% Mizar problem: t54_bilinear,bilinear,2894,5 
fof(t54_bilinear, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(D, B, A) &  (v1_hahnban1(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) )  =>  ( ~ (E=k7_hahnban1(A, C))  =>  (k13_bilinear(A, B, C, k9_bilinear(A, B, C, D, E))=k9_vectsp10(A, B, D) & r1_funct_2(k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k13_bilinear(A, B, C, k9_bilinear(A, B, C, D, E)))), u1_struct_0(C)), u1_struct_0(A), k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k9_vectsp10(A, B, D))), u1_struct_0(C)), u1_struct_0(A), k15_bilinear(A, B, C, k9_bilinear(A, B, C, D, E)), k9_bilinear(A, k6_vectsp10(A, B, k9_vectsp10(A, B, D)), C, k11_vectsp10(A, B, D), E))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v7_vectsp_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_vectsp_1(B, A))  =>  (v7_vectsp_1(B, A) => B=g1_vectsp_1(A, u1_struct_0(B), u1_algstr_0(B), u2_struct_0(B), u1_vectsp_1(A, B))) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ) ).
fof(cc1_hahnban1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_hahnban1(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v2_hahnban1(C, A, B)) ) ) ) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_vectsp10, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v13_vectsp_1(C, B, A)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v2_hahnban1(C, A, B)) ) ) ) ) ) ) ).
fof(cc1_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v5_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) ) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc2_vectsp10, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) =>  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v1_hahnban1(C, A, B)) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) & v2_hahnban1(C, A, B)) ) ) ) ) ) ) ).
fof(cc2_vectsp_1, axiom,  (! [A] :  (l6_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v1_vectsp_1(A) & v2_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v5_vectsp_1(A)) ) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc3_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) ) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc5_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_vectsp_1(A))  =>  ( ~ (v2_struct_0(A))  & v1_group_1(A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc6_vectsp_1, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & v6_vectsp_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v3_vectsp_1(A)) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k8_group_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k8_group_1(A, B, C)=k8_group_1(A, C, B)) ) ).
fof(d10_bilinear, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(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)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) )  =>  (F=k9_bilinear(A, B, C, D, E) <=>  (! [G] :  (m1_subset_1(G, u1_struct_0(B)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(C)) => k2_binop_1(u1_struct_0(B), u1_struct_0(C), u1_struct_0(A), F, G, H)=k6_algstr_0(A, k3_funct_2(u1_struct_0(B), u1_struct_0(A), D, G), k3_funct_2(u1_struct_0(C), u1_struct_0(A), E, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d11_vectsp10, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) &  (v1_hahnban1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) )  =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v7_vectsp_1(D, A) & m1_vectsp_4(D, A, B)) )  =>  (D=k9_vectsp10(A, B, C) <=> u1_struct_0(D)=k8_vectsp10(B, A, C)) ) ) ) ) ) ) ) ) ).
fof(d15_bilinear, axiom,  (! [A] :  (l2_struct_0(A) =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l1_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)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) )  => k10_bilinear(A, B, C, D)=a_4_0_bilinear(A, B, C, D)) ) ) ) ) ) ) ) ).
fof(d18_bilinear, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l1_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) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) )  =>  (! [E] :  ( ( ~ (v2_struct_0(E))  &  (v7_vectsp_1(E, A) & m1_vectsp_4(E, A, B)) )  =>  (E=k13_bilinear(A, B, C, D) <=> u1_struct_0(E)=k10_bilinear(A, B, C, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_binop_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (! [C] : k1_binop_1(A, B, C)=k1_funct_1(A, k4_tarski(B, C))) ) ) ) ).
fof(d1_funct_2, axiom,  (! [A] :  (! [B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( ( ~ (B=k1_xboole_0)  =>  (v1_funct_2(C, A, B) <=> A=k1_relset_1(A, C)) )  &  (B=k1_xboole_0 =>  (v1_funct_2(C, A, B) <=> C=k1_xboole_0) ) ) ) ) ) ) ).
fof(d20_bilinear, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l1_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) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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, k13_bilinear(A, B, C, D))), u1_struct_0(C)), u1_struct_0(A)) &  (v2_bilinear(E, A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) &  (v4_bilinear(E, A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k13_bilinear(A, B, C, D))), u1_struct_0(C)), u1_struct_0(A))))) ) ) )  =>  (E=k15_bilinear(A, B, C, D) <=>  (! [F] :  (m1_subset_1(F, u1_struct_0(k6_vectsp10(A, B, k13_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, k13_bilinear(A, B, C, D)) => k2_binop_1(u1_struct_0(k6_vectsp10(A, B, k13_bilinear(A, B, C, D))), u1_struct_0(C), u1_struct_0(A), E, F, G)=k2_binop_1(u1_struct_0(B), u1_struct_0(C), u1_struct_0(A), D, H, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k2_struct_0(A)=u1_struct_0(A)) ) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(d7_hahnban1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  =>  (! [B] :  (l1_vectsp_1(B, A) => k7_hahnban1(A, B)=k8_funcop_1(u1_struct_0(A), k2_struct_0(B), k4_struct_0(A))) ) ) ) ).
fof(dt_g1_vectsp_1, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) ) ) ) )  =>  (v7_vectsp_1(g1_vectsp_1(A, B, C, D, E), A) & l1_vectsp_1(g1_vectsp_1(A, B, C, D, E), A)) ) ) ).
fof(dt_k10_bilinear, axiom,  (! [A, B, C, D] :  ( (l2_struct_0(A) &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) )  => m1_subset_1(k10_bilinear(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) ) ).
fof(dt_k11_vectsp10, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) &  (v1_hahnban1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) ) ) )  =>  (v1_funct_1(k11_vectsp10(A, B, C)) &  (v1_funct_2(k11_vectsp10(A, B, C), u1_struct_0(k6_vectsp10(A, B, k9_vectsp10(A, B, C))), u1_struct_0(A)) &  (v13_vectsp_1(k11_vectsp10(A, B, C), k6_vectsp10(A, B, k9_vectsp10(A, B, C)), A) &  (v1_hahnban1(k11_vectsp10(A, B, C), A, k6_vectsp10(A, B, k9_vectsp10(A, B, C))) & m1_subset_1(k11_vectsp10(A, B, C), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k9_vectsp10(A, B, C))), u1_struct_0(A))))) ) ) ) ) ) ).
fof(dt_k13_bilinear, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k13_bilinear(A, B, C, D)))  &  (v7_vectsp_1(k13_bilinear(A, B, C, D), A) & m1_vectsp_4(k13_bilinear(A, B, C, D), A, B)) ) ) ) ).
fof(dt_k15_bilinear, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ) ) )  =>  (v1_funct_1(k15_bilinear(A, B, C, D)) &  (v1_funct_2(k15_bilinear(A, B, C, D), k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k13_bilinear(A, B, C, D))), u1_struct_0(C)), u1_struct_0(A)) &  (v2_bilinear(k15_bilinear(A, B, C, D), A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) &  (v4_bilinear(k15_bilinear(A, B, C, D), A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) & m1_subset_1(k15_bilinear(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k13_bilinear(A, B, C, D))), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ) ) ).
fof(dt_k1_binop_1, axiom, $true).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) ) ).
fof(dt_k2_funcop_1, axiom, $true).
fof(dt_k2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k2_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_vectsp_4, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (m1_subset_1(C, u1_struct_0(B)) & m1_vectsp_4(D, A, B)) ) )  => m1_subset_1(k3_vectsp_4(A, B, C, D), k1_zfmisc_1(u1_struct_0(B)))) ) ).
fof(dt_k4_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_algstr_0, axiom,  (! [A, B, C] :  ( (l3_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k6_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k6_vectsp10, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  & m1_vectsp_4(C, A, B)) )  =>  ( ~ (v2_struct_0(k6_vectsp10(A, B, C)))  &  (v13_algstr_0(k6_vectsp10(A, B, C)) &  (v2_rlvect_1(k6_vectsp10(A, B, C)) &  (v3_rlvect_1(k6_vectsp10(A, B, C)) &  (v4_rlvect_1(k6_vectsp10(A, B, C)) &  (v7_vectsp_1(k6_vectsp10(A, B, C), A) &  (v8_vectsp_1(k6_vectsp10(A, B, C), A) &  (v9_vectsp_1(k6_vectsp10(A, B, C), A) &  (v10_vectsp_1(k6_vectsp10(A, B, C), A) &  (v11_vectsp_1(k6_vectsp10(A, B, C), A) & l1_vectsp_1(k6_vectsp10(A, B, C), A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k7_hahnban1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  & l1_vectsp_1(B, A))  =>  (v1_funct_1(k7_hahnban1(A, B)) &  (v1_funct_2(k7_hahnban1(A, B), u1_struct_0(B), u1_struct_0(A)) & m1_subset_1(k7_hahnban1(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) ) ).
fof(dt_k8_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  =>  (v1_funct_1(k8_funcop_1(A, B, C)) &  (v1_funct_2(k8_funcop_1(A, B, C), B, A) & m1_subset_1(k8_funcop_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(B, A)))) ) ) ) ).
fof(dt_k8_group_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k8_group_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k8_vectsp10, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  (l2_struct_0(B) &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) )  => m1_subset_1(k8_vectsp10(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k9_bilinear, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  & l3_algstr_0(A))  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) ) ) ) ) )  =>  (v1_funct_1(k9_bilinear(A, B, C, D, E)) &  (v1_funct_2(k9_bilinear(A, B, C, D, E), k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)) & m1_subset_1(k9_bilinear(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ).
fof(dt_k9_vectsp10, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) &  (v1_hahnban1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) ) ) )  =>  ( ~ (v2_struct_0(k9_vectsp10(A, B, C)))  &  (v7_vectsp_1(k9_vectsp10(A, B, C), A) & m1_vectsp_4(k9_vectsp10(A, B, C), A, B)) ) ) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l1_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (! [B] :  (l1_vectsp_1(B, A) => l2_algstr_0(B)) ) ) ) ).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_algstr_0, axiom,  (! [A] :  (l3_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l3_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => l1_struct_0(A)) ) ).
fof(dt_l4_algstr_0, axiom,  (! [A] :  (l4_algstr_0(A) =>  (l3_struct_0(A) & l3_algstr_0(A)) ) ) ).
fof(dt_l4_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  (l2_struct_0(A) & l3_struct_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(dt_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m2_vectsp_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  & m1_vectsp_4(C, A, B)) )  =>  (! [D] :  (m2_vectsp_4(D, A, B, C) => m1_subset_1(D, k1_zfmisc_1(u1_struct_0(B)))) ) ) ) ).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_u1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v1_funct_1(u1_algstr_0(A)) &  (v1_funct_2(u1_algstr_0(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m1_subset_1(u1_algstr_0(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))) ) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u1_vectsp_1, axiom,  (! [A, B] :  ( (l1_struct_0(A) & l1_vectsp_1(B, A))  =>  (v1_funct_1(u1_vectsp_1(A, B)) &  (v1_funct_2(u1_vectsp_1(A, B), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u1_struct_0(B)) & m1_subset_1(u1_vectsp_1(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)), u1_struct_0(B))))) ) ) ) ).
fof(dt_u2_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(u2_struct_0(A), u1_struct_0(A))) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l1_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l1_vectsp_1(B, A)) ) ) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_l3_algstr_0, axiom,  (? [A] : l3_algstr_0(A)) ).
fof(existence_l3_struct_0, axiom,  (? [A] : l3_struct_0(A)) ).
fof(existence_l4_algstr_0, axiom,  (? [A] : l4_algstr_0(A)) ).
fof(existence_l4_struct_0, axiom,  (? [A] : l4_struct_0(A)) ).
fof(existence_l5_algstr_0, axiom,  (? [A] : l5_algstr_0(A)) ).
fof(existence_l6_algstr_0, axiom,  (? [A] : l6_algstr_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (? [C] : m1_vectsp_4(C, A, B)) ) ) ).
fof(existence_m2_vectsp_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  & m1_vectsp_4(C, A, B)) )  =>  (? [D] : m2_vectsp_4(D, A, B, C)) ) ) ).
fof(fc10_bilinear, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(D, B, A) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) ) ) ) ) )  =>  (v1_funct_1(k9_bilinear(A, B, C, D, E)) &  (v1_funct_2(k9_bilinear(A, B, C, D, E), k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)) & v2_bilinear(k9_bilinear(A, B, C, D, E), A, B, C)) ) ) ) ).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc10_vectsp10, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_rlvect_1(A) & l2_algstr_0(A)) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v2_hahnban1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) ) )  =>  ~ (v1_xboole_0(k8_vectsp10(B, A, C))) ) ) ).
fof(fc11_bilinear, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) ) ) ) ) ) )  =>  (v1_funct_1(k9_bilinear(A, B, C, D, E)) &  (v1_funct_2(k9_bilinear(A, B, C, D, E), k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)) & v3_bilinear(k9_bilinear(A, B, C, D, E), A, B, C)) ) ) ) ).
fof(fc12_bilinear, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) ) ) ) ) )  =>  (v1_funct_1(k9_bilinear(A, B, C, D, E)) &  (v1_funct_2(k9_bilinear(A, B, C, D, E), k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)) & v4_bilinear(k9_bilinear(A, B, C, D, E), A, B, C)) ) ) ) ).
fof(fc12_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ~ (v1_subset_1(k2_struct_0(A), u1_struct_0(A))) ) ) ).
fof(fc12_vectsp10, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) &  (v1_hahnban1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) ) ) )  =>  (v1_funct_1(k11_vectsp10(A, B, C)) &  (v1_funct_2(k11_vectsp10(A, B, C), u1_struct_0(k6_vectsp10(A, B, k9_vectsp10(A, B, C))), u1_struct_0(A)) &  (v13_vectsp_1(k11_vectsp10(A, B, C), k6_vectsp10(A, B, k9_vectsp10(A, B, C)), A) &  (v1_hahnban1(k11_vectsp10(A, B, C), A, k6_vectsp10(A, B, k9_vectsp10(A, B, C))) &  ~ (v2_vectsp10(k11_vectsp10(A, B, C), A, k6_vectsp10(A, B, k9_vectsp10(A, B, C)))) ) ) ) ) ) ) ).
fof(fc1_hahnban1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_rlvect_1(A) & l2_algstr_0(A)) )  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (v1_funct_1(k7_hahnban1(A, B)) &  (v1_funct_2(k7_hahnban1(A, B), u1_struct_0(B), u1_struct_0(A)) & v13_vectsp_1(k7_hahnban1(A, B), B, A)) ) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc2_hahnban1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (v1_funct_1(k7_hahnban1(A, B)) &  (v1_funct_2(k7_hahnban1(A, B), u1_struct_0(B), u1_struct_0(A)) & v1_hahnban1(k7_hahnban1(A, B), A, B)) ) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc32_bilinear, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) )  &  ( ( ~ (v2_struct_0(C))  & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ) )  =>  ~ (v1_xboole_0(k10_bilinear(A, B, C, D))) ) ) ).
fof(fc33_bilinear, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ) )  =>  ~ (v1_xboole_0(k10_bilinear(A, B, C, D))) ) ) ).
fof(fc3_hahnban1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (v1_funct_1(k7_hahnban1(A, B)) &  (v1_funct_2(k7_hahnban1(A, B), u1_struct_0(B), u1_struct_0(A)) & v2_hahnban1(k7_hahnban1(A, B), A, B)) ) ) ) ).
fof(fc40_bilinear, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) & l1_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_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A))))) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k15_bilinear(A, B, C, D)) &  (v1_funct_2(k15_bilinear(A, B, C, D), k2_zfmisc_1(u1_struct_0(k6_vectsp10(A, B, k13_bilinear(A, B, C, D))), u1_struct_0(C)), u1_struct_0(A)) &  (v1_bilinear(k15_bilinear(A, B, C, D), A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) &  (v2_bilinear(k15_bilinear(A, B, C, D), A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) &  (v3_bilinear(k15_bilinear(A, B, C, D), A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C) & v4_bilinear(k15_bilinear(A, B, C, D), A, k6_vectsp10(A, B, k13_bilinear(A, B, C, D)), C)) ) ) ) ) ) ) ).
fof(fc4_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(k2_struct_0(A))) ) ).
fof(fc5_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(k2_struct_0(A))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc8_vectsp10, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (v1_funct_1(k7_hahnban1(A, B)) &  (v3_funct_1(k7_hahnban1(A, B)) & v1_funct_2(k7_hahnban1(A, B), u1_struct_0(B), u1_struct_0(A))) ) ) ) ).
fof(fc9_bilinear, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) )  &  (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(C), u1_struct_0(A)) &  (v13_vectsp_1(E, C, A) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) ) ) ) ) ) )  =>  (v1_funct_1(k9_bilinear(A, B, C, D, E)) &  (v1_funct_2(k9_bilinear(A, B, C, D, E), k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)) & v1_bilinear(k9_bilinear(A, B, C, D, E), A, B, C)) ) ) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fc9_vectsp_1, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(A) &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) ) ) ) ) )  =>  ( ~ (v2_struct_0(g1_vectsp_1(A, B, C, D, E)))  & v7_vectsp_1(g1_vectsp_1(A, B, C, D, E), A)) ) ) ).
fof(fraenkel_a_4_0_bilinear, axiom,  (! [A, B, C, D, E] :  ( (l2_struct_0(B) &  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, B))  &  ( ( ~ (v2_struct_0(D))  & l1_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)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(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)) => k2_binop_1(u1_struct_0(C), u1_struct_0(D), u1_struct_0(B), E, F, G)=k4_struct_0(B)) ) ) ) ) ) ) ) ).
fof(free_g1_vectsp_1, axiom,  (! [A, B, C, D, E] :  ( (l1_struct_0(A) &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(B, B), B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B, B), B)))) )  &  (m1_subset_1(D, B) &  (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(u1_struct_0(A), B), B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), B), B)))) ) ) ) )  =>  (! [F, G, H, I, J] :  (g1_vectsp_1(A, B, C, D, E)=g1_vectsp_1(F, G, H, I, J) =>  (A=F &  (B=G &  (C=H &  (D=I & E=J) ) ) ) ) ) ) ) ).
fof(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc17_struct_0, axiom,  (! [A] :  (l2_struct_0(A) =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) & v9_struct_0(B, A)) ) ) ) ).
fof(rc19_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l2_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, u1_struct_0(A)) &  ~ (v9_struct_0(B, A)) ) ) ) ) ).
fof(rc1_bilinear, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_rlvect_1(A) & l2_algstr_0(A)) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A)) ) )  =>  (? [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)))) &  ( ~ (v1_xboole_0(D))  &  (v1_relat_1(D) &  (v4_relat_1(D, k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))) &  (v5_relat_1(D, u1_struct_0(A)) &  (v1_funct_1(D) &  (v1_partfun1(D, k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))) &  (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(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(rc1_hahnban1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v5_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) &  (v1_hahnban1(C, A, B) & v2_hahnban1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_vectsp_4, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) ) )  =>  (? [C] :  (m1_vectsp_4(C, A, B) &  ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v7_vectsp_1(C, A) &  (v8_vectsp_1(C, A) &  (v9_vectsp_1(C, A) &  (v10_vectsp_1(C, A) &  (v11_vectsp_1(C, A) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) & v4_rlvect_1(C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc2_bilinear, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  &  ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A)) ) )  =>  (? [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C)), u1_struct_0(A)))) &  ( ~ (v1_xboole_0(D))  &  (v1_relat_1(D) &  (v4_relat_1(D, k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))) &  (v5_relat_1(D, u1_struct_0(A)) &  (v1_funct_1(D) &  (v1_partfun1(D, k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))) &  (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(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_vectsp10, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & v7_vectsp_1(B, A)) ) ) ) ) ) ) ) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_vectsp10, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_vectsp_1(A) &  (v6_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v7_vectsp_1(B, A) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) & v11_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v1_group_1(A) &  (v3_group_1(A) & v5_group_1(A)) ) ) ) ) ).
fof(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc5_vectsp10, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_rlvect_1(A) & l2_algstr_0(A)) )  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v5_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(B)) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) & v2_hahnban1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_vectsp10, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l2_struct_0(A))  &  ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A)) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v5_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  (v3_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(B)) & v1_funct_2(C, u1_struct_0(B), u1_struct_0(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(rc6_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_vectsp_1(B, A) & v7_vectsp_1(B, A)) ) ) ) ).
fof(rc7_vectsp10, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l6_algstr_0(A)) ) ) )  &  ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l1_vectsp_1(B, A)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(B)) &  (v5_relat_1(C, u1_struct_0(A)) &  (v1_funct_1(C) &  (v3_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(B)) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) & v2_hahnban1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc7_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  & v7_vectsp_1(B, A)) ) ) ) ) ).
fof(rc8_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v3_group_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v7_vectsp_1(B, A) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) & v11_vectsp_1(B, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rd3_vectsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (v9_struct_0(C, A) & m1_subset_1(C, u1_struct_0(A))) ) )  => k6_algstr_0(A, B, C)=C) ) ).
fof(rd4_vectsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v2_vectsp_1(A) & l6_algstr_0(A)) ) ) ) )  &  ( (v9_struct_0(B, A) & m1_subset_1(B, u1_struct_0(A)))  & m1_subset_1(C, u1_struct_0(A))) )  => k6_algstr_0(A, B, C)=B) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => k2_binop_1(A, B, C, D, E, F)=k1_binop_1(D, E, F)) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k8_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(C, A))  => k8_funcop_1(A, B, C)=k2_funcop_1(B, C)) ) ).
fof(redefinition_k8_group_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v5_group_1(A) & l3_algstr_0(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k8_group_1(A, B, C)=k6_algstr_0(A, B, C)) ) ).
fof(redefinition_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) <=> E=F) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  => r1_funct_2(A, B, C, D, E, E)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(symmetry_r1_funct_2, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(D))  &  ( (v1_funct_1(E) &  (v1_funct_2(E, A, B) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(F) &  (v1_funct_2(F, C, D) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(C, D)))) ) ) ) )  =>  (r1_funct_2(A, B, C, D, E, F) => r1_funct_2(A, B, C, D, F, E)) ) ) ).
fof(t1_domain_1, axiom,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  ~ ( (r2_tarski(A, k2_zfmisc_1(B, C)) &  (! [D] :  (m1_subset_1(D, B) =>  (! [E] :  (m1_subset_1(E, C) =>  ~ (A=k4_tarski(D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t22_vectsp10, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  (m1_vectsp_4(C, A, B) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k6_vectsp10(A, B, C))) =>  (m2_vectsp_4(D, A, B, C) &  (? [E] :  (m1_subset_1(E, u1_struct_0(B)) & D=k3_vectsp_4(A, B, E, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  ( (v1_relat_1(B) & v1_funct_1(B))  =>  ( (k9_xtuple_0(A)=k9_xtuple_0(B) &  (! [C] :  (r2_hidden(C, k9_xtuple_0(A)) => k1_funct_1(A, C)=k1_funct_1(B, C)) ) )  => A=B) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t35_vectsp10, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v8_vectsp_1(B, A) &  (v9_vectsp_1(B, A) &  (v10_vectsp_1(B, A) &  (v11_vectsp_1(B, A) & l1_vectsp_1(B, A)) ) ) ) ) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, u1_struct_0(B), u1_struct_0(A)) &  (v13_vectsp_1(C, B, A) &  (v1_hahnban1(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(A))))) ) ) )  =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k6_vectsp10(A, B, k9_vectsp10(A, B, C)))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (D=k3_vectsp_4(A, B, E, k9_vectsp10(A, B, C)) => k3_funct_2(u1_struct_0(k6_vectsp10(A, B, k9_vectsp10(A, B, C))), u1_struct_0(A), k11_vectsp10(A, B, C), D)=k3_funct_2(u1_struct_0(B), u1_struct_0(A), C, E)) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t51_bilinear, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v33_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v4_vectsp_1(A) &  (v5_vectsp_1(A) &  (v3_group_1(A) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l1_vectsp_1(B, A))  =>  (! [C] :  ( ( ~ (v2_struct_0(C))  & l1_vectsp_1(C, A))  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(A)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(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)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(A))))) )  =>  ( ~ (E=k7_hahnban1(A, C))  => k10_bilinear(A, B, C, k9_bilinear(A, B, C, D, E))=k8_vectsp10(B, A, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
