SET007 Axioms: SET007+748.ax
%------------------------------------------------------------------------------
% File : SET007+748 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bilinear Functionals in Vector Spaces
% 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 : bilinear [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 180 ( 1 unt; 0 def)
% Number of atoms : 3357 ( 114 equ)
% Maximal formula atoms : 46 ( 18 avg)
% Number of connectives : 3725 ( 548 ~; 1 |;2574 &)
% ( 23 <=>; 579 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 17 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-4 aty)
% Number of functors : 52 ( 52 usr; 0 con; 1-5 aty)
% Number of variables : 860 ( 848 !; 12 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ( v1_relat_1(k1_bilinear(A,B,C))
& v1_funct_1(k1_bilinear(A,B,C))
& v1_funct_2(k1_bilinear(A,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k1_bilinear(A,B,C),A,B,C) ) ) ).
fof(fc2_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ( v1_relat_1(k1_bilinear(A,B,C))
& v1_funct_1(k1_bilinear(A,B,C))
& v1_funct_2(k1_bilinear(A,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k1_bilinear(A,B,C),A,B,C) ) ) ).
fof(rc1_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ? [D] :
( m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_relat_1(D)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C) ) ) ).
fof(fc3_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ( v1_relat_1(k1_bilinear(A,B,C))
& v1_funct_1(k1_bilinear(A,B,C))
& v1_funct_2(k1_bilinear(A,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k1_bilinear(A,B,C),A,B,C)
& v2_bilinear(k1_bilinear(A,B,C),A,B,C)
& v3_bilinear(k1_bilinear(A,B,C),A,B,C) ) ) ).
fof(fc4_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ( v1_relat_1(k1_bilinear(A,B,C))
& v1_funct_1(k1_bilinear(A,B,C))
& v1_funct_2(k1_bilinear(A,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k1_bilinear(A,B,C),A,B,C)
& v2_bilinear(k1_bilinear(A,B,C),A,B,C)
& v4_bilinear(k1_bilinear(A,B,C),A,B,C) ) ) ).
fof(rc2_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ? [D] :
( m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_relat_1(D)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C) ) ) ).
fof(fc5_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( v1_relat_1(k9_bilinear(A,B,C,D,E))
& v1_funct_1(k9_bilinear(A,B,C,D,E))
& v1_funct_2(k9_bilinear(A,B,C,D,E),u1_struct_0(C),u1_struct_0(A))
& v1_hahnban1(k9_bilinear(A,B,C,D,E),A,C) ) ) ).
fof(fc6_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(C)) )
=> ( v1_relat_1(k10_bilinear(A,B,C,D,E))
& v1_funct_1(k10_bilinear(A,B,C,D,E))
& v1_funct_2(k10_bilinear(A,B,C,D,E),u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(k10_bilinear(A,B,C,D,E),A,B) ) ) ).
fof(fc7_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( v1_relat_1(k9_bilinear(A,B,C,D,E))
& v1_funct_1(k9_bilinear(A,B,C,D,E))
& v1_funct_2(k9_bilinear(A,B,C,D,E),u1_struct_0(C),u1_struct_0(A))
& v2_hahnban1(k9_bilinear(A,B,C,D,E),A,C) ) ) ).
fof(fc8_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(C)) )
=> ( v1_relat_1(k10_bilinear(A,B,C,D,E))
& v1_funct_1(k10_bilinear(A,B,C,D,E))
& v1_funct_2(k10_bilinear(A,B,C,D,E),u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(k10_bilinear(A,B,C,D,E),A,B) ) ) ).
fof(fc9_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& v1_hahnban1(E,A,C)
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc10_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc11_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& v2_hahnban1(E,A,C)
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc12_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(k11_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc13_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& ~ v1_realset1(k11_bilinear(A,B,C,D,E)) ) ) ).
fof(fc14_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& ~ v3_realset2(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& ~ v1_realset1(k11_bilinear(A,B,C,D,E)) ) ) ).
fof(fc15_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& ~ v3_realset2(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(D)
& v3_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& ~ v5_seqm_3(E)
& v3_hahnban1(E,A,C)
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_relat_1(k11_bilinear(A,B,C,D,E))
& v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& ~ v5_seqm_3(k11_bilinear(A,B,C,D,E))
& ~ v1_realset1(k11_bilinear(A,B,C,D,E)) ) ) ).
fof(rc3_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& ~ v3_realset2(C)
& l4_vectsp_1(C,A) )
=> ? [D] :
( m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_relat_1(D)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& ~ v5_seqm_3(D)
& ~ v1_realset1(D)
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C) ) ) ).
fof(fc16_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k2_bilinear(A,B,C,D,E))
& v1_funct_1(k2_bilinear(A,B,C,D,E))
& v1_funct_2(k2_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k2_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc17_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k2_bilinear(A,B,C,D,E))
& v1_funct_1(k2_bilinear(A,B,C,D,E))
& v1_funct_2(k2_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k2_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc18_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_relat_1(k3_bilinear(A,B,C,D,E))
& v1_funct_1(k3_bilinear(A,B,C,D,E))
& v1_funct_2(k3_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k3_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc19_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_relat_1(k3_bilinear(A,B,C,D,E))
& v1_funct_1(k3_bilinear(A,B,C,D,E))
& v1_funct_2(k3_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k3_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc20_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k4_bilinear(A,B,C,D))
& v1_funct_1(k4_bilinear(A,B,C,D))
& v1_funct_2(k4_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k4_bilinear(A,B,C,D),A,B,C) ) ) ).
fof(fc21_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k4_bilinear(A,B,C,D))
& v1_funct_1(k4_bilinear(A,B,C,D))
& v1_funct_2(k4_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k4_bilinear(A,B,C,D),A,B,C) ) ) ).
fof(fc22_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k6_bilinear(A,B,C,D,E))
& v1_funct_1(k6_bilinear(A,B,C,D,E))
& v1_funct_2(k6_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k6_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc23_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k6_bilinear(A,B,C,D,E))
& v1_funct_1(k6_bilinear(A,B,C,D,E))
& v1_funct_2(k6_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k6_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc24_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k2_bilinear(A,B,C,D,E))
& v1_funct_1(k2_bilinear(A,B,C,D,E))
& v1_funct_2(k2_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(k2_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc25_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k2_bilinear(A,B,C,D,E))
& v1_funct_1(k2_bilinear(A,B,C,D,E))
& v1_funct_2(k2_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(k2_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc26_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_relat_1(k3_bilinear(A,B,C,D,E))
& v1_funct_1(k3_bilinear(A,B,C,D,E))
& v1_funct_2(k3_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(k3_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc27_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_relat_1(k3_bilinear(A,B,C,D,E))
& v1_funct_1(k3_bilinear(A,B,C,D,E))
& v1_funct_2(k3_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(k3_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc28_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k4_bilinear(A,B,C,D))
& v1_funct_1(k4_bilinear(A,B,C,D))
& v1_funct_2(k4_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(k4_bilinear(A,B,C,D),A,B,C) ) ) ).
fof(fc29_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k4_bilinear(A,B,C,D))
& v1_funct_1(k4_bilinear(A,B,C,D))
& v1_funct_2(k4_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(k4_bilinear(A,B,C,D),A,B,C) ) ) ).
fof(fc30_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k6_bilinear(A,B,C,D,E))
& v1_funct_1(k6_bilinear(A,B,C,D,E))
& v1_funct_2(k6_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(k6_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc31_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(E,A,B,C)
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k6_bilinear(A,B,C,D,E))
& v1_funct_1(k6_bilinear(A,B,C,D,E))
& v1_funct_2(k6_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(k6_bilinear(A,B,C,D,E),A,B,C) ) ) ).
fof(fc32_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k12_bilinear(A,B,C,D)) ) ).
fof(fc33_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k12_bilinear(A,B,C,D)) ) ).
fof(fc34_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v5_rlvect_1(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k13_bilinear(A,B,C,D)) ) ).
fof(fc35_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k13_bilinear(A,B,C,D)) ) ).
fof(fc36_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ).
fof(fc37_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v2_bilinear(C,A,B,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ).
fof(fc38_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v3_bilinear(C,A,B,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ).
fof(fc39_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v4_bilinear(C,A,B,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ~ v1_xboole_0(k14_bilinear(A,B,C)) ) ).
fof(fc40_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k17_bilinear(A,B,C,D))
& v1_funct_1(k17_bilinear(A,B,C,D))
& v1_funct_2(k17_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& v2_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& v3_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& v4_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C) ) ) ).
fof(fc41_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k18_bilinear(A,B,C,D))
& v1_funct_1(k18_bilinear(A,B,C,D))
& v1_funct_2(k18_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v2_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v4_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D))) ) ) ).
fof(fc42_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v5_rlvect_1(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k17_bilinear(A,B,C,D))
& v1_funct_1(k17_bilinear(A,B,C,D))
& v1_funct_2(k17_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& v4_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& ~ v5_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C) ) ) ).
fof(fc43_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k18_bilinear(A,B,C,D))
& v1_funct_1(k18_bilinear(A,B,C,D))
& v1_funct_2(k18_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v6_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D))) ) ) ).
fof(fc44_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k19_bilinear(A,B,C,D))
& v1_funct_1(k19_bilinear(A,B,C,D))
& v1_funct_2(k19_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v2_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v4_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v5_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v6_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D))) ) ) ).
fof(fc45_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)))
& v1_funct_1(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)))
& v1_funct_2(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))))),u1_struct_0(A))
& v1_bilinear(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))))
& v2_bilinear(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))))
& v3_bilinear(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))))
& v4_bilinear(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))))
& ~ v5_bilinear(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))))
& ~ v6_bilinear(k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)))) ) ) ).
fof(fc46_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)))
& v1_funct_1(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)))
& v1_funct_2(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v2_bilinear(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v4_bilinear(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v5_bilinear(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v6_bilinear(k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)),A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D))) ) ) ).
fof(fc47_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& ~ v3_realset2(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& ~ v5_seqm_3(D)
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_relat_1(k19_bilinear(A,B,C,D))
& v1_funct_1(k19_bilinear(A,B,C,D))
& v1_funct_2(k19_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& ~ v5_seqm_3(k19_bilinear(A,B,C,D))
& v1_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v2_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v4_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v5_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& ~ v6_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D))) ) ) ).
fof(fc48_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k1_bilinear(A,B,B))
& v1_funct_1(k1_bilinear(A,B,B))
& v1_funct_2(k1_bilinear(A,B,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(k1_bilinear(A,B,B),A,B) ) ) ).
fof(fc49_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k1_bilinear(A,B,B))
& v1_funct_1(k1_bilinear(A,B,B))
& v1_funct_2(k1_bilinear(A,B,B),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(k1_bilinear(A,B,B),A,B) ) ) ).
fof(rc4_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(C,A,B) ) ) ).
fof(rc5_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(C,A,B) ) ) ).
fof(rc6_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v3_bilinear(C,A,B,B)
& v4_bilinear(C,A,B,B)
& v7_bilinear(C,A,B) ) ) ).
fof(rc7_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v3_bilinear(C,A,B,B)
& v4_bilinear(C,A,B,B)
& v8_bilinear(C,A,B) ) ) ).
fof(rc8_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& ~ v5_seqm_3(C)
& ~ v1_realset1(C)
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v3_bilinear(C,A,B,B)
& v4_bilinear(C,A,B,B)
& v7_bilinear(C,A,B) ) ) ).
fof(rc9_bilinear,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v8_bilinear(C,A,B) ) ) ).
fof(fc50_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(D,A,B)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v1_relat_1(k2_bilinear(A,B,B,C,D))
& v1_funct_1(k2_bilinear(A,B,B,C,D))
& v1_funct_2(k2_bilinear(A,B,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(k2_bilinear(A,B,B,C,D),A,B) ) ) ).
fof(fc51_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> ( v1_relat_1(k3_bilinear(A,B,B,C,D))
& v1_funct_1(k3_bilinear(A,B,B,C,D))
& v1_funct_2(k3_bilinear(A,B,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(k3_bilinear(A,B,B,C,D),A,B) ) ) ).
fof(fc52_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v1_relat_1(k4_bilinear(A,B,B,C))
& v1_funct_1(k4_bilinear(A,B,B,C))
& v1_funct_2(k4_bilinear(A,B,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(k4_bilinear(A,B,B,C),A,B) ) ) ).
fof(fc53_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(D,A,B)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v1_relat_1(k6_bilinear(A,B,B,C,D))
& v1_funct_1(k6_bilinear(A,B,B,C,D))
& v1_funct_2(k6_bilinear(A,B,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v7_bilinear(k6_bilinear(A,B,B,C,D),A,B) ) ) ).
fof(fc54_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(D,A,B)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v1_relat_1(k2_bilinear(A,B,B,C,D))
& v1_funct_1(k2_bilinear(A,B,B,C,D))
& v1_funct_2(k2_bilinear(A,B,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(k2_bilinear(A,B,B,C,D),A,B) ) ) ).
fof(fc55_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> ( v1_relat_1(k3_bilinear(A,B,B,C,D))
& v1_funct_1(k3_bilinear(A,B,B,C,D))
& v1_funct_2(k3_bilinear(A,B,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(k3_bilinear(A,B,B,C,D),A,B) ) ) ).
fof(fc56_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v1_relat_1(k4_bilinear(A,B,B,C))
& v1_funct_1(k4_bilinear(A,B,B,C))
& v1_funct_2(k4_bilinear(A,B,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(k4_bilinear(A,B,B,C),A,B) ) ) ).
fof(fc57_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(D,A,B)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v1_relat_1(k6_bilinear(A,B,B,C,D))
& v1_funct_1(k6_bilinear(A,B,B,C,D))
& v1_funct_2(k6_bilinear(A,B,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v8_bilinear(k6_bilinear(A,B,B,C,D),A,B) ) ) ).
fof(d1_bilinear,axiom,
$true ).
fof(d2_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( l4_vectsp_1(B,A)
=> ! [C] :
( l4_vectsp_1(C,A)
=> k1_bilinear(A,B,C) = k1_borsuk_1(u1_struct_0(A),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),k1_rlvect_1(A)) ) ) ) ).
fof(d3_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( F = k2_bilinear(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),F,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)) = k2_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),E,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H))) ) ) ) ) ) ) ) ) ) ).
fof(d4_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( F = k3_bilinear(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),F,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)) = k1_group_1(A,E,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H))) ) ) ) ) ) ) ) ) ) ).
fof(d5_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( E = k4_bilinear(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),E,k1_domain_1(u1_struct_0(B),u1_struct_0(C),F,G)) = k5_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),F,G))) ) ) ) ) ) ) ) ) ).
fof(d6_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k5_bilinear(A,B,C,D) = k3_bilinear(A,B,C,D,k5_rlvect_1(A,k2_group_1(A))) ) ) ) ) ).
fof(d7_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k6_bilinear(A,B,C,D,E) = k2_bilinear(A,B,C,D,k4_bilinear(A,B,C,E)) ) ) ) ) ) ).
fof(d8_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( F = k7_bilinear(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),F,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)) = k6_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),E,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H))) ) ) ) ) ) ) ) ) ) ).
fof(t1_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),k1_bilinear(A,B,C),k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,E)) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t2_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k2_bilinear(A,B,C,D,k1_bilinear(A,B,C)) = D ) ) ) ) ).
fof(t3_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k2_bilinear(A,B,C,k2_bilinear(A,B,C,D,E),F) = k2_bilinear(A,B,C,D,k2_bilinear(A,B,C,E,F)) ) ) ) ) ) ) ).
fof(t4_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k7_bilinear(A,B,C,D,D) = k1_bilinear(A,B,C) ) ) ) ) ).
fof(t5_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k3_bilinear(A,B,C,k2_bilinear(A,B,C,E,F),D) = k2_bilinear(A,B,C,k3_bilinear(A,B,C,E,D),k3_bilinear(A,B,C,F,D)) ) ) ) ) ) ) ).
fof(t6_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k3_bilinear(A,B,C,F,k2_rlvect_1(A,D,E)) = k2_bilinear(A,B,C,k3_bilinear(A,B,C,F,D),k3_bilinear(A,B,C,F,E)) ) ) ) ) ) ) ).
fof(t7_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k3_bilinear(A,B,C,F,k1_group_1(A,D,E)) = k3_bilinear(A,B,C,k3_bilinear(A,B,C,F,E),D) ) ) ) ) ) ) ).
fof(t8_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k3_bilinear(A,B,C,D,k2_group_1(A)) = D ) ) ) ) ).
fof(d9_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k9_bilinear(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) ).
fof(d10_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k10_bilinear(A,B,C,D,E) = k1_funct_1(k5_funct_5(D),E) ) ) ) ) ) ).
fof(t9_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k4_relset_1(u1_struct_0(C),u1_struct_0(A),k9_bilinear(A,B,C,D,E)) = u1_struct_0(C)
& r1_tarski(k5_relset_1(u1_struct_0(C),u1_struct_0(A),k9_bilinear(A,B,C,D,E)),u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k8_funct_2(u1_struct_0(C),u1_struct_0(A),k9_bilinear(A,B,C,D,E),F) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F)) ) ) ) ) ) ) ) ).
fof(t10_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ( k4_relset_1(u1_struct_0(B),u1_struct_0(A),k10_bilinear(A,B,C,D,E)) = u1_struct_0(B)
& r1_tarski(k5_relset_1(u1_struct_0(B),u1_struct_0(A),k10_bilinear(A,B,C,D,E)),u1_struct_0(A))
& ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k10_bilinear(A,B,C,D,E),F) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),F,E)) ) ) ) ) ) ) ) ).
fof(t11_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k9_bilinear(A,B,C,k1_bilinear(A,B,C),D) = k7_hahnban1(A,C) ) ) ) ) ).
fof(t12_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> k10_bilinear(A,B,C,k1_bilinear(A,B,C),D) = k7_hahnban1(A,B) ) ) ) ) ).
fof(t13_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k10_bilinear(A,B,C,k2_bilinear(A,B,C,D,E),F) = k3_hahnban1(A,B,k10_bilinear(A,B,C,D,F),k10_bilinear(A,B,C,E,F)) ) ) ) ) ) ) ).
fof(t14_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k9_bilinear(A,B,C,k2_bilinear(A,B,C,D,E),F) = k3_hahnban1(A,C,k9_bilinear(A,B,C,D,F),k9_bilinear(A,B,C,E,F)) ) ) ) ) ) ) ).
fof(t15_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k10_bilinear(A,B,C,k3_bilinear(A,B,C,D,E),F) = k6_hahnban1(A,B,E,k10_bilinear(A,B,C,D,F)) ) ) ) ) ) ) ).
fof(t16_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k9_bilinear(A,B,C,k3_bilinear(A,B,C,D,E),F) = k6_hahnban1(A,C,E,k9_bilinear(A,B,C,D,F)) ) ) ) ) ) ) ).
fof(t17_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k10_bilinear(A,B,C,k4_bilinear(A,B,C,D),E) = k4_hahnban1(A,B,k10_bilinear(A,B,C,D,E)) ) ) ) ) ) ).
fof(t18_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k9_bilinear(A,B,C,k4_bilinear(A,B,C,D),E) = k4_hahnban1(A,C,k9_bilinear(A,B,C,D,E)) ) ) ) ) ) ).
fof(t19_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k10_bilinear(A,B,C,k7_bilinear(A,B,C,D,E),F) = k5_hahnban1(A,B,k10_bilinear(A,B,C,D,F),k10_bilinear(A,B,C,E,F)) ) ) ) ) ) ) ).
fof(t20_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k9_bilinear(A,B,C,k7_bilinear(A,B,C,D,E),F) = k5_hahnban1(A,C,k9_bilinear(A,B,C,D,F),k9_bilinear(A,B,C,E,F)) ) ) ) ) ) ) ).
fof(d11_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( F = k11_bilinear(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),F,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)) = k1_group_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,G),k8_funct_2(u1_struct_0(C),u1_struct_0(A),E,H)) ) ) ) ) ) ) ) ) ) ).
fof(t21_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),k11_bilinear(A,B,C,D,k7_hahnban1(A,C)),k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F)) = k1_rlvect_1(A) ) ) ) ) ) ) ).
fof(t22_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v5_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),k11_bilinear(A,B,C,k7_hahnban1(A,B),D),k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F)) = k1_rlvect_1(A) ) ) ) ) ) ) ).
fof(t23_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> k11_bilinear(A,B,C,D,k7_hahnban1(A,C)) = k1_bilinear(A,B,C) ) ) ) ) ).
fof(t24_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v5_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(A)) )
=> k11_bilinear(A,B,C,k7_hahnban1(A,B),D) = k1_bilinear(A,B,C) ) ) ) ) ).
fof(t25_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k9_bilinear(A,B,C,k11_bilinear(A,B,C,D,E),F) = k6_hahnban1(A,C,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F),E) ) ) ) ) ) ) ).
fof(t26_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k10_bilinear(A,B,C,k11_bilinear(A,B,C,D,E),F) = k6_hahnban1(A,B,k8_funct_2(u1_struct_0(C),u1_struct_0(A),E,F),D) ) ) ) ) ) ) ).
fof(d12_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_bilinear(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> v1_hahnban1(k9_bilinear(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(d13_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v2_bilinear(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> v1_hahnban1(k10_bilinear(A,B,C,D,E),A,B) ) ) ) ) ) ) ).
fof(d14_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v3_bilinear(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> v2_hahnban1(k9_bilinear(A,B,C,D,E),A,C) ) ) ) ) ) ) ).
fof(d15_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v4_bilinear(D,A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> v2_hahnban1(k10_bilinear(A,B,C,D,E),A,B) ) ) ) ) ) ) ).
fof(t27_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v2_bilinear(G,A,B,C)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k2_rlvect_1(B,D,E),F)) = k2_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F))) ) ) ) ) ) ) ) ) ).
fof(t28_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_bilinear(G,A,B,C)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,k2_rlvect_1(C,E,F))) = k2_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,E)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F))) ) ) ) ) ) ) ) ) ).
fof(t29_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(H,A,B,C)
& v2_bilinear(H,A,B,C)
& m2_relset_1(H,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k2_rlvect_1(B,D,E),k2_rlvect_1(C,F,G))) = k2_rlvect_1(A,k2_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,G))),k2_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,G)))) ) ) ) ) ) ) ) ) ).
fof(t30_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v5_rlvect_1(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,k1_rlvect_1(C))) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t31_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v5_rlvect_1(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k1_rlvect_1(B),E)) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t32_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v4_bilinear(G,A,B,C)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k6_vectsp_1(A,B,F,D),E)) = k1_group_1(A,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,E))) ) ) ) ) ) ) ) ) ).
fof(t33_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v3_bilinear(G,A,B,C)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,k6_vectsp_1(A,C,F,E))) = k1_group_1(A,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,E))) ) ) ) ) ) ) ) ) ).
fof(t34_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k1_rlvect_1(B),E)) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t35_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v3_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,k1_rlvect_1(C))) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t36_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(G,A,B,C)
& v4_bilinear(G,A,B,C)
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k6_rlvect_1(B,D,E),F)) = k6_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F))) ) ) ) ) ) ) ) ).
fof(t37_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(G,A,B,C)
& v3_bilinear(G,A,B,C)
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,k6_rlvect_1(C,E,F))) = k6_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,E)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),G,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F))) ) ) ) ) ) ) ) ).
fof(t38_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(H,A,B,C)
& v2_bilinear(H,A,B,C)
& v3_bilinear(H,A,B,C)
& v4_bilinear(H,A,B,C)
& m2_relset_1(H,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k6_rlvect_1(B,D,E),k6_rlvect_1(C,F,G))) = k6_rlvect_1(A,k6_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,G))),k6_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F)),k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),H,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,G)))) ) ) ) ) ) ) ) ) ).
fof(t39_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(J,A,B,C)
& v2_bilinear(J,A,B,C)
& v3_bilinear(J,A,B,C)
& v4_bilinear(J,A,B,C)
& m2_relset_1(J,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k2_rlvect_1(B,D,k6_vectsp_1(A,B,H,E)),k2_rlvect_1(C,F,k6_vectsp_1(A,C,I,G)))) = k2_rlvect_1(A,k2_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F)),k1_group_1(A,I,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,G)))),k2_rlvect_1(A,k1_group_1(A,H,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F))),k1_group_1(A,H,k1_group_1(A,I,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,G)))))) ) ) ) ) ) ) ) ) ) ) ).
fof(t40_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(J,A,B,C)
& v2_bilinear(J,A,B,C)
& v3_bilinear(J,A,B,C)
& v4_bilinear(J,A,B,C)
& m2_relset_1(J,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),k6_rlvect_1(B,D,k6_vectsp_1(A,B,H,E)),k6_rlvect_1(C,F,k6_vectsp_1(A,C,I,G)))) = k6_rlvect_1(A,k6_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,F)),k1_group_1(A,I,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),D,G)))),k6_rlvect_1(A,k1_group_1(A,H,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F))),k1_group_1(A,H,k1_group_1(A,I,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),J,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,G)))))) ) ) ) ) ) ) ) ) ) ) ).
fof(t41_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v5_rlvect_1(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v5_rlvect_1(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( ( v1_bilinear(D,A,B,C)
| v2_bilinear(D,A,B,C) )
=> ( v5_seqm_3(D)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),E,F)) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ).
fof(t42_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( r1_tarski(k12_bilinear(A,B,B,C),k14_bilinear(A,B,C))
& r1_tarski(k13_bilinear(A,B,B,C),k14_bilinear(A,B,C)) ) ) ) ) ).
fof(t43_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> v1_vectsp_4(k12_bilinear(A,B,C,D),A,B) ) ) ) ) ).
fof(t44_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> v1_vectsp_4(k13_bilinear(A,B,C,D),A,C) ) ) ) ) ).
fof(d19_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v11_vectsp_1(E,A)
& m1_vectsp_4(E,A,B) )
=> ( E = k15_bilinear(A,B,C,D)
<=> u1_struct_0(E) = k12_bilinear(A,B,C,D) ) ) ) ) ) ) ).
fof(d20_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v11_vectsp_1(E,A)
& m1_vectsp_4(E,A,C) )
=> ( E = k16_bilinear(A,B,C,D)
<=> u1_struct_0(E) = k13_bilinear(A,B,C,D) ) ) ) ) ) ) ).
fof(d21_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(E,A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& v4_bilinear(E,A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A)) )
=> ( E = k17_bilinear(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( F = k3_vectsp_4(A,B,H,k15_bilinear(A,B,C,D))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A),E,k1_domain_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C),F,G)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),H,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(d22_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(E,A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(E,A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A)) )
=> ( E = k18_bilinear(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D))))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( F = k3_vectsp_4(A,C,H,k16_bilinear(A,B,C,D))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A),E,k1_domain_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D))),G,F)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(d23_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(E,A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v2_bilinear(E,A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(E,A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v4_bilinear(E,A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A)) )
=> ( E = k19_bilinear(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D))))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(C))
=> ( ( F = k3_vectsp_4(A,B,H,k15_bilinear(A,B,C,D))
& G = k3_vectsp_4(A,C,I,k16_bilinear(A,B,C,D)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A),E,k1_domain_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D))),F,G)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A),D,k1_domain_1(u1_struct_0(B),u1_struct_0(C),H,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t45_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k13_bilinear(A,B,C,D) = k13_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)) ) ) ) ) ).
fof(t46_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k12_bilinear(A,B,C,D) = k12_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)) ) ) ) ) ).
fof(t47_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k16_bilinear(A,B,C,D) = k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)) ) ) ) ) ).
fof(t48_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k15_bilinear(A,B,C,D) = k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)) ) ) ) ) ).
fof(t49_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( k19_bilinear(A,B,C,D) = k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))
& k19_bilinear(A,B,C,D) = k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)) ) ) ) ) ) ).
fof(t50_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( k12_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k19_bilinear(A,B,C,D)) = k12_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))),k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)))
& k13_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k19_bilinear(A,B,C,D)) = k13_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D))),k18_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C,k17_bilinear(A,B,C,D)))
& k12_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k19_bilinear(A,B,C,D)) = k12_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D)))
& k13_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k19_bilinear(A,B,C,D)) = k13_bilinear(A,k6_vectsp10(A,B,k15_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k17_bilinear(A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)),k18_bilinear(A,B,C,D))) ) ) ) ) ) ).
fof(t51_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> r1_tarski(k8_vectsp10(A,B,D),k12_bilinear(A,B,C,k11_bilinear(A,B,C,D,E))) ) ) ) ) ) ).
fof(t52_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( E != k7_hahnban1(A,C)
=> k12_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k8_vectsp10(A,B,D) ) ) ) ) ) ) ).
fof(t53_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> r1_tarski(k8_vectsp10(A,C,E),k13_bilinear(A,B,C,k11_bilinear(A,B,C,D,E))) ) ) ) ) ) ).
fof(t54_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( D != k7_hahnban1(A,B)
=> k13_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k8_vectsp10(A,C,E) ) ) ) ) ) ) ).
fof(t55_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& v2_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( E != k7_hahnban1(A,C)
=> ( k15_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k9_vectsp10(A,B,D)
& k17_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k11_bilinear(A,k6_vectsp10(A,B,k9_vectsp10(A,B,D)),C,k11_vectsp10(A,B,D),E) ) ) ) ) ) ) ) ).
fof(t56_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& v1_hahnban1(E,A,C)
& v2_hahnban1(E,A,C)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( D != k7_hahnban1(A,B)
=> ( k16_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k9_vectsp10(A,C,E)
& k18_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k11_bilinear(A,B,k6_vectsp10(A,C,k9_vectsp10(A,C,E)),D,k11_vectsp10(A,C,E)) ) ) ) ) ) ) ) ).
fof(t57_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& ~ v3_realset2(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& ~ v3_realset2(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& ~ v5_seqm_3(D)
& v1_hahnban1(D,A,B)
& v2_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& ~ v5_seqm_3(E)
& v1_hahnban1(E,A,C)
& v2_hahnban1(E,A,C)
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> k19_bilinear(A,B,C,k11_bilinear(A,B,C,D,E)) = k11_bilinear(A,k6_vectsp10(A,B,k9_vectsp10(A,B,D)),k6_vectsp10(A,C,k9_vectsp10(A,C,E)),k11_vectsp10(A,B,D),k11_vectsp10(A,C,E)) ) ) ) ) ) ).
fof(d24_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v5_bilinear(D,A,B,C)
<=> k12_bilinear(A,B,C,D) != k6_domain_1(u1_struct_0(B),k1_rlvect_1(B)) ) ) ) ) ) ).
fof(d25_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v6_bilinear(D,A,B,C)
<=> k13_bilinear(A,B,C,D) != k6_domain_1(u1_struct_0(C),k1_rlvect_1(C)) ) ) ) ) ) ).
fof(d26_bilinear,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l4_vectsp_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v7_bilinear(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k1_funct_1(C,k4_tarski(D,E)) = k1_funct_1(C,k4_tarski(E,D)) ) ) ) ) ) ) ).
fof(d27_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( l4_vectsp_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v8_bilinear(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k1_funct_1(C,k4_tarski(D,D)) = k1_rlvect_1(A) ) ) ) ) ) ).
fof(t58_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v3_bilinear(C,A,B,B)
& v4_bilinear(C,A,B,B)
& v7_bilinear(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> k12_bilinear(A,B,B,C) = k13_bilinear(A,B,B,C) ) ) ) ).
fof(t59_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v8_bilinear(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A),C,k1_domain_1(u1_struct_0(B),u1_struct_0(B),D,E)) = k5_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A),C,k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,D))) ) ) ) ) ) ).
fof(d28_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& v13_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> ( v8_bilinear(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A),C,k1_domain_1(u1_struct_0(B),u1_struct_0(B),D,E)) = k5_rlvect_1(A,k8_funct_2(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A),C,k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,D))) ) ) ) ) ) ) ).
fof(t60_bilinear,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& v1_bilinear(C,A,B,B)
& v2_bilinear(C,A,B,B)
& v3_bilinear(C,A,B,B)
& v4_bilinear(C,A,B,B)
& v8_bilinear(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> k12_bilinear(A,B,B,C) = k13_bilinear(A,B,B,C) ) ) ) ).
fof(dt_k1_bilinear,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& l4_vectsp_1(B,A)
& l4_vectsp_1(C,A) )
=> ( v1_funct_1(k1_bilinear(A,B,C))
& v1_funct_2(k1_bilinear(A,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k1_bilinear(A,B,C),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k2_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k2_bilinear(A,B,C,D,E))
& v1_funct_2(k2_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k2_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k3_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_funct_1(k3_bilinear(A,B,C,D,E))
& v1_funct_2(k3_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k3_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k4_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k4_bilinear(A,B,C,D))
& v1_funct_2(k4_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k4_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k5_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k5_bilinear(A,B,C,D))
& v1_funct_2(k5_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k5_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(redefinition_k5_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k5_bilinear(A,B,C,D) = k4_bilinear(A,B,C,D) ) ).
fof(dt_k6_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k6_bilinear(A,B,C,D,E))
& v1_funct_2(k6_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k6_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k7_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k7_bilinear(A,B,C,D,E))
& v1_funct_2(k7_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k7_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(redefinition_k7_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k7_bilinear(A,B,C,D,E) = k6_bilinear(A,B,C,D,E) ) ).
fof(dt_k8_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k8_bilinear(A,B,C,D,E))
& v1_funct_2(k8_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k8_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(commutativity_k8_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_bilinear(A,B,C,D,E) = k8_bilinear(A,B,C,E,D) ) ).
fof(redefinition_k8_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k8_bilinear(A,B,C,D,E) = k2_bilinear(A,B,C,D,E) ) ).
fof(dt_k9_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( v1_funct_1(k9_bilinear(A,B,C,D,E))
& v1_funct_2(k9_bilinear(A,B,C,D,E),u1_struct_0(C),u1_struct_0(A))
& m2_relset_1(k9_bilinear(A,B,C,D,E),u1_struct_0(C),u1_struct_0(A)) ) ) ).
fof(dt_k10_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(C)) )
=> ( v1_funct_1(k10_bilinear(A,B,C,D,E))
& v1_funct_2(k10_bilinear(A,B,C,D,E),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k10_bilinear(A,B,C,D,E),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k11_bilinear,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(A))
& m1_relset_1(E,u1_struct_0(C),u1_struct_0(A)) )
=> ( v1_funct_1(k11_bilinear(A,B,C,D,E))
& v1_funct_2(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(k11_bilinear(A,B,C,D,E),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k12_bilinear,axiom,
! [A,B,C,D] :
( ( l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> m1_subset_1(k12_bilinear(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k13_bilinear,axiom,
! [A,B,C,D] :
( ( l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> m1_subset_1(k13_bilinear(A,B,C,D),k1_zfmisc_1(u1_struct_0(C))) ) ).
fof(dt_k14_bilinear,axiom,
! [A,B,C] :
( ( l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> m1_subset_1(k14_bilinear(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k15_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k15_bilinear(A,B,C,D))
& v11_vectsp_1(k15_bilinear(A,B,C,D),A)
& m1_vectsp_4(k15_bilinear(A,B,C,D),A,B) ) ) ).
fof(dt_k16_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k16_bilinear(A,B,C,D))
& v11_vectsp_1(k16_bilinear(A,B,C,D),A)
& m1_vectsp_4(k16_bilinear(A,B,C,D),A,C) ) ) ).
fof(dt_k17_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k17_bilinear(A,B,C,D))
& v1_funct_2(k17_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A))
& v2_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& v4_bilinear(k17_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),C)
& m2_relset_1(k17_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(C)),u1_struct_0(A)) ) ) ).
fof(dt_k18_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k18_bilinear(A,B,C,D))
& v1_funct_2(k18_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k18_bilinear(A,B,C,D),A,B,k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& m2_relset_1(k18_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A)) ) ) ).
fof(dt_k19_bilinear,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& v1_bilinear(D,A,B,C)
& v2_bilinear(D,A,B,C)
& v3_bilinear(D,A,B,C)
& v4_bilinear(D,A,B,C)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> ( v1_funct_1(k19_bilinear(A,B,C,D))
& v1_funct_2(k19_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A))
& v1_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v2_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v3_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& v4_bilinear(k19_bilinear(A,B,C,D),A,k6_vectsp10(A,B,k15_bilinear(A,B,C,D)),k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))
& m2_relset_1(k19_bilinear(A,B,C,D),k2_zfmisc_1(u1_struct_0(k6_vectsp10(A,B,k15_bilinear(A,B,C,D))),u1_struct_0(k6_vectsp10(A,C,k16_bilinear(A,B,C,D)))),u1_struct_0(A)) ) ) ).
fof(d16_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k12_bilinear(A,B,C,D) = a_4_0_bilinear(A,B,C,D) ) ) ) ) ).
fof(d17_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)),u1_struct_0(A)) )
=> k13_bilinear(A,B,C,D) = a_4_1_bilinear(A,B,C,D) ) ) ) ) ).
fof(d18_bilinear,axiom,
! [A] :
( l2_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) )
=> k14_bilinear(A,B,C) = a_3_0_bilinear(A,B,C) ) ) ) ).
fof(fraenkel_a_4_0_bilinear,axiom,
! [A,B,C,D,E] :
( ( l2_struct_0(B)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,B)
& ~ v3_struct_0(D)
& l4_vectsp_1(D,B)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_0_bilinear(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(C))
& A = F
& ! [G] :
( m1_subset_1(G,u1_struct_0(D))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B),E,k1_domain_1(u1_struct_0(C),u1_struct_0(D),F,G)) = k1_rlvect_1(B) ) ) ) ) ).
fof(fraenkel_a_4_1_bilinear,axiom,
! [A,B,C,D,E] :
( ( l2_struct_0(B)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,B)
& ~ v3_struct_0(D)
& l4_vectsp_1(D,B)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_1_bilinear(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(D))
& A = F
& ! [G] :
( m1_subset_1(G,u1_struct_0(C))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B),E,k1_domain_1(u1_struct_0(C),u1_struct_0(D),G,F)) = k1_rlvect_1(B) ) ) ) ) ).
fof(fraenkel_a_3_0_bilinear,axiom,
! [A,B,C,D] :
( ( l2_struct_0(B)
& ~ v3_struct_0(C)
& l4_vectsp_1(C,B)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_bilinear(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(C))
& A = E
& k8_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B),D,k1_domain_1(u1_struct_0(C),u1_struct_0(C),E,E)) = k1_rlvect_1(B) ) ) ) ).
%------------------------------------------------------------------------------