% Mizar problem: t26_lmod_xx1,lmod_xx1,2365,61 
fof(t26_lmod_xx1, conjecture,  (! [A] :  ( ( ~ (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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v8_vectsp_1(D, A) &  (v9_vectsp_1(D, A) &  (v10_vectsp_1(D, A) &  (v11_vectsp_1(D, A) &  (v2_rlvect_1(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l1_vectsp_1(D, A)) ) ) ) ) ) ) ) )  =>  (! [E] :  (m1_lmod_xx1(E, A, C, D) => m1_lmod_xx1(k26_lmod_xx1(A, B, C, D, E), A, k24_lmod_xx1(A, B, C), k24_lmod_xx1(A, B, D))) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, 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_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
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_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
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_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(cc10_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) => v4_funct_1(C)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc1_vectsp_2, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v6_vectsp_1(A) & v5_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ) ).
fof(cc2_vectsp_2, axiom,  (! [A] :  (l4_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & v5_group_1(A)) )  =>  ( ~ (v2_struct_0(A))  & v4_vectsp_1(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_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(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(fc10_funct_2, axiom,  (! [A, B] : v4_funct_1(k1_funct_2(A, B))) ).
fof(fc14_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funcop_1(k5_relat_1(A, B))) ) ) ).
fof(fc17_funcop_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) )  =>  (v1_relat_1(k5_relat_1(A, B)) & v3_funct_1(k5_relat_1(A, B))) ) ) ).
fof(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
fof(fc2_funct_2, axiom,  (! [A] :  ~ (v1_xboole_0(k1_funct_2(A, A))) ) ).
fof(fc3_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc8_funct_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (v1_relat_1(k5_relat_1(A, B)) & v1_funct_1(k5_relat_1(A, B))) ) ) ).
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(rc3_vectsp_1, axiom,  (? [A] :  (l3_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v3_group_1(A) & v5_group_1(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(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
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(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(redefinition_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  => k2_partfun1(A, B, C, D)=k5_relat_1(C, D)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(dt_k14_lmod_xx1, 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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k14_lmod_xx1(A, B, C)) &  (v1_funct_2(k14_lmod_xx1(A, B, C), k2_zfmisc_1(k9_funct_2(u1_struct_0(B), u1_struct_0(C)), k9_funct_2(u1_struct_0(B), u1_struct_0(C))), k9_funct_2(u1_struct_0(B), u1_struct_0(C))) & m1_subset_1(k14_lmod_xx1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k9_funct_2(u1_struct_0(B), u1_struct_0(C)), k9_funct_2(u1_struct_0(B), u1_struct_0(C))), k9_funct_2(u1_struct_0(B), u1_struct_0(C)))))) ) ) ) ).
fof(dt_k16_lmod_xx1, 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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k16_lmod_xx1(A, B, C)) &  (v1_funct_2(k16_lmod_xx1(A, B, C), k2_zfmisc_1(u1_struct_0(A), k9_funct_2(u1_struct_0(B), u1_struct_0(C))), k9_funct_2(u1_struct_0(B), u1_struct_0(C))) & m1_subset_1(k16_lmod_xx1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k9_funct_2(u1_struct_0(B), u1_struct_0(C))), k9_funct_2(u1_struct_0(B), u1_struct_0(C)))))) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_partfun1, axiom,  (! [A, B, C, D] :  ( (v1_funct_1(C) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))  =>  (v1_funct_1(k2_partfun1(A, B, C, D)) & m1_subset_1(k2_partfun1(A, B, C, D), k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  &  ( ~ (v2_struct_0(B))  & l2_struct_0(B)) )  =>  (v1_funct_1(k6_grcat_1(A, B)) &  (v1_funct_2(k6_grcat_1(A, B), u1_struct_0(A), u1_struct_0(B)) & m1_subset_1(k6_grcat_1(A, B), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B))))) ) ) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l2_struct_0, axiom,  (! [A] :  (l2_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_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, 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(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_funcop_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_funcop_1(B)) ) ) ) ) ) ).
fof(cc2_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funcop_1(A)) ) ) ) ).
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(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_funcop_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) )  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(B, k9_funct_2(A, C)))) =>  ( (v1_funct_1(D) & v1_funct_2(D, B, k9_funct_2(A, C)))  =>  (v1_funct_1(D) &  (v1_funct_2(D, B, k9_funct_2(A, C)) & v1_funcop_1(D)) ) ) ) ) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(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_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(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_funct_1(B)) ) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(fc1_mod_2, 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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k6_grcat_1(B, C)) &  (v1_funct_2(k6_grcat_1(B, C), u1_struct_0(B), u1_struct_0(C)) & v1_mod_2(k6_grcat_1(B, C), A, B, C)) ) ) ) ).
fof(fc4_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_algstr_0(A))  &  ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) )  =>  (v1_funct_1(k6_grcat_1(A, B)) &  (v1_funct_2(k6_grcat_1(A, B), u1_struct_0(A), u1_struct_0(B)) & v13_vectsp_1(k6_grcat_1(A, B), A, B)) ) ) ) ).
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_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(rc10_vectsp_2, axiom,  (! [A] :  ( ( ~ (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)) ) ) ) ) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(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) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) & v4_rlvect_1(B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc11_vectsp_1, axiom,  (? [A] :  (l4_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc1_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ).
fof(rc1_grcat_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_algstr_0(A))  &  ( ~ (v2_struct_0(B))  &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) )  =>  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(B)))) &  (v1_relat_1(C) &  (v4_relat_1(C, u1_struct_0(A)) &  (v5_relat_1(C, u1_struct_0(B)) &  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  &  (v1_partfun1(C, u1_struct_0(A)) &  (v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v13_vectsp_1(C, A, B)) ) ) ) ) ) ) ) ) ) ) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc2_funcop_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc3_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(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) &  (v3_funct_1(C) &  (v1_partfun1(C, A) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
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(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc6_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] :  (l1_vectsp_1(B, A) & v7_vectsp_1(B, A)) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
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(rc7_vectsp_2, axiom,  (! [A] :  ( ( ~ (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)) ) ) ) ) ) ) )  =>  (? [B] :  (l1_vectsp_1(B, A) &  ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v7_vectsp_1(B, A) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) & v4_rlvect_1(B)) ) ) ) ) ) ) ) ) ).
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(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(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(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(fraenkel_a_3_0_lmod_xx1, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v4_vectsp_1(B) &  (v5_vectsp_1(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) &  (v3_group_1(B) &  (v5_group_1(B) & l6_algstr_0(B)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v8_vectsp_1(C, B) &  (v9_vectsp_1(C, B) &  (v10_vectsp_1(C, B) &  (v11_vectsp_1(C, B) &  (v2_rlvect_1(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l1_vectsp_1(C, B)) ) ) ) ) ) ) ) )  &  ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v8_vectsp_1(D, B) &  (v9_vectsp_1(D, B) &  (v10_vectsp_1(D, B) &  (v11_vectsp_1(D, B) &  (v2_rlvect_1(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l1_vectsp_1(D, B)) ) ) ) ) ) ) ) ) ) )  =>  (r2_hidden(A, a_3_0_lmod_xx1(B, C, D)) <=>  (? [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(C), u1_struct_0(D)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C), u1_struct_0(D))))) )  &  (A=E & m1_lmod_xx1(E, B, C, D)) ) ) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
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(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l5_algstr_0, axiom,  (? [A] : l5_algstr_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_k19_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v1_xboole_0(k19_lmod_xx1(A, B, C)))  & m1_subset_1(k19_lmod_xx1(A, B, C), k1_zfmisc_1(k9_funct_2(u1_struct_0(B), u1_struct_0(C))))) ) ) ).
fof(dt_k20_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k20_lmod_xx1(A, B, C)) &  (v1_funct_2(k20_lmod_xx1(A, B, C), k2_zfmisc_1(k19_lmod_xx1(A, B, C), k19_lmod_xx1(A, B, C)), k19_lmod_xx1(A, B, C)) & m1_subset_1(k20_lmod_xx1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k19_lmod_xx1(A, B, C), k19_lmod_xx1(A, B, C)), k19_lmod_xx1(A, B, C))))) ) ) ) ).
fof(dt_k22_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (v1_funct_1(k22_lmod_xx1(A, B, C)) &  (v1_funct_2(k22_lmod_xx1(A, B, C), k2_zfmisc_1(u1_struct_0(A), k19_lmod_xx1(A, B, C)), k19_lmod_xx1(A, B, C)) & m1_subset_1(k22_lmod_xx1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), k19_lmod_xx1(A, B, C)), k19_lmod_xx1(A, B, C))))) ) ) ) ).
fof(dt_k23_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  => m2_subset_1(k23_lmod_xx1(A, B, C), k9_funct_2(u1_struct_0(B), u1_struct_0(C)), k19_lmod_xx1(A, B, C))) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (l2_struct_0(A) & l1_algstr_0(A)) ) ) ).
fof(dt_l5_algstr_0, axiom,  (! [A] :  (l5_algstr_0(A) =>  (l4_algstr_0(A) & l4_struct_0(A)) ) ) ).
fof(cc12_algstr_0, axiom,  (! [A] :  ( (v13_algstr_0(A) & l2_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v10_algstr_0(B, A)) ) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(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_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(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_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_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_funcop_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_xboole_0(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_funcop_1(A)) ) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_funct_1(B)) ) ) ) ).
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(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(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(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(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(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(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(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
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_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(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc4_funcop_1, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(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_partfun1(C, 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(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
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)) ) ) ) ) ).
fof(d18_lmod_xx1, axiom,  (! [A] :  ( ( ~ (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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  => k19_lmod_xx1(A, B, C)=a_3_0_lmod_xx1(A, B, C)) ) ) ) ) ) ).
fof(d19_lmod_xx1, axiom,  (! [A] :  ( ( ~ (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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  => k20_lmod_xx1(A, B, C)=k2_partfun1(k2_zfmisc_1(k9_funct_2(u1_struct_0(B), u1_struct_0(C)), k9_funct_2(u1_struct_0(B), u1_struct_0(C))), k9_funct_2(u1_struct_0(B), u1_struct_0(C)), k14_lmod_xx1(A, B, C), k2_zfmisc_1(k19_lmod_xx1(A, B, C), k19_lmod_xx1(A, B, C)))) ) ) ) ) ) ).
fof(d20_lmod_xx1, axiom,  (! [A] :  ( ( ~ (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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  => k22_lmod_xx1(A, B, C)=k2_partfun1(k2_zfmisc_1(u1_struct_0(A), k9_funct_2(u1_struct_0(B), u1_struct_0(C))), k9_funct_2(u1_struct_0(B), u1_struct_0(C)), k16_lmod_xx1(A, B, C), k2_zfmisc_1(u1_struct_0(A), k19_lmod_xx1(A, B, C)))) ) ) ) ) ) ).
fof(d21_lmod_xx1, axiom,  (! [A] :  ( ( ~ (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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  => k23_lmod_xx1(A, B, C)=k6_grcat_1(B, C)) ) ) ) ) ) ).
fof(existence_l1_vectsp_1, axiom,  (! [A] :  (l1_struct_0(A) =>  (? [B] : l1_vectsp_1(B, A)) ) ) ).
fof(existence_l6_algstr_0, axiom,  (? [A] : l6_algstr_0(A)) ).
fof(existence_m1_lmod_xx1, 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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (? [D] : m1_lmod_xx1(D, A, B, C)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k24_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k24_lmod_xx1(A, B, C)))  & l1_vectsp_1(k24_lmod_xx1(A, B, C), A)) ) ) ).
fof(dt_k26_lmod_xx1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ( ~ (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)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v8_vectsp_1(D, A) &  (v9_vectsp_1(D, A) &  (v10_vectsp_1(D, A) &  (v11_vectsp_1(D, A) &  (v2_rlvect_1(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l1_vectsp_1(D, A)) ) ) ) ) ) ) ) )  & m1_lmod_xx1(E, A, C, D)) ) ) )  =>  (v1_funct_1(k26_lmod_xx1(A, B, C, D, E)) &  (v1_funct_2(k26_lmod_xx1(A, B, C, D, E), u1_struct_0(k24_lmod_xx1(A, B, C)), u1_struct_0(k24_lmod_xx1(A, B, D))) & m1_subset_1(k26_lmod_xx1(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k24_lmod_xx1(A, B, C)), u1_struct_0(k24_lmod_xx1(A, B, D)))))) ) ) ) ).
fof(dt_k2_zfmisc_1, 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_l6_algstr_0, axiom,  (! [A] :  (l6_algstr_0(A) =>  (l2_algstr_0(A) & l5_algstr_0(A)) ) ) ).
fof(dt_m1_lmod_xx1, 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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  (! [D] :  (m1_lmod_xx1(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) ) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
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_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_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(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(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(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc4_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  ~ (v2_struct_0(k24_lmod_xx1(A, B, C))) ) ) ).
fof(fc5_lmod_xx1, 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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ~ (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)) ) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k24_lmod_xx1(A, B, C)))  &  (v13_algstr_0(k24_lmod_xx1(A, B, C)) &  (v8_vectsp_1(k24_lmod_xx1(A, B, C), A) &  (v9_vectsp_1(k24_lmod_xx1(A, B, C), A) &  (v10_vectsp_1(k24_lmod_xx1(A, B, C), A) &  (v11_vectsp_1(k24_lmod_xx1(A, B, C), A) &  (v2_rlvect_1(k24_lmod_xx1(A, B, C)) &  (v3_rlvect_1(k24_lmod_xx1(A, B, C)) & v4_rlvect_1(k24_lmod_xx1(A, B, C))) ) ) ) ) ) ) ) ) ) ).
fof(fc7_lmod_xx1, axiom,  (! [A, B, C, D, E] :  ( ( ( ~ (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) &  (v5_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)) ) ) ) ) ) ) ) )  &  ( ( ~ (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)) ) ) ) ) ) ) ) )  &  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v8_vectsp_1(D, A) &  (v9_vectsp_1(D, A) &  (v10_vectsp_1(D, A) &  (v11_vectsp_1(D, A) &  (v2_rlvect_1(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l1_vectsp_1(D, A)) ) ) ) ) ) ) ) )  & m1_lmod_xx1(E, A, C, D)) ) ) )  =>  (v1_funct_1(k26_lmod_xx1(A, B, C, D, E)) &  (v1_funct_2(k26_lmod_xx1(A, B, C, D, E), u1_struct_0(k24_lmod_xx1(A, B, C)), u1_struct_0(k24_lmod_xx1(A, B, D))) &  (v13_vectsp_1(k26_lmod_xx1(A, B, C, D, E), k24_lmod_xx1(A, B, C), k24_lmod_xx1(A, B, D)) & v1_mod_2(k26_lmod_xx1(A, B, C, D, E), A, k24_lmod_xx1(A, B, C), k24_lmod_xx1(A, B, D))) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(d22_lmod_xx1, axiom,  (! [A] :  ( ( ~ (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) &  (v5_group_1(A) & l6_algstr_0(A)) ) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  => k24_lmod_xx1(A, B, C)=g1_vectsp_1(A, k19_lmod_xx1(A, B, C), k20_lmod_xx1(A, B, C), k23_lmod_xx1(A, B, C), k22_lmod_xx1(A, B, C))) ) ) ) ) ) ).
fof(d10_lmod_xx1, axiom,  (! [A] :  ( ( ~ (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)) ) ) ) ) ) ) )  =>  (! [B] :  ( ( ~ (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] :  ( ( ~ (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)) ) ) ) ) ) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, u1_struct_0(B), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B), u1_struct_0(C))))) )  =>  (m1_lmod_xx1(D, A, B, C) <=>  (v13_vectsp_1(D, B, C) & v1_mod_2(D, A, B, C)) ) ) ) ) ) ) ) ) ) ).
