SET007 Axioms: SET007+649.ax
%------------------------------------------------------------------------------
% File : SET007+649 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Evaluation of Multivariate Polynomials
% 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 : polynom2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 55 ( 2 unt; 0 def)
% Number of atoms : 761 ( 70 equ)
% Maximal formula atoms : 28 ( 13 avg)
% Number of connectives : 773 ( 67 ~; 11 |; 484 &)
% ( 4 <=>; 207 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 13 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 63 ( 61 usr; 1 prp; 0-3 aty)
% Number of functors : 69 ( 69 usr; 20 con; 0-6 aty)
% Number of variables : 199 ( 191 !; 8 ?)
% 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_polynom2,axiom,
? [A] :
( l3_vectsp_1(A)
& ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& v5_vectsp_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(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(rc2_polynom2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_seq_1(B)
& v7_seqm_3(B)
& v1_polynom1(B)
& ~ v1_polynom2(B,A) ) ) ).
fof(fc1_polynom2,axiom,
! [A,B,C,D] :
( ( 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_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_relat_1(k25_polynom1(A,B,C,D))
& v1_funct_1(k25_polynom1(A,B,C,D))
& v1_funct_2(k25_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k25_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ).
fof(fc2_polynom2,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& 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_finset_1(k12_polynom1(k14_polynom1(A),B,C)) ) ).
fof(fc3_polynom2,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> ( ~ v3_struct_0(k30_polynom1(A,B))
& v3_rlvect_1(k30_polynom1(A,B))
& v4_rlvect_1(k30_polynom1(A,B))
& v5_rlvect_1(k30_polynom1(A,B))
& v6_rlvect_1(k30_polynom1(A,B))
& v2_group_1(k30_polynom1(A,B))
& v4_group_1(k30_polynom1(A,B))
& v3_vectsp_1(k30_polynom1(A,B))
& v4_vectsp_1(k30_polynom1(A,B))
& v6_vectsp_1(k30_polynom1(A,B))
& v8_vectsp_1(k30_polynom1(A,B))
& v1_algstr_1(k30_polynom1(A,B))
& v2_algstr_1(k30_polynom1(A,B))
& v3_algstr_1(k30_polynom1(A,B))
& v4_algstr_1(k30_polynom1(A,B))
& v5_algstr_1(k30_polynom1(A,B))
& v6_algstr_1(k30_polynom1(A,B)) ) ) ).
fof(fc4_polynom2,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_relat_1(k6_polynom2(A,B,C))
& v1_funct_1(k6_polynom2(A,B,C))
& v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
& v1_endalg(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) ).
fof(fc5_polynom2,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& 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,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_relat_1(k6_polynom2(A,B,C))
& v1_funct_1(k6_polynom2(A,B,C))
& v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
& v1_grcat_1(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) ).
fof(fc6_polynom2,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_relat_1(k6_polynom2(A,B,C))
& v1_funct_1(k6_polynom2(A,B,C))
& v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
& v1_grcat_1(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
& v1_endalg(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
& v1_group_6(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) ).
fof(fc7_polynom2,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_relat_1(k6_polynom2(A,B,C))
& v1_funct_1(k6_polynom2(A,B,C))
& v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
& v1_quofield(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
& v1_grcat_1(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
& v1_endalg(k6_polynom2(A,B,C),k30_polynom1(A,B),B)
& v1_group_6(k6_polynom2(A,B,C),k30_polynom1(A,B),B) ) ) ).
fof(t1_polynom2,axiom,
$true ).
fof(t2_polynom2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),B,k1_nat_1(C,D)) = k1_group_1(A,k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),B,C),k2_binop_1(u1_struct_0(A),k5_numbers,u1_struct_0(A),k5_group_1(A),B,D)) ) ) ) ) ).
fof(t3_polynom2,axiom,
$true ).
fof(t4_polynom2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k4_finseq_1(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,B) )
=> r2_hidden(C,k4_finseq_1(A)) ) ) ) ) ) ).
fof(t5_polynom2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& v1_algstr_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k4_finseq_1(B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_finseq_1(B))
=> ( D = C
| k4_finseq_4(k5_numbers,u1_struct_0(A),B,D) = k1_rlvect_1(A) ) ) ) )
=> k9_rlvect_1(A,B) = k4_finseq_4(k5_numbers,u1_struct_0(A),B,C) ) ) ) ) ).
fof(t6_polynom2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v7_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ( ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& r2_hidden(C,k4_finseq_1(B))
& k4_finseq_4(k5_numbers,u1_struct_0(A),B,C) = k1_rlvect_1(A) )
=> k3_group_4(A,B) = k1_rlvect_1(A) ) ) ) ).
fof(t7_polynom2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( k3_finseq_1(C) = k3_finseq_1(D)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(C))
& k4_finseq_4(k5_numbers,u1_struct_0(A),D,E) = k4_rlvect_1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k4_finseq_1(C))
=> ( F = E
| k4_finseq_4(k5_numbers,u1_struct_0(A),D,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),C,F) ) ) ) ) )
| k9_rlvect_1(A,D) = k4_rlvect_1(A,B,k9_rlvect_1(A,C)) ) ) ) ) ) ) ).
fof(t8_polynom2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& v7_group_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( k3_finseq_1(C) = k3_finseq_1(D)
=> ( ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(C))
& k4_finseq_4(k5_numbers,u1_struct_0(A),D,E) = k10_group_1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),C,E))
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k4_finseq_1(C))
=> ( F = E
| k4_finseq_4(k5_numbers,u1_struct_0(A),D,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),C,F) ) ) ) ) )
| k3_group_4(A,D) = k10_group_1(A,B,k3_group_4(A,C)) ) ) ) ) ) ) ).
fof(t9_polynom2,axiom,
! [A,B] :
( ( v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ( r3_orders_1(C,B)
=> k2_triang_1(A,B,C) = k1_xboole_0 ) ) ) ).
fof(t10_polynom2,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& v1_partfun1(C,A,A)
& m2_relset_1(C,A,A) )
=> ( r3_orders_1(C,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k4_finseq_1(k2_triang_1(A,B,C)))
& r2_hidden(E,k4_finseq_1(k2_triang_1(A,B,C)))
& k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,C),D) = k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,C),E) )
=> D = E ) ) ) ) ) ) ).
fof(t11_polynom2,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,B)
=> ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ( D = k2_xboole_0(k1_tarski(C),B)
=> ! [E] :
( ( v1_relat_2(E)
& v4_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,A,A)
& m2_relset_1(E,A,A) )
=> ( r3_orders_1(E,D)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r2_hidden(F,k4_finseq_1(k2_triang_1(A,D,E)))
& k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),F) = C )
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k5_real_1(F,np__1)) )
=> k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),G) = k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,E),G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t12_polynom2,axiom,
! [A,B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,B)
=> ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ( D = k2_xboole_0(k1_tarski(C),B)
=> ! [E] :
( ( v1_relat_2(E)
& v4_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,A,A)
& m2_relset_1(E,A,A) )
=> ( r3_orders_1(E,D)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r2_hidden(F,k4_finseq_1(k2_triang_1(A,D,E)))
& k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),F) = C )
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(F,G)
& r1_xreal_0(G,k3_finseq_1(k2_triang_1(A,B,E))) )
=> k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),k1_nat_1(G,np__1)) = k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,E),G) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_polynom2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,B)
=> ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ( D = k2_xboole_0(k1_tarski(C),B)
=> ! [E] :
( ( v1_relat_2(E)
& v4_relat_2(E)
& v8_relat_2(E)
& v1_partfun1(E,A,A)
& m2_relset_1(E,A,A) )
=> ( r3_orders_1(E,D)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r2_hidden(k1_nat_1(F,np__1),k4_finseq_1(k2_triang_1(A,D,E)))
& k4_finseq_4(k5_numbers,A,k2_triang_1(A,D,E),k1_nat_1(F,np__1)) = C )
=> k2_triang_1(A,D,E) = k5_finseq_5(A,k2_triang_1(A,B,E),C,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t14_polynom2,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( k11_polynom1(B) = k1_xboole_0
=> B = k16_polynom1(A) ) ) ).
fof(d1_polynom2,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( v1_polynom2(B,A)
<=> B = k16_polynom1(A) ) ) ).
fof(t15_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r3_orders_1(k1_yellow_1(A),k1_polynom2(A,B)) ) ) ).
fof(d2_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_group_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m2_relset_1(D,A,u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( E = k3_polynom2(A,B,C,D)
<=> ? [F] :
( m2_finseq_1(F,u1_struct_0(C))
& k3_finseq_1(F) = k3_finseq_1(k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)))
& E = k3_group_4(C,F)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k3_finseq_1(F)) )
=> k4_finseq_4(k5_numbers,u1_struct_0(C),F,G) = k2_binop_1(u1_struct_0(C),k5_numbers,u1_struct_0(C),k5_group_1(C),k4_finseq_4(k5_numbers,u1_struct_0(C),k1_partfun1(k5_numbers,A,A,u1_struct_0(C),k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),D),G),k4_finseq_4(k5_numbers,k5_numbers,k2_polynom2(A,k2_triang_1(A,k1_polynom2(A,B),k1_yellow_1(A)),B),G)) ) ) ) ) ) ) ) ) ) ).
fof(t16_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_group_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k3_polynom2(A,k16_polynom1(A),B,C) = k2_group_1(B) ) ) ) ).
fof(t17_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_group_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> ! [C,D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( k1_polynom2(A,D) = k1_tarski(C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k3_polynom2(A,D,B,E) = k1_binop_1(k5_group_1(B),k1_funct_1(E,C),k8_polynom1(D,C)) ) ) ) ) ) ).
fof(t18_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_group_1(B)
& v7_group_1(B)
& v7_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> ! [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] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k3_polynom2(A,k9_polynom1(A,C,D),B,E) = k10_group_1(B,k3_polynom2(A,C,B,E),k3_polynom2(A,D,B,E)) ) ) ) ) ) ).
fof(t19_polynom2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v7_vectsp_1(A)
& ~ v3_realset2(A)
& l3_vectsp_1(A) )
=> ! [B] :
( v3_ordinal1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_polynom1(B),u1_struct_0(A))
& v2_polynom1(C,k14_polynom1(B),A)
& m2_relset_1(C,k14_polynom1(B),u1_struct_0(A)) )
=> ( k12_polynom1(k14_polynom1(B),A,C) = k1_xboole_0
=> C = k26_polynom1(B,A) ) ) ) ) ).
fof(t20_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [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)) )
=> r3_orders_1(k17_polynom1(A),k12_polynom1(k14_polynom1(A),B,C)) ) ) ) ).
fof(d3_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( m1_polynom1(B,A,k14_polynom1(A))
=> k4_polynom2(A,B) = B ) ) ).
fof(d4_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [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,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( E = k5_polynom2(A,B,C,D)
<=> ? [F] :
( m2_finseq_1(F,u1_struct_0(B))
& k3_finseq_1(F) = k3_finseq_1(k2_triang_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k17_polynom1(A)))
& E = k9_rlvect_1(B,F)
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k3_finseq_1(F)) )
=> k4_finseq_4(k5_numbers,u1_struct_0(B),F,G) = k1_group_1(B,k4_finseq_4(k5_numbers,u1_struct_0(B),k1_partfun1(k5_numbers,k14_polynom1(A),k14_polynom1(A),u1_struct_0(B),k2_triang_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k17_polynom1(A)),C),G),k3_polynom2(A,k4_polynom2(A,k4_finseq_4(k5_numbers,k14_polynom1(A),k2_triang_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k17_polynom1(A)),G)),B,D)) ) ) ) ) ) ) ) ) ) ).
fof(t21_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [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) )
=> ( k12_polynom1(k14_polynom1(A),B,C) = k1_tarski(D)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,C,E) = k1_group_1(B,k15_polynom1(A,B,C,D),k3_polynom2(A,D,B,E)) ) ) ) ) ) ) ).
fof(t22_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,k26_polynom1(A,B),C) = k1_rlvect_1(B) ) ) ) ).
fof(t23_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,k27_polynom1(A,B),C) = k2_group_1(B) ) ) ) ).
fof(t24_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [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,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,k24_polynom1(A,B,C),D) = k5_rlvect_1(B,k5_polynom2(A,B,C,D)) ) ) ) ) ).
fof(t25_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& 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) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,k23_polynom1(A,B,C,D),E) = k4_rlvect_1(B,k5_polynom2(A,B,C,E),k5_polynom2(A,B,D,E)) ) ) ) ) ) ).
fof(t26_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& 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) )
=> ! [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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,k25_polynom1(A,B,C,D),E) = k6_rlvect_1(B,k5_polynom2(A,B,C,E),k5_polynom2(A,B,D,E)) ) ) ) ) ) ).
fof(t27_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,A,u1_struct_0(B))
& m2_relset_1(E,A,u1_struct_0(B)) )
=> k5_polynom2(A,B,k29_polynom1(A,B,C,D),E) = k10_group_1(B,k5_polynom2(A,B,C,E),k5_polynom2(A,B,D,E)) ) ) ) ) ) ).
fof(d5_polynom2,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& 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) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B)) )
=> ( D = k6_polynom2(A,B,C)
<=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(E,k14_polynom1(A),B)
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
=> k1_funct_1(D,E) = k5_polynom2(A,B,E,C) ) ) ) ) ) ) ).
fof(s1_polynom2,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(A,k2_finseq_1(f2_s1_polynom2))
& ! [B] :
( m1_subset_1(B,f1_s1_polynom2)
=> ~ p1_s1_polynom2(A,B) ) ) )
=> ? [A] :
( m2_finseq_1(A,f1_s1_polynom2)
& k4_finseq_1(A) = k2_finseq_1(f2_s1_polynom2)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r2_hidden(B,k2_finseq_1(f2_s1_polynom2))
=> p1_s1_polynom2(B,k4_finseq_4(k5_numbers,f1_s1_polynom2,A,B)) ) ) ) ) ).
fof(s2_polynom2,axiom,
( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_real_1(f3_s2_polynom2,np__1)) )
=> ! [B] :
( m1_subset_1(B,f1_s2_polynom2)
=> ? [C] :
( m1_subset_1(C,f1_s2_polynom2)
& p1_s2_polynom2(A,B,C) ) ) ) )
=> ? [A] :
( m2_finseq_1(A,f1_s2_polynom2)
& k3_finseq_1(A) = f3_s2_polynom2
& ( k4_finseq_4(k5_numbers,f1_s2_polynom2,A,np__1) = f2_s2_polynom2
| f3_s2_polynom2 = np__0 )
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(B,k5_real_1(f3_s2_polynom2,np__1)) )
=> p1_s2_polynom2(B,k4_finseq_4(k5_numbers,f1_s2_polynom2,A,B),k4_finseq_4(k5_numbers,f1_s2_polynom2,A,k1_nat_1(B,np__1))) ) ) ) ) ).
fof(s3_polynom2,axiom,
( ( ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_real_1(f3_s3_polynom2,np__1)) )
=> ! [B] :
( m1_subset_1(B,f1_s3_polynom2)
=> ! [C] :
( m1_subset_1(C,f1_s3_polynom2)
=> ! [D] :
( m1_subset_1(D,f1_s3_polynom2)
=> ( ( p1_s3_polynom2(A,B,C)
& p1_s3_polynom2(A,B,D) )
=> C = D ) ) ) ) ) )
& k3_finseq_1(f4_s3_polynom2) = f3_s3_polynom2
& ( k4_finseq_4(k5_numbers,f1_s3_polynom2,f4_s3_polynom2,np__1) = f2_s3_polynom2
| f3_s3_polynom2 = np__0 )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_real_1(f3_s3_polynom2,np__1)) )
=> p1_s3_polynom2(A,k4_finseq_4(k5_numbers,f1_s3_polynom2,f4_s3_polynom2,A),k4_finseq_4(k5_numbers,f1_s3_polynom2,f4_s3_polynom2,k1_nat_1(A,np__1))) ) )
& k3_finseq_1(f5_s3_polynom2) = f3_s3_polynom2
& ( k4_finseq_4(k5_numbers,f1_s3_polynom2,f5_s3_polynom2,np__1) = f2_s3_polynom2
| f3_s3_polynom2 = np__0 )
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k5_real_1(f3_s3_polynom2,np__1)) )
=> p1_s3_polynom2(A,k4_finseq_4(k5_numbers,f1_s3_polynom2,f5_s3_polynom2,A),k4_finseq_4(k5_numbers,f1_s3_polynom2,f5_s3_polynom2,k1_nat_1(A,np__1))) ) ) )
=> f4_s3_polynom2 = f5_s3_polynom2 ) ).
fof(s4_polynom2,axiom,
( ( p1_s4_polynom2(f1_s4_polynom2)
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(f1_s4_polynom2,A)
& p1_s4_polynom2(A) )
=> ( r1_xreal_0(f2_s4_polynom2,A)
| p1_s4_polynom2(k1_nat_1(A,np__1)) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(f1_s4_polynom2,A)
& r1_xreal_0(A,f2_s4_polynom2) )
=> p1_s4_polynom2(A) ) ) ) ).
fof(s5_polynom2,axiom,
( ( p1_s5_polynom2(f1_s5_polynom2)
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(f1_s5_polynom2,A)
& ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(f1_s5_polynom2,B)
& r1_xreal_0(B,A) )
=> p1_s5_polynom2(B) ) ) )
=> ( r1_xreal_0(f2_s5_polynom2,A)
| p1_s5_polynom2(k1_nat_1(A,np__1)) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(f1_s5_polynom2,A)
& r1_xreal_0(A,f2_s5_polynom2) )
=> p1_s5_polynom2(A) ) ) ) ).
fof(s6_polynom2,axiom,
( ( p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,np__1))
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,A)) )
=> ( r1_xreal_0(k3_finseq_1(f2_s6_polynom2),A)
| p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,k1_nat_1(A,np__1))) ) ) ) )
=> ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(f2_s6_polynom2)) )
=> p1_s6_polynom2(k1_funct_1(f2_s6_polynom2,A)) ) ) ) ).
fof(dt_k1_polynom2,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( v1_finset_1(k1_polynom2(A,B))
& m1_subset_1(k1_polynom2(A,B),k1_zfmisc_1(A)) ) ) ).
fof(redefinition_k1_polynom2,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> k1_polynom2(A,B) = k11_polynom1(B) ) ).
fof(dt_k2_polynom2,axiom,
! [A,B,C] :
( ( m1_finseq_1(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( v1_funct_1(k2_polynom2(A,B,C))
& m2_relset_1(k2_polynom2(A,B,C),k5_numbers,k5_numbers) ) ) ).
fof(redefinition_k2_polynom2,axiom,
! [A,B,C] :
( ( m1_finseq_1(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> k2_polynom2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k3_polynom2,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& ~ v3_struct_0(C)
& v2_group_1(C)
& ~ v3_realset2(C)
& l3_vectsp_1(C)
& v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(C))
& m1_relset_1(D,A,u1_struct_0(C)) )
=> m1_subset_1(k3_polynom2(A,B,C,D),u1_struct_0(C)) ) ).
fof(dt_k4_polynom2,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& m1_subset_1(B,k14_polynom1(A)) )
=> ( v7_seqm_3(k4_polynom2(A,B))
& v1_polynom1(k4_polynom2(A,B))
& m1_pboole(k4_polynom2(A,B),A) ) ) ).
fof(dt_k5_polynom2,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& 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,A,u1_struct_0(B))
& m1_relset_1(D,A,u1_struct_0(B)) )
=> m1_subset_1(k5_polynom2(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k6_polynom2,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& 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,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> ( v1_funct_1(k6_polynom2(A,B,C))
& v1_funct_2(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B))
& m2_relset_1(k6_polynom2(A,B,C),u1_struct_0(k30_polynom1(A,B)),u1_struct_0(B)) ) ) ).
%------------------------------------------------------------------------------