SET007 Axioms: SET007+625.ax
%------------------------------------------------------------------------------
% File : SET007+625 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Multivariate Polynomials with Arbitrary Number of Variables
% 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 : polynom1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 235 ( 16 unt; 0 def)
% Number of atoms : 1975 ( 133 equ)
% Maximal formula atoms : 46 ( 8 avg)
% Number of connectives : 1893 ( 153 ~; 4 |;1261 &)
% ( 30 <=>; 445 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 81 ( 79 usr; 1 prp; 0-3 aty)
% Number of functors : 99 ( 99 usr; 9 con; 0-6 aty)
% Number of variables : 653 ( 634 !; 19 ?)
% 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_polynom1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,A)
& m1_subset_1(E,A) )
=> ( ~ v3_struct_0(g3_vectsp_1(A,B,C,D,E))
& v3_vectsp_1(g3_vectsp_1(A,B,C,D,E)) ) ) ).
fof(rc1_polynom1,axiom,
! [A] :
? [B] :
( m1_relset_1(B,A,A)
& v1_relat_1(B)
& v1_partfun1(B,A,A)
& v3_orders_1(B)
& v2_wellord1(B)
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B) ) ).
fof(fc2_polynom1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A))
& v1_partfun1(C,A,A)
& v3_orders_1(C)
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m1_relset_1(C,A,A) )
=> ( v1_relat_1(k2_triang_1(A,B,C))
& v1_funct_1(k2_triang_1(A,B,C))
& v2_funct_1(k2_triang_1(A,B,C))
& ~ v1_xboole_0(k2_triang_1(A,B,C))
& v1_finset_1(k2_triang_1(A,B,C))
& v1_finseq_1(k2_triang_1(A,B,C)) ) ) ).
fof(fc3_polynom1,axiom,
( v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v1_funcop_1(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0)
& v1_matrlin(k1_xboole_0) ) ).
fof(rc2_polynom1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_funcop_1(A)
& v1_matrlin(A) ) ).
fof(fc4_polynom1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v1_relat_1(k2_finseq_2(A,B))
& v1_funct_1(k2_finseq_2(A,B))
& v1_finset_1(k2_finseq_2(A,B))
& v1_finseq_1(k2_finseq_2(A,B))
& v1_funcop_1(k2_finseq_2(A,B))
& v1_matrlin(k2_finseq_2(A,B)) ) ) ).
fof(fc5_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_matrlin(A) )
=> ( v1_relat_1(k1_funct_1(A,B))
& v1_funct_1(k1_funct_1(A,B))
& v1_finset_1(k1_funct_1(A,B))
& v1_finseq_1(k1_funct_1(A,B)) ) ) ).
fof(fc6_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_relat_1(k1_card_3(A))
& v1_funct_1(k1_card_3(A))
& v1_finset_1(k1_card_3(A))
& v1_finseq_1(k1_card_3(A))
& v1_card_3(k1_card_3(A)) ) ) ).
fof(rc3_polynom1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_card_3(A) ) ).
fof(fc7_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_card_3(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_card_3(B) )
=> ( v1_relat_1(k7_finseq_1(A,B))
& v1_funct_1(k7_finseq_1(A,B))
& v1_finset_1(k7_finseq_1(A,B))
& v1_finseq_1(k7_finseq_1(A,B))
& v1_card_3(k7_finseq_1(A,B)) ) ) ).
fof(cc1_polynom1,axiom,
! [A] :
( m1_finseq_1(A,k5_numbers)
=> v1_card_3(A) ) ).
fof(rc4_polynom1,axiom,
? [A] :
( m1_finseq_1(A,k5_numbers)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_card_3(A) ) ).
fof(fc8_polynom1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v1_card_3(k7_relat_1(A,B)) ) ) ).
fof(fc9_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_xboole_0(A) )
=> ( v1_relat_1(k1_card_3(A))
& v1_funct_1(k1_card_3(A))
& v2_funct_1(k1_card_3(A))
& v1_xboole_0(k1_card_3(A))
& v1_finset_1(k1_card_3(A))
& v1_membered(k1_card_3(A))
& v2_membered(k1_card_3(A))
& v3_membered(k1_card_3(A))
& v4_membered(k1_card_3(A))
& v5_membered(k1_card_3(A))
& v1_card_3(k1_card_3(A)) ) ) ).
fof(fc10_polynom1,axiom,
! [A] :
( v1_relat_1(k6_finseq_1(A))
& v1_funct_1(k6_finseq_1(A))
& v2_funct_1(k6_finseq_1(A))
& v1_xboole_0(k6_finseq_1(A))
& v1_finset_1(k6_finseq_1(A))
& v1_finseq_1(k6_finseq_1(A))
& v1_funcop_1(k6_finseq_1(A))
& v1_membered(k6_finseq_1(A))
& v2_membered(k6_finseq_1(A))
& v3_membered(k6_finseq_1(A))
& v4_membered(k6_finseq_1(A))
& v5_membered(k6_finseq_1(A))
& v1_matrlin(k6_finseq_1(A)) ) ).
fof(fc11_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_relat_1(k5_finseq_1(A))
& v1_funct_1(k5_finseq_1(A))
& ~ v1_xboole_0(k5_finseq_1(A))
& v1_finset_1(k5_finseq_1(A))
& v1_finseq_1(k5_finseq_1(A))
& v1_funcop_1(k5_finseq_1(A))
& v1_matrlin(k5_finseq_1(A)) ) ) ).
fof(fc12_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_matrlin(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_matrlin(B) )
=> ( v1_relat_1(k7_finseq_1(A,B))
& v1_funct_1(k7_finseq_1(A,B))
& v1_finset_1(k7_finseq_1(A,B))
& v1_finseq_1(k7_finseq_1(A,B))
& v1_funcop_1(k7_finseq_1(A,B))
& v1_matrlin(k7_finseq_1(A,B)) ) ) ).
fof(cc2_polynom1,axiom,
! [A] :
( l2_vectsp_1(A)
=> ( ( ~ v3_struct_0(A)
& ~ v10_vectsp_1(A) )
=> ( ~ v3_struct_0(A)
& ~ v3_realset2(A) ) ) ) ).
fof(rc5_polynom1,axiom,
? [A] :
( l2_vectsp_1(A)
& ~ v3_struct_0(A)
& v2_group_1(A)
& v2_vectsp_1(A)
& v6_vectsp_1(A)
& v8_vectsp_1(A) ) ).
fof(rc6_polynom1,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)
& v3_vectsp_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)
& ~ v3_realset2(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) ) ).
fof(fc13_polynom1,axiom,
! [A,B] :
( ( v1_xboole_0(B)
& m1_finseq_1(B,k3_finseq_2(A)) )
=> ( v1_relat_1(k15_dtconstr(A,B))
& v1_funct_1(k15_dtconstr(A,B))
& v2_funct_1(k15_dtconstr(A,B))
& v1_xboole_0(k15_dtconstr(A,B))
& v1_finset_1(k15_dtconstr(A,B))
& v1_finseq_1(k15_dtconstr(A,B))
& v1_membered(k15_dtconstr(A,B))
& v2_membered(k15_dtconstr(A,B))
& v3_membered(k15_dtconstr(A,B))
& v4_membered(k15_dtconstr(A,B))
& v5_membered(k15_dtconstr(A,B)) ) ) ).
fof(cc3_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_seq_1(A) ) ) ).
fof(fc14_polynom1,axiom,
( v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v1_funcop_1(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0)
& v1_seq_1(k1_xboole_0)
& v1_matrlin(k1_xboole_0)
& v7_seqm_3(k1_xboole_0) ) ).
fof(rc7_polynom1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_seq_1(A)
& v7_seqm_3(A) ) ).
fof(fc15_polynom1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A)
& m1_subset_1(C,k5_numbers) )
=> ( v1_relat_1(k2_funct_7(A,B,C))
& v1_funct_1(k2_funct_7(A,B,C))
& v1_seq_1(k2_funct_7(A,B,C))
& v7_seqm_3(k2_funct_7(A,B,C)) ) ) ).
fof(fc16_polynom1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_seq_1(A)
& m1_subset_1(C,k5_numbers) )
=> ( v1_relat_1(k2_funct_7(A,B,C))
& v1_funct_1(k2_funct_7(A,B,C))
& v1_seq_1(k2_funct_7(A,B,C)) ) ) ).
fof(cc4_polynom1,axiom,
! [A,B] :
( m1_relset_1(B,A,k5_numbers)
=> ( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers) )
=> ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v7_seqm_3(B) ) ) ) ).
fof(rc8_polynom1,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_seq_1(B)
& v7_seqm_3(B) ) ).
fof(rc9_polynom1,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_seq_1(B) ) ).
fof(rc10_polynom1,axiom,
! [A] :
? [B] :
( m1_pboole(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_seq_1(B) ) ).
fof(fc17_polynom1,axiom,
! [A,B,C] :
( ( v1_seq_1(B)
& m1_pboole(B,A)
& v1_seq_1(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k9_polynom1(A,B,C))
& v1_funct_1(k9_polynom1(A,B,C))
& v1_seq_1(k9_polynom1(A,B,C)) ) ) ).
fof(fc18_polynom1,axiom,
! [A,B,C] :
( ( v7_seqm_3(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k9_polynom1(A,B,C))
& v1_funct_1(k9_polynom1(A,B,C))
& v1_seq_1(k9_polynom1(A,B,C))
& v7_seqm_3(k9_polynom1(A,B,C)) ) ) ).
fof(fc19_polynom1,axiom,
! [A,B,C] :
( ( v7_seqm_3(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k10_polynom1(A,B,C))
& v1_funct_1(k10_polynom1(A,B,C))
& v1_seq_1(k10_polynom1(A,B,C))
& v7_seqm_3(k10_polynom1(A,B,C)) ) ) ).
fof(fc20_polynom1,axiom,
( v1_relat_1(k1_xboole_0)
& v3_relat_1(k1_xboole_0)
& v1_funct_1(k1_xboole_0)
& v2_funct_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0)
& v1_finset_1(k1_xboole_0)
& v1_finseq_1(k1_xboole_0)
& v1_funcop_1(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0)
& v1_seq_1(k1_xboole_0)
& v1_matrlin(k1_xboole_0)
& v7_seqm_3(k1_xboole_0)
& v1_polynom1(k1_xboole_0) ) ).
fof(cc5_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_polynom1(A) ) ) ).
fof(rc11_polynom1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_seq_1(A)
& v7_seqm_3(A)
& v1_polynom1(A) ) ).
fof(fc21_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_polynom1(A) )
=> v1_finset_1(k11_polynom1(A)) ) ).
fof(rc12_polynom1,axiom,
! [A] :
? [B] :
( m1_relset_1(B,A,k5_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v1_seq_1(B)
& v7_seqm_3(B)
& v1_polynom1(B) ) ).
fof(fc22_polynom1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_polynom1(A) )
=> ( v1_relat_1(k2_funct_7(A,B,C))
& v1_funct_1(k2_funct_7(A,B,C))
& v1_polynom1(k2_funct_7(A,B,C)) ) ) ).
fof(rc13_polynom1,axiom,
! [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) ) ).
fof(cc6_polynom1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_pboole(B,A)
=> v1_polynom1(B) ) ) ).
fof(fc23_polynom1,axiom,
! [A,B,C] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k9_polynom1(A,B,C))
& v1_funct_1(k9_polynom1(A,B,C))
& v1_seq_1(k9_polynom1(A,B,C))
& v7_seqm_3(k9_polynom1(A,B,C))
& v1_polynom1(k9_polynom1(A,B,C)) ) ) ).
fof(fc24_polynom1,axiom,
! [A,B,C] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( v1_relat_1(k10_polynom1(A,B,C))
& v1_funct_1(k10_polynom1(A,B,C))
& v1_seq_1(k10_polynom1(A,B,C))
& v7_seqm_3(k10_polynom1(A,B,C))
& v1_polynom1(k10_polynom1(A,B,C)) ) ) ).
fof(fc25_polynom1,axiom,
! [A] : ~ v1_xboole_0(k13_polynom1(A)) ).
fof(fc26_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_relat_1(k17_polynom1(A))
& v1_partfun1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A))
& v3_orders_1(k17_polynom1(A))
& v1_relat_2(k17_polynom1(A))
& v4_relat_2(k17_polynom1(A))
& v8_relat_2(k17_polynom1(A)) ) ) ).
fof(fc27_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m1_relset_1(B,A,k5_numbers) )
=> ( ~ v1_xboole_0(k18_polynom1(A,B))
& v1_fraenkel(k18_polynom1(A,B)) ) ) ).
fof(cc7_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m1_relset_1(B,A,k5_numbers) )
=> ! [C] :
( m1_subset_1(C,k18_polynom1(A,B))
=> ( v1_relat_1(C)
& v1_funct_1(C)
& v1_seq_1(C)
& v7_seqm_3(C) ) ) ) ).
fof(fc28_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v1_polynom1(B)
& m1_relset_1(B,A,k5_numbers) )
=> ( ~ v1_xboole_0(k18_polynom1(A,B))
& v1_finset_1(k18_polynom1(A,B))
& v1_fraenkel(k18_polynom1(A,B)) ) ) ).
fof(fc29_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( v1_relat_1(k20_polynom1(A,B))
& v1_funct_1(k20_polynom1(A,B))
& v2_funct_1(k20_polynom1(A,B))
& ~ v1_xboole_0(k20_polynom1(A,B))
& v1_finset_1(k20_polynom1(A,B))
& v1_finseq_1(k20_polynom1(A,B))
& v1_polynom1(k20_polynom1(A,B)) ) ) ).
fof(fc30_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( v1_relat_1(k21_polynom1(A,B))
& v1_funct_1(k21_polynom1(A,B))
& v2_funct_1(k21_polynom1(A,B))
& ~ v1_xboole_0(k21_polynom1(A,B))
& v1_finset_1(k21_polynom1(A,B))
& v1_finseq_1(k21_polynom1(A,B))
& v1_funcop_1(k21_polynom1(A,B))
& v1_matrlin(k21_polynom1(A,B))
& v1_polynom1(k21_polynom1(A,B)) ) ) ).
fof(fc31_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& m1_subset_1(B,k14_polynom1(A)) )
=> ( v1_relat_1(k21_polynom1(A,B))
& v1_funct_1(k21_polynom1(A,B))
& v2_funct_1(k21_polynom1(A,B))
& ~ v1_xboole_0(k21_polynom1(A,B))
& v1_finset_1(k21_polynom1(A,B))
& v1_finseq_1(k21_polynom1(A,B))
& v1_funcop_1(k21_polynom1(A,B))
& v1_matrlin(k21_polynom1(A,B))
& v1_polynom1(k21_polynom1(A,B)) ) ) ).
fof(rc14_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(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) ) ) ).
fof(fc32_polynom1,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v5_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(k22_polynom1(A,B,C,D))
& v1_funct_1(k22_polynom1(A,B,C,D))
& v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k22_polynom1(A,B,C,D),k14_polynom1(A),B) ) ) ).
fof(fc33_polynom1,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_relat_1(k24_polynom1(A,B,C))
& v1_funct_1(k24_polynom1(A,B,C))
& v1_funct_2(k24_polynom1(A,B,C),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k24_polynom1(A,B,C),k14_polynom1(A),B) ) ) ).
fof(fc34_polynom1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& ~ 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(fc35_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ( v1_relat_1(k26_polynom1(A,B))
& v1_funct_1(k26_polynom1(A,B))
& v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k26_polynom1(A,B),k14_polynom1(A),B) ) ) ).
fof(fc36_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_group_1(B)
& v4_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> ( v1_relat_1(k27_polynom1(A,B))
& v1_funct_1(k27_polynom1(A,B))
& v1_funct_2(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(k27_polynom1(A,B),k14_polynom1(A),B) ) ) ).
fof(fc37_polynom1,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)
& 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_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) ) ) ).
fof(fc38_polynom1,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)
& 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))
& v3_vectsp_1(k30_polynom1(A,B)) ) ) ).
fof(fc39_polynom1,axiom,
! [A,B] :
( ( 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) )
=> ( ~ v3_struct_0(k30_polynom1(A,B))
& v4_rlvect_1(k30_polynom1(A,B))
& v3_vectsp_1(k30_polynom1(A,B)) ) ) ).
fof(fc40_polynom1,axiom,
! [A,B] :
( ( 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) )
=> ( ~ v3_struct_0(k30_polynom1(A,B))
& v4_rlvect_1(k30_polynom1(A,B))
& v5_rlvect_1(k30_polynom1(A,B))
& v3_vectsp_1(k30_polynom1(A,B)) ) ) ).
fof(fc41_polynom1,axiom,
! [A,B] :
( ( 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) )
=> ( ~ v3_struct_0(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))
& v3_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(fc42_polynom1,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)
& v7_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))
& v7_group_1(k30_polynom1(A,B))
& v3_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(fc43_polynom1,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))
& v4_group_1(k30_polynom1(A,B))
& v3_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(fc44_polynom1,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(t1_polynom1,axiom,
$true ).
fof(t2_polynom1,axiom,
! [A,B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ! [E] :
( m1_subset_1(E,B)
=> k1_relat_1(k4_funcop_1(C,D,E)) = A ) ) ) ) ).
fof(t3_polynom1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k5_binarith(k5_binarith(A,B),C) = k5_binarith(A,k1_nat_1(B,C)) ) ) ) ).
fof(t4_polynom1,axiom,
! [A,B] :
( v1_relat_1(B)
=> ( r1_tarski(k3_relat_1(B),A)
=> m2_relset_1(B,A,A) ) ) ).
fof(t5_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( k4_finseq_1(B) = k4_finseq_1(C)
=> k4_finseq_1(k3_fvsum_1(A,B,C)) = k4_finseq_1(B) ) ) ) ) ).
fof(t6_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] : r1_tarski(k2_relat_1(k2_funct_7(A,B,C)),k2_xboole_0(k2_relat_1(A),k1_tarski(C))) ) ).
fof(t7_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) )
=> k1_card_1(A) = k1_card_1(k2_relat_1(A)) ) ).
fof(t8_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( ( r2_hidden(D,B)
& r3_orders_1(C,B)
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,B)
=> r2_hidden(k4_tarski(D,E),C) ) ) )
=> k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,C),np__1) = D ) ) ) ) ) ).
fof(t9_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(A)) )
=> ! [C] :
( ( v1_partfun1(C,A,A)
& v1_relat_2(C)
& v4_relat_2(C)
& v8_relat_2(C)
& m2_relset_1(C,A,A) )
=> ! [D] :
( m1_subset_1(D,A)
=> ( ( r2_hidden(D,B)
& r3_orders_1(C,B)
& ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,B)
=> r2_hidden(k4_tarski(E,D),C) ) ) )
=> k4_finseq_4(k5_numbers,A,k2_triang_1(A,B,C),k3_finseq_1(k2_triang_1(A,B,C))) = D ) ) ) ) ) ).
fof(t10_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_card_3(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> v1_card_1(B) ) ) ) ).
fof(t11_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] : k1_card_3(k7_relat_1(A,B)) = k7_relat_1(k1_card_3(A),B) ) ).
fof(t12_polynom1,axiom,
! [A] : k1_card_3(k9_finseq_1(A)) = k9_finseq_1(k1_card_1(A)) ).
fof(t13_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> k1_card_3(k7_finseq_1(A,B)) = k7_finseq_1(k1_card_3(A),k1_card_3(B)) ) ) ).
fof(t14_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_matrlin(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) ) ) ) ) ).
fof(t15_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
=> k4_finseq_1(k8_matrlin(A,B)) = k4_finseq_1(B) ) ) ).
fof(t16_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
=> k8_matrlin(A,k6_finseq_1(k3_finseq_2(u1_struct_0(A)))) = k6_finseq_1(u1_struct_0(A)) ) ) ).
fof(t17_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A)))
=> k13_binarith(u1_struct_0(A),k9_rlvect_1(A,B)) = k8_matrlin(A,k3_matrlin(u1_struct_0(A),B)) ) ) ).
fof(t18_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_1(C,k3_finseq_2(u1_struct_0(A)))
=> k8_matrlin(A,k8_finseq_1(k3_finseq_2(u1_struct_0(A)),B,C)) = k8_finseq_1(u1_struct_0(A),k8_matrlin(A,B),k8_matrlin(A,C)) ) ) ) ).
fof(d1_polynom1,axiom,
$true ).
fof(d2_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( D = k6_polynom1(A,B,C)
<=> ( k4_finseq_1(D) = k4_finseq_1(B)
& ! [E] :
( r2_hidden(E,k4_finseq_1(B))
=> k4_finseq_4(k5_numbers,u1_struct_0(A),D,E) = k1_group_1(A,C,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E)) ) ) ) ) ) ) ) ).
fof(d3_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( D = k7_polynom1(A,B,C)
<=> ( k4_finseq_1(D) = k4_finseq_1(B)
& ! [E] :
( r2_hidden(E,k4_finseq_1(B))
=> k4_finseq_4(k5_numbers,u1_struct_0(A),D,E) = k1_group_1(A,k4_finseq_4(k5_numbers,u1_struct_0(A),B,E),C) ) ) ) ) ) ) ) ).
fof(t19_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_polynom1(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)) ) ) ).
fof(t20_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_polynom1(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)) ) ) ).
fof(t21_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_polynom1(A,k13_binarith(u1_struct_0(A),C),B) = k13_binarith(u1_struct_0(A),k1_group_1(A,B,C)) ) ) ) ).
fof(t22_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k7_polynom1(A,k13_binarith(u1_struct_0(A),C),B) = k13_binarith(u1_struct_0(A),k1_group_1(A,C,B)) ) ) ) ).
fof(t23_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_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))
=> k6_polynom1(A,k8_finseq_1(u1_struct_0(A),C,D),B) = k8_finseq_1(u1_struct_0(A),k6_polynom1(A,C,B),k6_polynom1(A,D,B)) ) ) ) ) ).
fof(t24_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_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))
=> k7_polynom1(A,k8_finseq_1(u1_struct_0(A),C,D),B) = k8_finseq_1(u1_struct_0(A),k7_polynom1(A,C,B),k7_polynom1(A,D,B)) ) ) ) ) ).
fof(t25_polynom1,axiom,
$true ).
fof(t26_polynom1,axiom,
$true ).
fof(t27_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ( k1_rlvect_1(A) = k2_group_1(A)
=> v3_realset2(A) ) ) ).
fof(t28_polynom1,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k6_polynom1(A,C,B)) = k1_group_1(A,B,k9_rlvect_1(A,C)) ) ) ) ).
fof(t29_polynom1,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] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> k9_rlvect_1(A,k7_polynom1(A,C,B)) = k1_group_1(A,k9_rlvect_1(A,C),B) ) ) ) ).
fof(t30_polynom1,axiom,
! [A,B] :
( m2_finseq_1(B,k3_finseq_2(A))
=> k3_finseq_1(k15_dtconstr(A,B)) = k9_wsierp_1(k5_polynom1(A,B)) ) ).
fof(t31_polynom1,axiom,
! [A,B,C] :
( m2_finseq_1(C,k3_finseq_2(A))
=> ! [D] :
( m2_finseq_1(D,k3_finseq_2(B))
=> ( k5_polynom1(A,C) = k5_polynom1(B,D)
=> k3_finseq_1(k15_dtconstr(A,C)) = k3_finseq_1(k15_dtconstr(B,D)) ) ) ) ).
fof(t32_polynom1,axiom,
! [A,B] :
( m2_finseq_1(B,k3_finseq_2(A))
=> ! [C] :
~ ( r2_hidden(C,k4_finseq_1(k15_dtconstr(A,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(B))
& r2_hidden(E,k4_finseq_1(k1_funct_1(B,D)))
& C = k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(D,np__1)))),E)
& k1_funct_1(k1_funct_1(B,D),E) = k1_funct_1(k15_dtconstr(A,B),C) ) ) ) ) ) ).
fof(t33_polynom1,axiom,
! [A,B] :
( m2_finseq_1(B,k3_finseq_2(A))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k4_finseq_1(B))
& r2_hidden(D,k4_finseq_1(k1_funct_1(B,C))) )
=> ( r2_hidden(k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(C,np__1)))),D),k4_finseq_1(k15_dtconstr(A,B)))
& k1_funct_1(k1_funct_1(B,C),D) = k1_funct_1(k15_dtconstr(A,B),k1_nat_1(k9_wsierp_1(k5_polynom1(A,k16_finseq_1(k3_finseq_2(A),B,k5_binarith(C,np__1)))),D)) ) ) ) ) ) ).
fof(t34_polynom1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
=> k9_rlvect_1(A,k15_dtconstr(u1_struct_0(A),B)) = k9_rlvect_1(A,k8_matrlin(A,B)) ) ) ).
fof(t35_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,k3_finseq_2(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> m2_finseq_1(k13_pboole(C,k2_funcop_1(k4_finseq_1(C),D)),k3_finseq_2(B)) ) ) ) ) ).
fof(t36_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m2_finseq_1(C,k3_finseq_2(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ? [E] :
( m2_finseq_1(E,k3_finseq_2(B))
& E = k13_pboole(C,k2_funcop_1(k4_finseq_1(C),D))
& k1_partfun1(k5_numbers,A,A,B,k15_dtconstr(A,C),D) = k15_dtconstr(B,E) ) ) ) ) ) ).
fof(d4_polynom1,axiom,
$true ).
fof(d5_polynom1,axiom,
! [A,B] :
( ( v1_seq_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_seq_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k9_polynom1(A,B,C)
<=> ! [E] : k1_funct_1(D,E) = k9_binop_2(k1_seq_1(B,E),k1_seq_1(C,E)) ) ) ) ) ).
fof(d6_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& m1_pboole(C,A) )
=> ! [D] :
( m1_pboole(D,A)
=> ( D = k10_polynom1(A,B,C)
<=> ! [E] : k1_funct_1(D,E) = k5_binarith(k8_polynom1(B,E),k8_polynom1(C,E)) ) ) ) ) ).
fof(t37_polynom1,axiom,
! [A,B] :
( ( v1_seq_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_seq_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v1_seq_1(D)
& m1_pboole(D,A) )
=> ( ! [E] :
( r2_hidden(E,A)
=> k1_seq_1(B,E) = k9_binop_2(k1_seq_1(C,E),k1_seq_1(D,E)) )
=> r6_pboole(A,B,k9_polynom1(A,C,D)) ) ) ) ) ).
fof(t38_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& m1_pboole(D,A) )
=> ( ! [E] :
( r2_hidden(E,A)
=> k8_polynom1(B,E) = k5_binarith(k8_polynom1(C,E),k8_polynom1(D,E)) )
=> r6_pboole(A,B,k10_polynom1(A,C,D)) ) ) ) ) ).
fof(t39_polynom1,axiom,
! [A,B] :
( ( v1_seq_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_seq_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v1_seq_1(D)
& m1_pboole(D,A) )
=> r6_pboole(A,k9_polynom1(A,k9_polynom1(A,B,C),D),k9_polynom1(A,B,k9_polynom1(A,C,D))) ) ) ) ).
fof(t40_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& m1_pboole(C,A) )
=> ! [D] :
( ( v7_seqm_3(D)
& m1_pboole(D,A) )
=> r6_pboole(A,k10_polynom1(A,k10_polynom1(A,B,C),D),k10_polynom1(A,B,k9_polynom1(A,C,D))) ) ) ) ).
fof(d7_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( B = k11_polynom1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> k1_funct_1(A,C) != np__0 ) ) ) ).
fof(t41_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> r1_tarski(k11_polynom1(A),k1_relat_1(A)) ) ).
fof(d8_polynom1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_polynom1(A)
<=> v1_finset_1(k11_polynom1(A)) ) ) ).
fof(t42_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& m1_pboole(C,A) )
=> k11_polynom1(k9_polynom1(A,B,C)) = k2_xboole_0(k11_polynom1(B),k11_polynom1(C)) ) ) ).
fof(t43_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v7_seqm_3(C)
& m1_pboole(C,A) )
=> r1_tarski(k11_polynom1(k10_polynom1(A,B,C)),k11_polynom1(B)) ) ) ).
fof(d9_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( l2_struct_0(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] :
( m1_subset_1(D,k1_zfmisc_1(A))
=> ( D = k12_polynom1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( r2_hidden(E,D)
<=> k8_funct_2(A,u1_struct_0(B),C,E) != k1_rlvect_1(B) ) ) ) ) ) ) ) ).
fof(d10_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( l2_struct_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ( v2_polynom1(C,A,B)
<=> v1_finset_1(k12_polynom1(A,B,C)) ) ) ) ) ).
fof(t44_polynom1,axiom,
! [A] :
( v7_seqm_3(k2_funcop_1(A,np__0))
& v1_polynom1(k2_funcop_1(A,np__0))
& m1_pboole(k2_funcop_1(A,np__0),A) ) ).
fof(d11_polynom1,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) )
=> ( r1_polynom1(A,B,C)
<=> ? [D] :
( v3_ordinal1(D)
& ~ r1_xreal_0(k8_polynom1(C,D),k8_polynom1(B,D))
& ! [E] :
( v3_ordinal1(E)
=> ( r2_hidden(E,D)
=> k8_polynom1(B,E) = k8_polynom1(C,E) ) ) ) ) ) ) ) ).
fof(t45_polynom1,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] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( ( r1_polynom1(A,B,C)
& r1_polynom1(A,C,D) )
=> r1_polynom1(A,B,D) ) ) ) ) ) ).
fof(d12_polynom1,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) )
=> ( r2_polynom1(A,B,C)
<=> ( r1_polynom1(A,B,C)
| r6_pboole(A,B,C) ) ) ) ) ) ).
fof(t46_polynom1,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] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( ( r2_polynom1(A,B,C)
& r2_polynom1(A,C,D) )
=> r2_polynom1(A,B,D) ) ) ) ) ) ).
fof(t47_polynom1,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] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( ( r1_polynom1(A,B,C)
& r2_polynom1(A,C,D) )
=> r1_polynom1(A,B,D) ) ) ) ) ) ).
fof(t48_polynom1,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] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( ( r2_polynom1(A,B,C)
& r1_polynom1(A,C,D) )
=> r1_polynom1(A,B,D) ) ) ) ) ) ).
fof(t49_polynom1,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) )
=> ( r2_polynom1(A,B,C)
| r2_polynom1(A,C,B) ) ) ) ) ).
fof(d13_polynom1,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) )
=> ( r3_polynom1(A,B,C)
<=> ! [D] : r1_xreal_0(k8_polynom1(B,D),k8_polynom1(C,D)) ) ) ) ).
fof(t50_polynom1,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) )
=> ( ! [D] :
( r2_hidden(D,A)
=> r1_xreal_0(k8_polynom1(B,D),k8_polynom1(C,D)) )
=> r3_polynom1(A,B,C) ) ) ) ).
fof(t51_polynom1,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) )
=> ( r3_polynom1(A,B,C)
=> r6_pboole(A,k9_polynom1(A,k10_polynom1(A,C,B),B),C) ) ) ) ) ).
fof(t52_polynom1,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) )
=> r6_pboole(A,k10_polynom1(A,k9_polynom1(A,C,B),B),C) ) ) ).
fof(t53_polynom1,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) )
=> ( r3_polynom1(A,B,C)
=> r2_polynom1(A,B,C) ) ) ) ) ).
fof(t54_polynom1,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) )
=> ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ( r6_pboole(A,B,k9_polynom1(A,C,D))
=> r3_polynom1(A,C,B) ) ) ) ) ).
fof(d14_polynom1,axiom,
! [A,B] :
( B = k13_polynom1(A)
<=> ! [C] :
( r2_hidden(C,B)
<=> ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) ) ) ) ).
fof(t55_polynom1,axiom,
k14_polynom1(k1_xboole_0) = k1_tarski(k1_xboole_0) ).
fof(d15_polynom1,axiom,
! [A] : k16_polynom1(A) = k2_funcop_1(A,np__0) ).
fof(t56_polynom1,axiom,
! [A,B] : k8_polynom1(k16_polynom1(A),B) = np__0 ).
fof(t57_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r6_pboole(A,k9_polynom1(A,B,k16_polynom1(A)),B) ) ).
fof(t58_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r6_pboole(A,k10_polynom1(A,B,k16_polynom1(A)),B) ) ).
fof(t59_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r6_pboole(A,k10_polynom1(A,k16_polynom1(A),B),k16_polynom1(A)) ) ).
fof(t60_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r6_pboole(A,k10_polynom1(A,B,B),k16_polynom1(A)) ) ).
fof(t61_polynom1,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) )
=> ( ( r3_polynom1(A,B,C)
& r6_pboole(A,k10_polynom1(A,C,B),k16_polynom1(A)) )
=> r6_pboole(A,C,B) ) ) ) ).
fof(t62_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( r3_polynom1(A,B,k16_polynom1(A))
=> r6_pboole(A,k16_polynom1(A),B) ) ) ).
fof(t63_polynom1,axiom,
! [A,B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r3_polynom1(A,k16_polynom1(A),B) ) ).
fof(t64_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> r2_polynom1(A,k16_polynom1(A),B) ) ) ).
fof(d16_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v1_partfun1(B,k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& m2_relset_1(B,k14_polynom1(A),k14_polynom1(A)) )
=> ( B = k17_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) )
=> ( r2_hidden(k4_tarski(C,D),B)
<=> r2_polynom1(A,C,D) ) ) ) ) ) ) ).
fof(d17_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m2_relset_1(B,A,k5_numbers) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_fraenkel(A,k5_numbers)))
=> ( C = k18_polynom1(A,B)
<=> ! [D] :
( ( v7_seqm_3(D)
& m1_pboole(D,A) )
=> ( r2_hidden(D,C)
<=> ! [E] :
( r2_hidden(E,A)
=> r1_xreal_0(k8_polynom1(D,E),k8_polynom1(B,E)) ) ) ) ) ) ) ).
fof(t65_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m2_relset_1(B,A,k5_numbers) )
=> r2_hidden(B,k18_polynom1(A,B)) ) ).
fof(t66_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v1_polynom1(B)
& m2_relset_1(B,A,k5_numbers) )
=> r1_tarski(k18_polynom1(A,B),k14_polynom1(A)) ) ).
fof(t67_polynom1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v1_polynom1(B)
& m2_relset_1(B,A,k5_numbers) )
=> k1_card_1(k18_polynom1(A,B)) = k7_setwiseo(A,k5_numbers,k48_binop_2,k19_polynom1(A,B),k7_funcop_1(k5_numbers,A,k47_binop_2,B,np__1)) ) ) ).
fof(d18_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m1_trees_4(C,k13_polynom1(A),k14_polynom1(A))
=> ( C = k20_polynom1(A,B)
<=> ? [D] :
( ~ v1_xboole_0(D)
& v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(k14_polynom1(A)))
& C = k2_triang_1(k14_polynom1(A),D,k17_polynom1(A))
& ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( r2_hidden(E,D)
<=> r3_polynom1(A,E,B) ) ) ) ) ) ) ) ).
fof(t68_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( r2_hidden(B,k4_finseq_1(k20_polynom1(A,C)))
=> r3_polynom1(A,k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,C),B),C) ) ) ) ) ).
fof(t69_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,B),np__1) = k16_polynom1(A)
& k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,B),k3_finseq_1(k20_polynom1(A,B))) = B ) ) ) ).
fof(t70_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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_xreal_0(B,np__1)
& ~ r1_xreal_0(k3_finseq_1(k20_polynom1(A,C)),B)
& ~ ( k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,C),B) != k16_polynom1(A)
& k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,C),B) != C ) ) ) ) ) ) ) ).
fof(t71_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> k20_polynom1(A,k16_polynom1(A)) = k13_binarith(k14_polynom1(A),k16_polynom1(A)) ) ).
fof(d19_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m2_finseq_1(C,k4_finseq_2(np__2,k14_polynom1(A)))
=> ( C = k21_polynom1(A,B)
<=> ( k4_finseq_1(C) = k4_finseq_1(k20_polynom1(A,B))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ( ( r2_hidden(D,k4_finseq_1(C))
& E = k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,B),D) )
=> k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),C,D) = k10_finseq_1(E,k10_polynom1(A,B,E)) ) ) ) ) ) ) ) ) ).
fof(t72_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ~ ( r2_hidden(B,k4_finseq_1(k21_polynom1(A,C)))
& ! [D] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> ~ ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,C),B) = k10_finseq_1(D,E)
& r6_pboole(A,C,k9_polynom1(A,D,E)) ) ) ) ) ) ) ) ).
fof(t73_polynom1,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] :
( ( v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> ~ ( r6_pboole(A,B,k9_polynom1(A,C,D))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_finseq_1(k21_polynom1(A,B)))
& k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E) = k10_finseq_1(C,D) ) ) ) ) ) ) ) ).
fof(t74_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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_hidden(B,k4_finseq_1(k21_polynom1(A,C)))
& k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,C),B) = k10_finseq_1(D,E) )
=> D = k4_finseq_4(k5_numbers,k13_polynom1(A),k20_polynom1(A,C),B) ) ) ) ) ) ) ).
fof(t75_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),np__1) = k10_finseq_1(k16_polynom1(A),B)
& k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),k3_finseq_1(k21_polynom1(A,B))) = k10_finseq_1(B,k16_polynom1(A)) ) ) ) ).
fof(t76_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [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) )
=> ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,C),B) = k10_finseq_1(D,E)
=> ( r1_xreal_0(B,np__1)
| r1_xreal_0(k3_finseq_1(k21_polynom1(A,C)),B)
| ( D != k16_polynom1(A)
& E != k16_polynom1(A) ) ) ) ) ) ) ) ) ).
fof(t77_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> k21_polynom1(A,k16_polynom1(A)) = k3_matrlin(k14_polynom1(A),k2_finseq_4(k14_polynom1(A),k16_polynom1(A),k16_polynom1(A))) ) ).
fof(t78_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> ! [C] :
( m2_finseq_1(C,k3_finseq_2(k4_finseq_2(np__3,k14_polynom1(A))))
=> ! [D] :
( m2_finseq_1(D,k3_finseq_2(k4_finseq_2(np__3,k14_polynom1(A))))
=> ~ ( k4_finseq_1(C) = k4_finseq_1(k21_polynom1(A,B))
& k4_finseq_1(D) = k4_finseq_1(k21_polynom1(A,B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(C))
=> k1_funct_1(C,E) = k4_polynom1(k21_polynom1(A,k4_finseq_4(k5_numbers,k14_polynom1(A),k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E),np__1)),k2_finseq_2(k3_finseq_1(k21_polynom1(A,k4_finseq_4(k5_numbers,k14_polynom1(A),k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E),np__1))),k13_binarith(k14_polynom1(A),k4_finseq_4(k5_numbers,k14_polynom1(A),k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E),np__2)))) ) )
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(D))
=> k1_funct_1(D,E) = k4_polynom1(k2_finseq_2(k3_finseq_1(k21_polynom1(A,k4_finseq_4(k5_numbers,k14_polynom1(A),k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E),np__2))),k13_binarith(k14_polynom1(A),k4_finseq_4(k5_numbers,k14_polynom1(A),k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E),np__1))),k21_polynom1(A,k4_finseq_4(k5_numbers,k14_polynom1(A),k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,B),E),np__2))) ) )
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)),k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)))
& v3_funct_2(E,k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)),k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)))
& m2_relset_1(E,k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)),k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C))) )
=> k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),D) != k1_partfun1(k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)),k4_finseq_1(k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)),k5_numbers,k4_finseq_2(np__3,k14_polynom1(A)),E,k15_dtconstr(k4_finseq_2(np__3,k14_polynom1(A)),C)) ) ) ) ) ) ) ).
fof(d20_polynom1,axiom,
$true ).
fof(d21_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(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)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
=> ( E = k22_polynom1(A,B,C,D)
<=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> k15_polynom1(A,B,E,F) = k2_rlvect_1(B,k15_polynom1(A,B,C,F),k15_polynom1(A,B,D,F)) ) ) ) ) ) ) ).
fof(t79_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v5_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)) )
=> r1_tarski(k12_polynom1(k14_polynom1(A),B,k22_polynom1(A,B,C,D)),k4_subset_1(k14_polynom1(A),k12_polynom1(k14_polynom1(A),B,C),k12_polynom1(k14_polynom1(A),B,D))) ) ) ) ).
fof(t80_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_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] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
=> k22_polynom1(A,B,k22_polynom1(A,B,C,D),E) = k22_polynom1(A,B,C,k22_polynom1(A,B,D,E)) ) ) ) ) ).
fof(d22_polynom1,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)) )
=> ! [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)) )
=> ( D = k24_polynom1(A,B,C)
<=> ! [E] :
( ( v7_seqm_3(E)
& v1_polynom1(E)
& m1_pboole(E,A) )
=> k15_polynom1(A,B,D,E) = k5_rlvect_1(B,k15_polynom1(A,B,C,E)) ) ) ) ) ) ).
fof(d23_polynom1,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)) )
=> ! [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)) )
=> k25_polynom1(A,B,C,D) = k22_polynom1(A,B,C,k24_polynom1(A,B,D)) ) ) ) ).
fof(d24_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> k26_polynom1(A,B) = k5_rfunct_3(k13_polynom1(A),u1_struct_0(B),k14_polynom1(A),k1_rlvect_1(B)) ) ).
fof(t81_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> k15_polynom1(A,B,k26_polynom1(A,B),C) = k1_rlvect_1(B) ) ) ).
fof(t82_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v5_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,C,k26_polynom1(A,B)) = C ) ) ).
fof(d25_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_group_1(B)
& l2_vectsp_1(B) )
=> k27_polynom1(A,B) = k1_polynom1(k14_polynom1(A),u1_struct_0(B),k26_polynom1(A,B),k16_polynom1(A),k2_group_1(B)) ) ).
fof(t83_polynom1,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,C) = k26_polynom1(A,B) ) ) ).
fof(t84_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_group_1(B)
& l2_vectsp_1(B) )
=> ( k15_polynom1(A,B,k27_polynom1(A,B),k16_polynom1(A)) = k2_group_1(B)
& ! [C] :
( ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( C != k16_polynom1(A)
=> k15_polynom1(A,B,k27_polynom1(A,B),C) = k1_rlvect_1(B) ) ) ) ) ).
fof(d26_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_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] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
=> ( E = k28_polynom1(A,B,C,D)
<=> ! [F] :
( ( v7_seqm_3(F)
& v1_polynom1(F)
& m1_pboole(F,A) )
=> ? [G] :
( m2_finseq_1(G,u1_struct_0(B))
& k15_polynom1(A,B,E,F) = k9_rlvect_1(B,G)
& k3_finseq_1(G) = k3_finseq_1(k21_polynom1(A,F))
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(H,k4_finseq_1(G))
& ! [I] :
( ( v7_seqm_3(I)
& v1_polynom1(I)
& m1_pboole(I,A) )
=> ! [J] :
( ( v7_seqm_3(J)
& v1_polynom1(J)
& m1_pboole(J,A) )
=> ~ ( k3_polynom1(k14_polynom1(A),k5_numbers,k4_finseq_2(np__2,k14_polynom1(A)),k21_polynom1(A,F),H) = k10_finseq_1(I,J)
& k4_finseq_4(k5_numbers,u1_struct_0(B),G,H) = k1_group_1(B,k15_polynom1(A,B,C,I),k15_polynom1(A,B,D,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t85_polynom1,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)
& v4_group_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] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
=> k28_polynom1(A,B,C,k23_polynom1(A,B,D,E)) = k23_polynom1(A,B,k28_polynom1(A,B,C,D),k28_polynom1(A,B,C,E)) ) ) ) ) ) ).
fof(t86_polynom1,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_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] :
( ( v1_funct_1(E)
& v1_funct_2(E,k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(E,k14_polynom1(A),u1_struct_0(B)) )
=> k28_polynom1(A,B,k28_polynom1(A,B,C,D),E) = k28_polynom1(A,B,C,k28_polynom1(A,B,D,E)) ) ) ) ) ) ).
fof(t87_polynom1,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)
& 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,C,k26_polynom1(A,B)) = k26_polynom1(A,B) ) ) ) ).
fof(t88_polynom1,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))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> k28_polynom1(A,B,C,k27_polynom1(A,B)) = C ) ) ) ).
fof(t89_polynom1,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))
& m2_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> k28_polynom1(A,B,k27_polynom1(A,B),C) = C ) ) ) ).
fof(d27_polynom1,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] :
( ( ~ v3_struct_0(C)
& v3_vectsp_1(C)
& l3_vectsp_1(C) )
=> ( C = k30_polynom1(A,B)
<=> ( ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ( 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)) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(F,k14_polynom1(A),B)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(G,k14_polynom1(A),B)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(B)) )
=> ( ( D = F
& E = G )
=> k2_rlvect_1(C,D,E) = k22_polynom1(A,B,F,G) ) ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(F,k14_polynom1(A),B)
& m2_relset_1(F,k14_polynom1(A),u1_struct_0(B)) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k14_polynom1(A),u1_struct_0(B))
& v2_polynom1(G,k14_polynom1(A),B)
& m2_relset_1(G,k14_polynom1(A),u1_struct_0(B)) )
=> ( ( D = F
& E = G )
=> k1_group_1(C,D,E) = k28_polynom1(A,B,F,G) ) ) ) ) )
& k1_rlvect_1(C) = k26_polynom1(A,B)
& k2_vectsp_1(C) = k27_polynom1(A,B) ) ) ) ) ) ).
fof(t90_polynom1,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_vectsp_1(B)
& ~ v3_realset2(B)
& l3_vectsp_1(B) )
=> k2_group_1(k30_polynom1(A,B)) = k27_polynom1(A,B) ) ) ).
fof(t91_polynom1,axiom,
! [A,B] :
( ( v1_seq_1(B)
& m1_pboole(B,A) )
=> ! [C] :
( ( v1_seq_1(C)
& m1_pboole(C,A) )
=> r1_tarski(k11_polynom1(k9_polynom1(A,B,C)),k2_xboole_0(k11_polynom1(B),k11_polynom1(C))) ) ) ).
fof(dt_m1_polynom1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) )
=> ! [C] :
( m1_polynom1(C,A,B)
=> ( v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) ) ) ) ).
fof(existence_m1_polynom1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) )
=> ? [C] : m1_polynom1(C,A,B) ) ).
fof(redefinition_m1_polynom1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k14_polynom1(A))) )
=> ! [C] :
( m1_polynom1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(antisymmetry_r1_polynom1,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> ( r1_polynom1(A,B,C)
=> ~ r1_polynom1(A,C,B) ) ) ).
fof(reflexivity_r2_polynom1,axiom,
! [A,B,C] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> r2_polynom1(A,B,B) ) ).
fof(reflexivity_r3_polynom1,axiom,
! [A,B,C] :
( ( v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& v1_polynom1(C)
& m1_pboole(C,A) )
=> r3_polynom1(A,B,B) ) ).
fof(dt_k1_polynom1,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(E,B) )
=> ( v1_funct_1(k1_polynom1(A,B,C,D,E))
& v1_funct_2(k1_polynom1(A,B,C,D,E),A,B)
& m2_relset_1(k1_polynom1(A,B,C,D,E),A,B) ) ) ).
fof(redefinition_k1_polynom1,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& m1_subset_1(E,B) )
=> k1_polynom1(A,B,C,D,E) = k2_funct_7(C,D,E) ) ).
fof(dt_k2_polynom1,axiom,
! [A,B,C,D] :
( m1_pboole(B,A)
=> m1_pboole(k2_polynom1(A,B,C,D),A) ) ).
fof(redefinition_k2_polynom1,axiom,
! [A,B,C,D] :
( m1_pboole(B,A)
=> k2_polynom1(A,B,C,D) = k2_funct_7(B,C,D) ) ).
fof(dt_k3_polynom1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(C)
& m1_finseq_2(C,A)
& v1_funct_1(D)
& m1_relset_1(D,B,C) )
=> m2_finseq_2(k3_polynom1(A,B,C,D,E),A,C) ) ).
fof(redefinition_k3_polynom1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(C)
& m1_finseq_2(C,A)
& v1_funct_1(D)
& m1_relset_1(D,B,C) )
=> k3_polynom1(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) ).
fof(dt_k4_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_matrlin(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_matrlin(B) )
=> ( v1_relat_1(k4_polynom1(A,B))
& v1_funct_1(k4_polynom1(A,B))
& v1_finseq_1(k4_polynom1(A,B))
& v1_matrlin(k4_polynom1(A,B)) ) ) ).
fof(redefinition_k4_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A)
& v1_matrlin(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& v1_matrlin(B) )
=> k4_polynom1(A,B) = k4_matrlin(A,B) ) ).
fof(dt_k5_polynom1,axiom,
! [A,B] :
( m1_finseq_1(B,k3_finseq_2(A))
=> ( v1_card_3(k5_polynom1(A,B))
& m1_trees_4(k5_polynom1(A,B),k1_numbers,k5_numbers) ) ) ).
fof(redefinition_k5_polynom1,axiom,
! [A,B] :
( m1_finseq_1(B,k3_finseq_2(A))
=> k5_polynom1(A,B) = k1_card_3(B) ) ).
fof(dt_k6_polynom1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& m1_finseq_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m2_finseq_1(k6_polynom1(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k6_polynom1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& m1_finseq_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k6_polynom1(A,B,C) = k9_fvsum_1(A,B,C) ) ).
fof(dt_k7_polynom1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& m1_finseq_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m2_finseq_1(k7_polynom1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k8_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A) )
=> m2_subset_1(k8_polynom1(A,B),k1_numbers,k5_numbers) ) ).
fof(redefinition_k8_polynom1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v7_seqm_3(A) )
=> k8_polynom1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k9_polynom1,axiom,
! [A,B,C] :
( ( v1_seq_1(B)
& m1_pboole(B,A)
& v1_seq_1(C)
& m1_pboole(C,A) )
=> m1_pboole(k9_polynom1(A,B,C),A) ) ).
fof(commutativity_k9_polynom1,axiom,
! [A,B,C] :
( ( v1_seq_1(B)
& m1_pboole(B,A)
& v1_seq_1(C)
& m1_pboole(C,A) )
=> k9_polynom1(A,B,C) = k9_polynom1(A,C,B) ) ).
fof(dt_k10_polynom1,axiom,
! [A,B,C] :
( ( v7_seqm_3(B)
& m1_pboole(B,A)
& v7_seqm_3(C)
& m1_pboole(C,A) )
=> m1_pboole(k10_polynom1(A,B,C),A) ) ).
fof(dt_k11_polynom1,axiom,
$true ).
fof(dt_k12_polynom1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& l2_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> m1_subset_1(k12_polynom1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(dt_k13_polynom1,axiom,
$true ).
fof(dt_k14_polynom1,axiom,
! [A] : m1_subset_1(k14_polynom1(A),k1_zfmisc_1(k13_polynom1(A))) ).
fof(redefinition_k14_polynom1,axiom,
! [A] : k14_polynom1(A) = k13_polynom1(A) ).
fof(dt_k15_polynom1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_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))
& v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> m1_subset_1(k15_polynom1(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k15_polynom1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_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))
& v7_seqm_3(D)
& v1_polynom1(D)
& m1_pboole(D,A) )
=> k15_polynom1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k16_polynom1,axiom,
! [A] : m1_polynom1(k16_polynom1(A),A,k14_polynom1(A)) ).
fof(dt_k17_polynom1,axiom,
! [A] :
( v3_ordinal1(A)
=> ( v1_partfun1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A))
& v1_relat_2(k17_polynom1(A))
& v4_relat_2(k17_polynom1(A))
& v8_relat_2(k17_polynom1(A))
& m2_relset_1(k17_polynom1(A),k14_polynom1(A),k14_polynom1(A)) ) ) ).
fof(dt_k18_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& m1_relset_1(B,A,k5_numbers) )
=> m1_subset_1(k18_polynom1(A,B),k1_zfmisc_1(k1_fraenkel(A,k5_numbers))) ) ).
fof(dt_k19_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v1_polynom1(B)
& m1_relset_1(B,A,k5_numbers) )
=> m1_subset_1(k19_polynom1(A,B),k5_finsub_1(A)) ) ).
fof(redefinition_k19_polynom1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,k5_numbers)
& v1_polynom1(B)
& m1_relset_1(B,A,k5_numbers) )
=> k19_polynom1(A,B) = k11_polynom1(B) ) ).
fof(dt_k20_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> m1_trees_4(k20_polynom1(A,B),k13_polynom1(A),k14_polynom1(A)) ) ).
fof(dt_k21_polynom1,axiom,
! [A,B] :
( ( v3_ordinal1(A)
& v7_seqm_3(B)
& v1_polynom1(B)
& m1_pboole(B,A) )
=> m2_finseq_1(k21_polynom1(A,B),k4_finseq_2(np__2,k14_polynom1(A))) ) ).
fof(dt_k22_polynom1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_funct_1(k22_polynom1(A,B,C,D))
& v1_funct_2(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k22_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(dt_k23_polynom1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v5_rlvect_1(B)
& l1_rlvect_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_funct_1(k23_polynom1(A,B,C,D))
& v1_funct_2(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k23_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(commutativity_k23_polynom1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v5_rlvect_1(B)
& l1_rlvect_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k23_polynom1(A,B,C,D) = k23_polynom1(A,B,D,C) ) ).
fof(redefinition_k23_polynom1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v5_rlvect_1(B)
& l1_rlvect_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k23_polynom1(A,B,C,D) = k22_polynom1(A,B,C,D) ) ).
fof(dt_k24_polynom1,axiom,
! [A,B,C] :
( ( ~ 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))
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_funct_1(k24_polynom1(A,B,C))
& v1_funct_2(k24_polynom1(A,B,C),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k24_polynom1(A,B,C),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(involutiveness_k24_polynom1,axiom,
! [A,B,C] :
( ( ~ 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))
& m1_relset_1(C,k14_polynom1(A),u1_struct_0(B)) )
=> k24_polynom1(A,B,k24_polynom1(A,B,C)) = C ) ).
fof(dt_k25_polynom1,axiom,
! [A,B,C,D] :
( ( ~ 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))
& 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))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( 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))
& m2_relset_1(k25_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(dt_k26_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> ( v1_funct_1(k26_polynom1(A,B))
& v1_funct_2(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k26_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(dt_k27_polynom1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_group_1(B)
& l2_vectsp_1(B) )
=> ( v1_funct_1(k27_polynom1(A,B))
& v1_funct_2(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k27_polynom1(A,B),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(dt_k28_polynom1,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l3_vectsp_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( 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))
& m2_relset_1(k28_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(dt_k29_polynom1,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_group_1(B)
& l3_vectsp_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> ( v1_funct_1(k29_polynom1(A,B,C,D))
& v1_funct_2(k29_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B))
& m2_relset_1(k29_polynom1(A,B,C,D),k14_polynom1(A),u1_struct_0(B)) ) ) ).
fof(commutativity_k29_polynom1,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_group_1(B)
& l3_vectsp_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k29_polynom1(A,B,C,D) = k29_polynom1(A,B,D,C) ) ).
fof(redefinition_k29_polynom1,axiom,
! [A,B,C,D] :
( ( v3_ordinal1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_group_1(B)
& l3_vectsp_1(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))
& v1_funct_1(D)
& v1_funct_2(D,k14_polynom1(A),u1_struct_0(B))
& m1_relset_1(D,k14_polynom1(A),u1_struct_0(B)) )
=> k29_polynom1(A,B,C,D) = k28_polynom1(A,B,C,D) ) ).
fof(dt_k30_polynom1,axiom,
! [A,B] :
( ( 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) )
=> ( ~ v3_struct_0(k30_polynom1(A,B))
& v3_vectsp_1(k30_polynom1(A,B))
& l3_vectsp_1(k30_polynom1(A,B)) ) ) ).
%------------------------------------------------------------------------------