A,C) ) ) ) ) ) ).
fof(t36_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( k5_groeb_3(A,B,C,D,np__1) = k5_termord(A,B,C,D)
& k6_groeb_3(A,B,C,D,np__1) = k6_termord(A,B,C,D) ) ) ) ) ) ).
fof(t37_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( E = k5_real_1(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),np__1)
=> ( v1_funct_1(k6_groeb_3(A,B,C,D,E))
& v1_funct_2(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
& v1_polynom7(k6_groeb_3(A,B,C,D,E),A,C)
& v3_polynom7(k6_groeb_3(A,B,C,D,E),A,C)
& m2_relset_1(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) ) ) ) ) ) ).
fof(t38_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
=> r1_termord(A,B,k3_termord(A,B,C,k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1))),k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) ).
fof(t39_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(E,np__0)
& ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
& ~ r2_termord(A,B,k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E)),k3_termord(A,B,C,D)) ) ) ) ) ) ) ).
fof(t40_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v1_polynom7(E,A,C)
& v3_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(F,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( r2_hidden(k9_polynom1(A,k2_polynom7(A,C,E),G),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,k28_polynom1(A,C,E,D),F)))
<=> r2_hidden(G,k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,F))) ) ) ) ) ) ) ) ) ) ).
fof(t41_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
=> r1_tarski(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1))),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) ).
fof(t42_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
=> k4_xboole_0(k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,E)),k12_polynom1(k14_polynom1(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1)))) = k1_tarski(k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) ).
fof(t43_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& ~ v3_realset2(C)
& l1_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k4_card_1(k12_polynom1(k14_polynom1(A),C,D)),E)
=> k6_groeb_3(A,B,C,D,k1_nat_1(E,np__1)) = k6_termord(A,B,C,k6_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) ).
fof(t44_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v1_polynom7(E,A,C)
& v3_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_xreal_0(F,k4_card_1(k12_polynom1(k14_polynom1(A),C,D)))
=> k6_groeb_3(A,B,C,k28_polynom1(A,C,E,D),F) = k28_polynom1(A,C,E,k6_groeb_3(A,B,C,D,F)) ) ) ) ) ) ) ) ).
fof(t45_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( r4_polyred(A,B,C,D,F,E)
=> r4_polyred(A,B,C,k24_polynom1(A,C,D),F,k24_polynom1(A,C,E)) ) ) ) ) ) ) ) ).
fof(t46_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(G,k14_polynom1(A),C)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r5_polyred(A,B,C,D,E,k1_groeb_1(A,C,G))
& ! [H] :
( ( v7_seqm_3(H)
& v1_polynom1(H)
& m1_pboole(H,A) )
=> ~ ( r2_hidden(H,k12_polynom1(k14_polynom1(A),C,F))
& r3_polynom1(A,k3_termord(A,B,C,G),H) ) ) )
=> r5_polyred(A,B,C,k23_polynom1(A,C,D,F),k23_polynom1(A,C,E,F),k1_groeb_1(A,C,G)) ) ) ) ) ) ) ) ) ).
fof(t47_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> r5_polyred(A,B,C,k29_polynom1(A,C,D,E),k29_polynom1(A,C,k6_termord(A,B,C,D),E),k1_groeb_1(A,C,E)) ) ) ) ) ) ).
fof(t48_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( k15_polynom1(A,C,F,k3_termord(A,B,C,k29_polynom1(A,C,D,E))) = k1_rlvect_1(C)
=> r5_polyred(A,B,C,k23_polynom1(A,C,k29_polynom1(A,C,D,E),F),k23_polynom1(A,C,k29_polynom1(A,C,k6_termord(A,B,C,D),E),F),k1_groeb_1(A,C,E)) ) ) ) ) ) ) ) ).
fof(t49_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( r1_rewrite1(k3_polyred(A,B,C,D),E,F)
=> r1_rewrite1(k3_polyred(A,B,C,D),k24_polynom1(A,C,E),k24_polynom1(A,C,F)) ) ) ) ) ) ) ) ).
fof(t50_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(G,k14_polynom1(A),C)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,G)),D,E)
& ! [H] :
( ( v7_seqm_3(H)
& v1_polynom1(H)
& m1_pboole(H,A) )
=> ~ ( r2_hidden(H,k12_polynom1(k14_polynom1(A),C,F))
& r3_polynom1(A,k3_termord(A,B,C,G),H) ) ) )
=> r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,G)),k23_polynom1(A,C,D,F),k23_polynom1(A,C,E,F)) ) ) ) ) ) ) ) ) ).
fof(t51_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,E)),k29_polynom1(A,C,D,E),k26_polynom1(A,C)) ) ) ) ) ) ).
fof(t52_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ~ ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,D)))
& r2_hidden(G,k12_polynom1(k14_polynom1(A),C,k6_termord(A,B,C,E)))
& k9_polynom1(A,k3_termord(A,B,C,D),G) = k9_polynom1(A,k3_termord(A,B,C,E),F) ) ) ) ) ) ) ) ) ) ).
fof(t53_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
=> k3_groeb_2(A,B,C,D,E) = k25_polynom1(A,C,k29_polynom1(A,C,k5_termord(A,B,C,E),k6_termord(A,B,C,D)),k29_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,E))) ) ) ) ) ) ) ).
fof(t54_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
=> k3_groeb_2(A,B,C,D,E) = k25_polynom1(A,C,k29_polynom1(A,C,k6_termord(A,B,C,D),E),k29_polynom1(A,C,k6_termord(A,B,C,E),D)) ) ) ) ) ) ) ).
fof(t55_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r1_groeb_2(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
& v1_polynom7(k6_termord(A,B,C,D),A,C)
& v1_polynom7(k6_termord(A,B,C,E),A,C) )
=> r1_rewrite1(k3_polyred(A,B,C,k1_groeb_1(A,C,D)),k25_polynom1(A,C,k29_polynom1(A,C,k5_termord(A,B,C,E),k6_termord(A,B,C,D)),k29_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,E))),k29_polynom1(A,C,E,k6_termord(A,B,C,D))) ) ) ) ) ) ) ).
fof(t56_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
=> r1_rewrite1(k3_polyred(A,B,C,k1_groeb_3(A,C,D,E)),k3_groeb_2(A,B,C,D,E),k26_polynom1(A,C)) ) ) ) ) ) ) ).
fof(t57_groeb_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( r1_groeb_1(A,B,C,D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r2_hidden(E,D)
& r2_hidden(F,D) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
| r1_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),k26_polynom1(A,C)) ) ) ) ) ) ) ) ) ) ).
fof(t58_groeb_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r2_hidden(E,D)
& r2_hidden(F,D) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
| r1_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),k26_polynom1(A,C)) ) ) ) )
=> ( r2_hidden(k26_polynom1(A,C),D)
| ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(G,k14_polynom1(A),C)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r2_hidden(E,D)
& r2_hidden(F,D)
& r4_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),G) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
| G = k26_polynom1(A,C) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t59_groeb_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v2_bagorder(B,A)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(E,k14_polynom1(A),C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(F,k14_polynom1(A),C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(G,k14_polynom1(A),C)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
=> ( ( r2_hidden(E,D)
& r2_hidden(F,D)
& r4_rewrite1(k3_polyred(A,B,C,D),k3_groeb_2(A,B,C,E,F),G) )
=> ( r1_groeb_2(A,k3_termord(A,B,C,E),k3_termord(A,B,C,F))
| G = k26_polynom1(A,C) ) ) ) ) )
=> ( r2_hidden(k26_polynom1(A,C),D)
| r1_groeb_1(A,B,C,D) ) ) ) ) ) ) ).
fof(dt_k1_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(D,k14_polynom1(A),B)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k1_groeb_3(A,B,C,D))
& v1_finset_1(k1_groeb_3(A,B,C,D))
& m1_subset_1(k1_groeb_3(A,B,C,D),k1_zfmisc_1(u1_struct_0(k30_polynom1(A,B)))) ) ) ).
fof(commutativity_k1_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(D,k14_polynom1(A),B)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k1_groeb_3(A,B,C,D) = k1_groeb_3(A,B,D,C) ) ).
fof(redefinition_k1_groeb_3,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(D,k14_polynom1(A),B)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k1_groeb_3(A,B,C,D) = k2_tarski(C,D) ) ).
fof(dt_k2_groeb_3,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A))) )
=> ( v1_funct_1(k2_groeb_3(A,B,C,D))
& v1_funct_2(k2_groeb_3(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k2_groeb_3(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(dt_k3_groeb_3,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C))
& m1_subset_1(E,k5_numbers) )
=> ( v1_finset_1(k3_groeb_3(A,B,C,D,E))
& m1_subset_1(k3_groeb_3(A,B,C,D,E),k1_zfmisc_1(k14_polynom1(A))) ) ) ).
fof(dt_k4_groeb_3,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C))
& m1_subset_1(E,k5_numbers) )
=> ( v1_finset_1(k4_groeb_3(A,B,C,D,E))
& m1_subset_1(k4_groeb_3(A,B,C,D,E),k1_zfmisc_1(k14_polynom1(A))) ) ) ).
fof(dt_k5_groeb_3,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C))
& m1_subset_1(E,k5_numbers) )
=> ( v1_funct_1(k5_groeb_3(A,B,C,D,E))
& v1_funct_2(k5_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k5_groeb_3(A,B,C,D,E),k14_polynom1(A),C)
& m2_relset_1(k5_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) ).
fof(dt_k6_groeb_3,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& l1_rlvect_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(A),C)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C))
& m1_subset_1(E,k5_numbers) )
=> ( v1_funct_1(k6_groeb_3(A,B,C,D,E))
& v1_funct_2(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),C)
& m2_relset_1(k6_groeb_3(A,B,C,D,E),k14_polynom1(A),u1_struct_0(C)) ) ) ).
fof(t9_groeb_3,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& v2_vectsp_2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& v1_polynom7(D,A,B)
& v3_polynom7(D,A,B)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k12_polynom1(k14_polynom1(A),B,k28_polynom1(A,B,D,C)) = a_4_0_groeb_3(A,B,C,D) ) ) ) ) ).
fof(fraenkel_a_4_0_groeb_3,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(B)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v2_group_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& v2_vectsp_2(C)
& l3_vectsp_1(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(B),u1_struct_0(C))
& v2_polynom1(D,k14_polynom1(B),C)
& m2_relset_1(D,k14_polynom1(B),u1_struct_0(C))
& v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(B),u1_struct_0(C))
& v1_polynom7(E,B,C)
& v3_polynom7(E,B,C)
& m2_relset_1(E,k14_polynom1(B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_4_0_groeb_3(B,C,D,E))
<=> ? [F] :
( m1_polynom1(F,B,k14_polynom1(B))
& A = k9_polynom1(B,k2_polynom7(B,C,E),F)
& r2_hidden(F,k12_polynom1(k14_polynom1(B),C,D)) ) ) ) ).
%------------------------------------------------------------------------------