SET007 Axioms: SET007+752.ax
%------------------------------------------------------------------------------
% File : SET007+752 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Polynomial Reduction
% Version : [Urb08] axioms.
% English :
% 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 : polyred [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 0 unt; 0 def)
% Number of atoms : 1854 ( 41 equ)
% Maximal formula atoms : 48 ( 21 avg)
% Number of connectives : 1887 ( 118 ~; 2 |;1333 &)
% ( 20 <=>; 414 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 15 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 83 ( 82 usr; 0 prp; 1-7 aty)
% Number of functors : 45 ( 45 usr; 2 con; 0-4 aty)
% Number of variables : 432 ( 420 !; 12 ?)
% 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(rc1_polyred,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& ~ v3_realset2(B)
& l2_struct_0(B) )
=> ? [C] :
( m1_relset_1(C,k14_polynom1(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(C,k14_polynom1(A),B)
& v1_polynom7(C,A,B)
& v3_polynom7(C,A,B) ) ) ).
fof(rc2_polyred,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& v2_vectsp_2(A)
& v1_binom(A)
& v1_algstr_1(A)
& v2_algstr_1(A)
& v3_algstr_1(A)
& v4_algstr_1(A)
& v5_algstr_1(A)
& v6_algstr_1(A)
& ~ v3_realset2(A) ) ).
fof(fc1_polyred,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v2_group_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_vectsp_1(B)
& v2_vectsp_2(B)
& v1_algstr_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)
& v1_polynom7(C,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)
& v1_polynom7(D,A,B)
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_relat_1(k28_polynom1(A,B,C,D))
& v1_funct_1(k28_polynom1(A,B,C,D))
& v1_funct_2(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k28_polynom1(A,B,C,D),k14_polynom1(A),B)
& v1_polynom7(k28_polynom1(A,B,C,D),A,B) ) ) ).
fof(fc2_polyred,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& ~ v3_struct_0(C)
& l2_struct_0(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)) )
=> ( v1_relat_1(k1_polyred(A,B,C,D))
& v1_funct_1(k1_polyred(A,B,C,D))
& v1_funct_2(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(k1_polyred(A,B,C,D),k14_polynom1(A),C) ) ) ).
fof(fc3_polyred,axiom,
! [A,B] :
( ( 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(g1_orders_2(k14_polynom1(A),B))
& v1_orders_2(g1_orders_2(k14_polynom1(A),B))
& v2_orders_2(g1_orders_2(k14_polynom1(A),B))
& v3_orders_2(g1_orders_2(k14_polynom1(A),B))
& v4_orders_2(g1_orders_2(k14_polynom1(A),B))
& v16_waybel_0(g1_orders_2(k14_polynom1(A),B)) ) ) ).
fof(fc4_polyred,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& 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)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( ~ v3_struct_0(g1_orders_2(k14_polynom1(A),B))
& v1_orders_2(g1_orders_2(k14_polynom1(A),B))
& v2_orders_2(g1_orders_2(k14_polynom1(A),B))
& v3_orders_2(g1_orders_2(k14_polynom1(A),B))
& v4_orders_2(g1_orders_2(k14_polynom1(A),B))
& v1_wellfnd1(g1_orders_2(k14_polynom1(A),B)) ) ) ).
fof(fc5_polyred,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& 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)
& m1_relset_1(B,k14_polynom1(A),k14_polynom1(A))
& ~ v3_struct_0(C)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_1(C)
& l3_vectsp_1(C)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) )
=> ( v1_relat_1(k3_polyred(A,B,C,D))
& v2_relat_2(k3_polyred(A,B,C,D))
& v1_rewrite1(k3_polyred(A,B,C,D))
& v2_rewrite1(k3_polyred(A,B,C,D))
& v3_rewrite1(k3_polyred(A,B,C,D)) ) ) ).
fof(t1_polyred,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k24_polynom1(A,B,k23_polynom1(A,B,C,D)) = k23_polynom1(A,B,k24_polynom1(A,B,C),k24_polynom1(A,B,D)) ) ) ) ).
fof(t2_polyred,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v1_algstr_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)) )
=> k22_polynom1(A,B,k26_polynom1(A,B),C) = C ) ) ).
fof(t3_polyred,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)) )
=> ( k22_polynom1(A,B,k24_polynom1(A,B,C),C) = k26_polynom1(A,B)
& k22_polynom1(A,B,C,k24_polynom1(A,B,C)) = k26_polynom1(A,B) ) ) ) ).
fof(t4_polyred,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,C,k26_polynom1(A,B)) = C ) ) ).
fof(t5_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v5_vectsp_1(B)
& v2_algstr_1(B)
& l3_vectsp_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)) )
=> k28_polynom1(A,B,k26_polynom1(A,B),C) = k26_polynom1(A,B) ) ) ) ).
fof(t6_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v2_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_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)) )
=> ( k24_polynom1(A,B,k29_polynom1(A,B,C,D)) = k29_polynom1(A,B,k24_polynom1(A,B,C),D)
& k24_polynom1(A,B,k29_polynom1(A,B,C,D)) = k29_polynom1(A,B,C,k24_polynom1(A,B,D)) ) ) ) ) ) ).
fof(t7_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_vectsp_1(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))
& 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) )
=> k15_polynom1(A,B,k28_polynom1(A,B,D,C),k9_polynom1(A,k2_polynom7(A,B,D),E)) = k1_group_1(B,k15_polynom1(A,B,D,k2_polynom7(A,B,D)),k15_polynom1(A,B,C,E)) ) ) ) ) ) ).
fof(t8_polyred,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v5_rlvect_1(B)
& v5_vectsp_1(B)
& v2_algstr_1(B)
& l3_vectsp_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)) )
=> k5_polynom7(A,B,C,k1_rlvect_1(B)) = k26_polynom1(A,B) ) ) ).
fof(t9_polyred,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_vectsp_1(B)
& l3_vectsp_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)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( k24_polynom1(A,B,k5_polynom7(A,B,C,D)) = k5_polynom7(A,B,C,k5_rlvect_1(B,D))
& k24_polynom1(A,B,k5_polynom7(A,B,C,D)) = k5_polynom7(A,B,k24_polynom1(A,B,C),D) ) ) ) ) ).
fof(t10_polyred,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v5_vectsp_1(B)
& l3_vectsp_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)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k22_polynom1(A,B,k5_polynom7(A,B,C,D),k5_polynom7(A,B,C,E)) = k5_polynom7(A,B,C,k2_rlvect_1(B,D,E)) ) ) ) ) ).
fof(t11_polyred,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v4_group_1(B)
& l2_vectsp_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)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k5_polynom7(A,B,C,k1_group_1(B,D,E)) = k5_polynom7(A,B,k5_polynom7(A,B,C,E),D) ) ) ) ) ).
fof(t12_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_vectsp_1(B)
& l3_vectsp_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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k5_polynom7(A,B,k28_polynom1(A,B,C,D),E) = k28_polynom1(A,B,C,k5_polynom7(A,B,D,E)) ) ) ) ) ) ).
fof(d1_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(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))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( E = k1_polyred(A,B,C,D)
<=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( r3_polynom1(A,B,F)
=> ( k15_polynom1(A,C,E,F) = k15_polynom1(A,C,D,k10_polynom1(A,F,B))
& ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( ~ r3_polynom1(A,B,G)
=> k15_polynom1(A,C,E,G) = k1_rlvect_1(C) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_polyred,axiom,
! [A] :
( v3_ordinal1(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) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l2_struct_0(D) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(D))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(D)) )
=> k15_polynom1(A,D,k1_polyred(A,B,D,E),k9_polynom1(A,C,B)) = k15_polynom1(A,D,E,C) ) ) ) ) ) ).
fof(t15_polyred,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_realset2(C)
& l2_struct_0(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] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> k3_termord(A,B,C,k1_polyred(A,E,C,D)) = k9_polynom1(A,E,k3_termord(A,B,C,D)) ) ) ) ) ) ).
fof(t16_polyred,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)
& l2_struct_0(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] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ( r2_hidden(F,k12_polynom1(k14_polynom1(A),C,k1_polyred(A,E,C,D)))
=> r1_termord(A,B,F,k9_polynom1(A,E,k3_termord(A,B,C,D))) ) ) ) ) ) ) ) ).
fof(t17_polyred,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)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> k1_polyred(A,k16_polynom1(A),C,D) = D ) ) ) ) ).
fof(t18_polyred,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)
& l2_struct_0(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> k1_polyred(A,k9_polynom1(A,E,F),C,D) = k1_polyred(A,E,C,k1_polyred(A,F,C,D)) ) ) ) ) ) ) ).
fof(t19_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_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] :
( m1_subset_1(D,u1_struct_0(B))
=> r1_tarski(k12_polynom1(k14_polynom1(A),B,k5_polynom7(A,B,C,D)),k12_polynom1(k14_polynom1(A),B,C)) ) ) ) ) ).
fof(t20_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v2_vectsp_2(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] :
( ( v8_rlvect_1(D,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),B,C),k12_polynom1(k14_polynom1(A),B,k5_polynom7(A,B,C,D))) ) ) ) ) ).
fof(t21_polyred,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)
& v7_vectsp_1(C)
& v2_vectsp_2(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] :
( ( v8_rlvect_1(E,C)
& m1_subset_1(E,u1_struct_0(C)) )
=> k3_termord(A,B,C,k5_polynom7(A,C,D,E)) = k3_termord(A,B,C,D) ) ) ) ) ) ).
fof(t22_polyred,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_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))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k5_polynom7(A,B,k1_polyred(A,D,B,C),E) = k28_polynom1(A,B,k1_polynom7(A,B,E,D),C) ) ) ) ) ) ).
fof(t23_polyred,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] :
( ( v2_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v2_vectsp_2(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)
& 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))
& v1_polynom7(F,A,C)
& v3_polynom7(F,A,C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( r2_hidden(k3_termord(A,B,C,D),k12_polynom1(k14_polynom1(A),C,E))
=> r2_hidden(k3_termord(A,B,C,k28_polynom1(A,C,F,D)),k12_polynom1(k14_polynom1(A),C,k28_polynom1(A,C,F,E))) ) ) ) ) ) ) ) ).
fof(d2_polyred,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)
& l2_struct_0(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_polyred(A,B,C,D,E)
<=> r2_hidden(k4_tarski(k12_polynom1(k14_polynom1(A),C,D),k12_polynom1(k14_polynom1(A),C,E)),k13_bagorder(g1_orders_2(k14_polynom1(A),B))) ) ) ) ) ) ) ).
fof(d3_polyred,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)
& l2_struct_0(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)) )
=> ( r2_polyred(A,B,C,D,E)
<=> ( r1_polyred(A,B,C,D,E)
& k12_polynom1(k14_polynom1(A),C,D) != k12_polynom1(k14_polynom1(A),C,E) ) ) ) ) ) ) ) ).
fof(d4_polyred,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)
& l2_struct_0(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)) )
=> k2_polyred(A,B,C,D) = k12_polynom1(k14_polynom1(A),C,D) ) ) ) ) ).
fof(t24_polyred,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_realset2(C)
& l2_struct_0(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)) )
=> k11_bagorder(g1_orders_2(k14_polynom1(A),B),k2_polyred(A,B,C,D)) = k3_termord(A,B,C,D) ) ) ) ) ).
fof(t25_polyred,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)
& 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)) )
=> r1_polyred(A,B,C,D,D) ) ) ) ) ).
fof(t26_polyred,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)
& 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] :
( ( 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_polyred(A,B,C,D,E)
& r1_polyred(A,B,C,E,D) )
<=> k12_polynom1(k14_polynom1(A),C,D) = k12_polynom1(k14_polynom1(A),C,E) ) ) ) ) ) ) ).
fof(t27_polyred,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)
& 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] :
( ( 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_polyred(A,B,C,D,E)
& r1_polyred(A,B,C,E,F) )
=> r1_polyred(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t28_polyred,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)
& 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] :
( ( 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_polyred(A,B,C,D,E)
| r1_polyred(A,B,C,E,D) ) ) ) ) ) ) ).
fof(t29_polyred,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)
& 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] :
( ( 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_polyred(A,B,C,D,E)
<=> ~ r2_polyred(A,B,C,E,D) ) ) ) ) ) ) ).
fof(t30_polyred,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)
& l2_struct_0(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)) )
=> r1_polyred(A,B,C,k26_polynom1(A,C),D) ) ) ) ) ).
fof(t31_polyred,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] :
( ( v2_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( ~ v1_xboole_0(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))
& r2_hidden(E,D)
& ! [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(F,D)
=> r1_polyred(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(t32_polyred,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] :
( ( 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)) )
=> ( r2_polyred(A,B,C,D,E)
<=> ~ ( ~ ( D = k26_polynom1(A,C)
& E != k26_polynom1(A,C) )
& ~ r2_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,E))
& ~ ( k3_termord(A,B,C,D) = k3_termord(A,B,C,E)
& r2_polyred(A,B,C,k6_termord(A,B,C,D),k6_termord(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(t33_polyred,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)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> r2_polyred(A,B,C,k6_termord(A,B,C,D),k5_termord(A,B,C,D)) ) ) ) ) ).
fof(t34_polyred,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)) )
=> r1_polyred(A,B,C,k5_termord(A,B,C,D),D) ) ) ) ) ).
fof(t35_polyred,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)
& v1_polynom7(D,A,C)
& m2_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> r2_polyred(A,B,C,k6_termord(A,B,C,D),D) ) ) ) ) ).
fof(d5_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( r3_polyred(A,B,C,D,E,F,G)
<=> ( D != k26_polynom1(A,C)
& E != k26_polynom1(A,C)
& r2_hidden(G,k12_polynom1(k14_polynom1(A),C,D))
& ? [H] :
( v7_seqm_3(H)
& v1_polynom1(H)
& m1_pboole(H,A)
& k9_polynom1(A,H,k3_termord(A,B,C,E)) = G
& F = k25_polynom1(A,C,D,k5_polynom7(A,C,k1_polyred(A,H,C,E),k5_vectsp_1(C,k15_polynom1(A,C,D,G),k4_termord(A,B,C,E)))) ) ) ) ) ) ) ) ) ) ) ).
fof(d6_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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,E,F)
<=> ? [G] :
( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A)
& r3_polyred(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) ).
fof(d7_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( r5_polyred(A,B,C,D,E,F)
<=> ? [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(G,F)
& r4_polyred(A,B,C,D,G,E) ) ) ) ) ) ) ) ) ).
fof(d8_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)) )
=> ( r6_polyred(A,B,C,D,E)
<=> ? [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,E,F) ) ) ) ) ) ) ) ).
fof(d9_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( r7_polyred(A,B,C,D,E)
<=> ? [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))
& r5_polyred(A,B,C,D,F,E) ) ) ) ) ) ) ) ).
fof(d10_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)) )
=> ( r8_polyred(A,B,C,D,E,F)
<=> r3_polyred(A,B,C,D,E,F,k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ).
fof(d11_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)) )
=> ( r9_polyred(A,B,C,D,E)
<=> ? [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))
& r8_polyred(A,B,C,D,E,F) ) ) ) ) ) ) ) ).
fof(d12_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( r10_polyred(A,B,C,D,E)
<=> ? [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(F,E)
& r9_polyred(A,B,C,D,F) ) ) ) ) ) ) ) ).
fof(t36_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)
& v1_polynom7(E,A,C)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(C)) )
=> ( r6_polyred(A,B,C,D,E)
<=> ? [F] :
( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A)
& r2_hidden(F,k12_polynom1(k14_polynom1(A),C,D))
& r3_polynom1(A,k3_termord(A,B,C,E),F) ) ) ) ) ) ) ) ).
fof(t37_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)) )
=> ~ r6_polyred(A,B,C,k26_polynom1(A,C),D) ) ) ) ) ).
fof(t38_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_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)) )
=> ! [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))
& v1_polynom7(F,A,C)
& v3_polynom7(F,A,C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( r4_polyred(A,B,C,D,E,k25_polynom1(A,C,D,k29_polynom1(A,C,F,E)))
=> r2_hidden(k3_termord(A,B,C,k29_polynom1(A,C,F,E)),k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ) ) ) ).
fof(t39_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_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)) )
=> ! [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] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ~ ( r3_polyred(A,B,C,D,E,F,G)
& r2_hidden(G,k12_polynom1(k14_polynom1(A),C,F)) ) ) ) ) ) ) ) ) ).
fof(t40_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ! [H] :
( ( v7_seqm_3(H)
& v1_polynom1(H)
& m1_pboole(H,A) )
=> ( ( r2_termord(A,B,G,H)
& r3_polyred(A,B,C,D,E,F,G) )
=> ( r2_hidden(H,k12_polynom1(k14_polynom1(A),C,F))
<=> r2_hidden(H,k12_polynom1(k14_polynom1(A),C,D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ! [H] :
( ( v7_seqm_3(H)
& v1_polynom1(H)
& m1_pboole(H,A) )
=> ( ( r2_termord(A,B,G,H)
& r3_polyred(A,B,C,D,E,F,G) )
=> k15_polynom1(A,C,D,H) = k15_polynom1(A,C,F,H) ) ) ) ) ) ) ) ) ) ).
fof(t42_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_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)) )
=> ! [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,E,F)
=> ! [G] :
( ( v7_seqm_3(G)
& v1_polynom1(G)
& m1_pboole(G,A) )
=> ( r2_hidden(G,k12_polynom1(k14_polynom1(A),C,F))
=> r1_termord(A,B,G,k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) ).
fof(t43_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_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)) )
=> ! [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,E,F)
=> r2_polyred(A,B,C,F,D) ) ) ) ) ) ) ) ).
fof(d13_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( m2_relset_1(E,k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C)))
=> ( E = k3_polyred(A,B,C,D)
<=> ! [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(k4_tarski(F,G),E)
<=> r5_polyred(A,B,C,F,G,D) ) ) ) ) ) ) ) ) ) ).
fof(t44_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_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)) )
=> ! [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] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C))))
=> ( r1_rewrite1(k3_polyred(A,B,C,F),D,E)
=> ( r1_polyred(A,B,C,E,D)
& ( E = k26_polynom1(A,C)
| r1_termord(A,B,k3_termord(A,B,C,E),k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) ).
fof(t45_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& v1_algstr_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)
=> r1_rewrite1(k3_polyred(A,B,C,D),k29_polynom1(A,C,F,E),k26_polynom1(A,C)) ) ) ) ) ) ) ) ).
fof(t46_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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))
& v1_polynom7(G,A,C)
& v3_polynom7(G,A,C)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(C)) )
=> ( r5_polyred(A,B,C,E,F,D)
=> r5_polyred(A,B,C,k29_polynom1(A,C,G,E),k29_polynom1(A,C,G,F),D) ) ) ) ) ) ) ) ) ).
fof(t47_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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))
& v3_polynom7(G,A,C)
& m2_relset_1(G,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),k29_polynom1(A,C,G,E),k29_polynom1(A,C,G,F)) ) ) ) ) ) ) ) ) ).
fof(t48_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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))
& v3_polynom7(F,A,C)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(C)) )
=> ( r1_rewrite1(k3_polyred(A,B,C,D),E,k26_polynom1(A,C))
=> r1_rewrite1(k3_polyred(A,B,C,D),k29_polynom1(A,C,F,E),k26_polynom1(A,C)) ) ) ) ) ) ) ) ).
fof(t49_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)) )
=> ! [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)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(H,k14_polynom1(A),C)
& m2_relset_1(H,k14_polynom1(A),u1_struct_0(C)) )
=> ~ ( k25_polynom1(A,C,E,F) = G
& r1_rewrite1(k3_polyred(A,B,C,D),G,H)
& ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(I,k14_polynom1(A),C)
& m2_relset_1(I,k14_polynom1(A),u1_struct_0(C)) )
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,k14_polynom1(A),u1_struct_0(C))
& v2_polynom1(J,k14_polynom1(A),C)
& m2_relset_1(J,k14_polynom1(A),u1_struct_0(C)) )
=> ~ ( k25_polynom1(A,C,I,J) = H
& r1_rewrite1(k3_polyred(A,B,C,D),E,I)
& r1_rewrite1(k3_polyred(A,B,C,D),F,J) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t50_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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),k25_polynom1(A,C,E,F),k26_polynom1(A,C))
=> r5_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) ).
fof(t51_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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),k25_polynom1(A,C,E,F),k26_polynom1(A,C))
=> r2_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) ).
fof(d14_polyred,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r11_polyred(A,B,C,D)
<=> r2_hidden(k6_rlvect_1(A,C,D),B) ) ) ) ) ) ).
fof(t52_polyred,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& v1_algstr_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v3_ideal_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r11_polyred(A,B,C,C) ) ) ) ).
fof(t53_polyred,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& v6_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v3_ideal_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r11_polyred(A,B,C,D)
=> r11_polyred(A,B,D,C) ) ) ) ) ) ).
fof(t54_polyred,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_ideal_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r11_polyred(A,B,C,D)
& r11_polyred(A,B,D,E) )
=> r11_polyred(A,B,C,E) ) ) ) ) ) ) ).
fof(t55_polyred,axiom,
! [A] :
( ( v2_group_1(A)
& v4_group_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_vectsp_1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_ideal_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r11_polyred(A,B,C,D)
& r11_polyred(A,B,E,F) )
=> r11_polyred(A,B,k4_rlvect_1(A,C,E),k4_rlvect_1(A,D,F)) ) ) ) ) ) ) ) ).
fof(t56_polyred,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_ideal_1(B,A)
& v3_ideal_1(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r11_polyred(A,B,C,D)
& r11_polyred(A,B,E,F) )
=> r11_polyred(A,B,k10_group_1(A,C,E),k10_group_1(A,D,F)) ) ) ) ) ) ) ) ).
fof(t57_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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] :
( m1_subset_1(E,u1_struct_0(k30_polynom1(A,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k30_polynom1(A,C)))
=> ( r2_rewrite1(k3_polyred(A,B,C,D),E,F)
=> r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),E,F) ) ) ) ) ) ) ) ).
fof(t58_polyred,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)
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k30_polynom1(A,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k30_polynom1(A,C)))
=> ( r11_polyred(k30_polynom1(A,C),k7_ideal_1(k30_polynom1(A,C),D),E,F)
=> r2_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) ).
fof(t59_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)
=> r2_hidden(k25_polynom1(A,C,E,F),k7_ideal_1(k30_polynom1(A,C),D)) ) ) ) ) ) ) ) ).
fof(t60_polyred,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] :
( ( v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_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)) )
=> ( r1_rewrite1(k3_polyred(A,B,C,D),E,k26_polynom1(A,C))
=> r2_hidden(E,k7_ideal_1(k30_polynom1(A,C),D)) ) ) ) ) ) ) ).
fof(dt_k1_polyred,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& ~ v3_struct_0(C)
& l2_struct_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(C))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(C)) )
=> ( v1_funct_1(k1_polyred(A,B,C,D))
& v1_funct_2(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C))
& m2_relset_1(k1_polyred(A,B,C,D),k14_polynom1(A),u1_struct_0(C)) ) ) ).
fof(dt_k2_polyred,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_struct_0(C)
& l2_struct_0(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(k2_polyred(A,B,C,D),k5_finsub_1(u1_struct_0(g1_orders_2(k14_polynom1(A),B)))) ) ).
fof(dt_k3_polyred,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))
& v2_group_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k30_polynom1(A,C)))) )
=> m2_relset_1(k3_polyred(A,B,C,D),k4_xboole_0(u1_struct_0(k30_polynom1(A,C)),k1_tarski(k26_polynom1(A,C))),u1_struct_0(k30_polynom1(A,C))) ) ).
fof(t14_polyred,axiom,
! [A] :
( v3_ordinal1(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))
& v2_polynom1(C,k14_polynom1(A),B)
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),B,k1_polyred(A,D,B,C)),a_4_0_polyred(A,B,C,D)) ) ) ) ) ).
fof(fraenkel_a_4_0_polyred,axiom,
! [A,B,C,D,E] :
( ( v3_ordinal1(B)
& ~ v3_struct_0(C)
& l2_struct_0(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))
& v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,B) )
=> ( r2_hidden(A,a_4_0_polyred(B,C,D,E))
<=> ? [F] :
( m1_polynom1(F,B,k14_polynom1(B))
& A = k9_polynom1(B,E,F)
& r2_hidden(F,k12_polynom1(k14_polynom1(B),C,D)) ) ) ) ).
%------------------------------------------------------------------------------