% Mizar problem: t5_parsp_2,parsp_2,431,5 
fof(t5_parsp_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(k9_parsp_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_parsp_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_parsp_1(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_parsp_1(A))) =>  (! [F] :  (m1_subset_1(F, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [G] :  (m1_subset_1(G, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [H] :  (m1_subset_1(H, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [I] :  (m1_subset_1(I, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  ( (r1_parsp_1(k9_parsp_1(A), B, C, D, E) &  (r1_parsp_1(k9_parsp_1(A), B, D, C, E) & k4_tarski(k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), B, C), k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), D, E))=k4_tarski(k4_tarski(F, G), k4_tarski(H, I))) )  =>  (r1_parsp_1(k9_parsp_1(A), B, C, B, D) |  (k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), I)=k5_algstr_0(A, k3_rlvect_1(A, k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), H)), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F)) &  (k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), I)=k5_algstr_0(A, k3_rlvect_1(A, k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), H)), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F)) & k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), I)=k5_algstr_0(A, k3_rlvect_1(A, k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), H)), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_parsp_1, axiom,  (! [A] :  (l1_parsp_1(A) =>  (v1_parsp_1(A) => A=g1_parsp_1(u1_struct_0(A), u1_parsp_1(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_mcart_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(A, B)) => v1_xtuple_0(C)) ) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
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(cc1_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc2_mcart_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  (! [D] :  (m1_subset_1(D, k3_zfmisc_1(A, B, C)) => v2_xtuple_0(D)) ) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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_struct_0, axiom,  (! [A] :  (l4_struct_0(A) =>  ( ~ (v6_struct_0(A))  =>  ~ (v7_struct_0(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(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_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(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k3_rlvect_1(A, C, B)) ) ).
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(dt_g1_parsp_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k2_zfmisc_1(A, A)))) =>  (v1_parsp_1(g1_parsp_1(A, B)) & l1_parsp_1(g1_parsp_1(A, B))) ) ) ).
fof(dt_k1_algstr_0, axiom,  (! [A, B, C] :  ( (l1_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_algstr_0(A, B, C), u1_struct_0(A))) ) ).
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_group_1, axiom,  (! [A] :  (l3_algstr_0(A) => m1_subset_1(k1_group_1(A), u1_struct_0(A))) ) ).
fof(dt_k1_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k1_mcart_1(A, B, C, D), A)) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k2_mcart_1(A, B, C, D), B)) ) ).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k3_mcart_1(A, B, C, D), C)) ) ).
fof(dt_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_rlvect_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k3_zfmisc_1, axiom, $true).
fof(dt_k4_algstr_0, axiom,  (! [A, B] :  ( (l2_algstr_0(A) & m1_subset_1(B, u1_struct_0(A)))  => m1_subset_1(k4_algstr_0(A, B), u1_struct_0(A))) ) ).
fof(dt_k4_domain_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (m1_subset_1(D, A) &  (m1_subset_1(E, B) & m1_subset_1(F, C)) ) ) ) )  => m1_subset_1(k4_domain_1(A, B, C, D, E, F), k3_zfmisc_1(A, B, C))) ) ).
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_k4_xtuple_0, axiom, $true).
fof(dt_k5_algstr_0, axiom,  (! [A, B, C] :  ( (l2_algstr_0(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k5_algstr_0(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_struct_0, axiom,  (! [A] :  (l3_struct_0(A) => m1_subset_1(k5_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k5_xtuple_0, 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_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_k9_parsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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)) ) ) ) ) ) ) ) ) ) )  => l1_parsp_1(k9_parsp_1(A))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_parsp_1, axiom,  (! [A] :  (l1_parsp_1(A) => l1_struct_0(A)) ) ).
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_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_u1_parsp_1, axiom,  (! [A] :  (l1_parsp_1(A) => m1_subset_1(u1_parsp_1(A), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_parsp_1, axiom,  (? [A] : l1_parsp_1(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_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(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc11_struct_0, axiom,  (! [A] :  ( ( ~ (v6_struct_0(A))  & l4_struct_0(A))  =>  ~ (v9_struct_0(k5_struct_0(A), A)) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(fc3_parsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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(k9_parsp_1(A)))  & v1_parsp_1(k9_parsp_1(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_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(free_g1_parsp_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), k2_zfmisc_1(A, A)))) =>  (! [C, D] :  (g1_parsp_1(A, B)=g1_parsp_1(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(ie10_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l4_algstr_0(A)) )  => k1_group_1(A)=k5_struct_0(A)) ) ).
fof(l10_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (k5_algstr_0(A, k8_group_1(A, B, k5_algstr_0(A, E, D)), k8_group_1(A, C, k5_algstr_0(A, E, F)))=k5_algstr_0(A, F, D) => k8_group_1(A, k3_rlvect_1(A, B, k4_algstr_0(A, k1_group_1(A))), k5_algstr_0(A, E, D))=k8_group_1(A, k3_rlvect_1(A, C, k4_algstr_0(A, k1_group_1(A))), k5_algstr_0(A, E, F))) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l11_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (k5_algstr_0(A, B, C)=k5_algstr_0(A, E, D) => D=k5_algstr_0(A, k3_rlvect_1(A, C, E), B)) ) ) ) ) ) ) ) ) ) ) ).
fof(l2_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & l2_algstr_0(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ( (k1_algstr_0(A, B, k4_algstr_0(A, C))=k4_struct_0(A) => B=C)  &  ( (B=C => k1_algstr_0(A, B, k4_algstr_0(A, C))=k4_struct_0(A))  &  ( (k5_algstr_0(A, B, C)=k4_struct_0(A) => B=C)  &  (B=C => k5_algstr_0(A, B, C)=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ).
fof(l9_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k5_algstr_0(A, k5_algstr_0(A, B, C), k5_algstr_0(A, D, C))=k5_algstr_0(A, B, D)) ) ) ) ) ) ) ) ).
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_parsp_1, axiom,  (? [A] :  (l1_parsp_1(A) & v1_parsp_1(A)) ) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
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_parsp_1, axiom,  (? [A] :  (l1_parsp_1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc2_vectsp_1, axiom,  (? [A] :  (l5_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v4_vectsp_1(A)) ) ) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(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_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(rd1_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l5_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd2_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v4_vectsp_1(A) & l5_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(A), B)=B) ) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
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(rd4_xtuple_0, axiom,  (! [A, B, C] : k4_xtuple_0(k3_xtuple_0(A, B, C))=A) ).
fof(rd5_xtuple_0, axiom,  (! [A, B, C] : k5_xtuple_0(k3_xtuple_0(A, B, C))=B) ).
fof(rd6_xtuple_0, axiom,  (! [A, B, C] : k2_xtuple_0(k3_xtuple_0(A, B, C))=C) ).
fof(rd7_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, B, k5_struct_0(A))=B) ) ).
fof(rd7_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => k3_xtuple_0(k4_xtuple_0(A), k5_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(rd8_vectsp_1, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v6_vectsp_1(A) & l4_algstr_0(A)) )  & m1_subset_1(B, u1_struct_0(A)))  => k6_algstr_0(A, k5_struct_0(A), B)=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_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k1_mcart_1(A, B, C, D)=k4_xtuple_0(D)) ) ).
fof(redefinition_k2_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k2_mcart_1(A, B, C, D)=k5_xtuple_0(D)) ) ).
fof(redefinition_k3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k3_mcart_1(A, B, C, D)=k2_xtuple_0(D)) ) ).
fof(redefinition_k3_rlvect_1, axiom,  (! [A, B, C] :  ( ( (v2_rlvect_1(A) & l1_algstr_0(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_rlvect_1(A, B, C)=k1_algstr_0(A, B, C)) ) ).
fof(redefinition_k4_domain_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (m1_subset_1(D, A) &  (m1_subset_1(E, B) & m1_subset_1(F, C)) ) ) ) )  => k4_domain_1(A, B, C, D, E, F)=k3_xtuple_0(D, E, F)) ) ).
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(t2_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(k9_parsp_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_parsp_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_parsp_1(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k9_parsp_1(A))) =>  (r1_parsp_1(k9_parsp_1(A), B, C, D, E) <=>  (? [F] :  (m1_subset_1(F, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) &  (? [G] :  (m1_subset_1(G, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) &  (? [H] :  (m1_subset_1(H, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) &  (? [I] :  (m1_subset_1(I, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) &  (k4_tarski(k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), B, C), k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), D, E))=k4_tarski(k4_tarski(F, G), k4_tarski(H, I)) &  ~ ( ( (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( (k8_group_1(A, J, k5_algstr_0(A, k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G)))=k5_algstr_0(A, k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), H), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), I)) &  (k8_group_1(A, J, k5_algstr_0(A, k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G)))=k5_algstr_0(A, k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), H), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), I)) & k8_group_1(A, J, k5_algstr_0(A, k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G)))=k5_algstr_0(A, k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), H), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), I))) ) ) ) )  &  ~ ( (k5_algstr_0(A, k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G))=k4_struct_0(A) &  (k5_algstr_0(A, k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G))=k4_struct_0(A) & k5_algstr_0(A, k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G))=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(k9_parsp_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_parsp_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_parsp_1(A))) =>  (! [E] :  (m1_subset_1(E, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [F] :  (m1_subset_1(F, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [G] :  (m1_subset_1(G, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (k4_tarski(k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), B, C), k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), B, D))=k4_tarski(k4_tarski(E, F), k4_tarski(E, G)) =>  (r1_parsp_1(k9_parsp_1(A), B, C, B, D) |  ( ~ (E=F)  &  ( ~ (E=G)  &  ~ (F=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v6_struct_0(A))  &  (v13_algstr_0(A) &  (v33_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] :  (m1_subset_1(B, u1_struct_0(k9_parsp_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k9_parsp_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k9_parsp_1(A))) =>  (! [E] :  (m1_subset_1(E, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [F] :  (m1_subset_1(F, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [G] :  (m1_subset_1(G, k3_zfmisc_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A))) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  ( (k4_tarski(k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), B, C), k1_domain_1(u1_struct_0(k9_parsp_1(A)), u1_struct_0(k9_parsp_1(A)), B, D))=k4_tarski(k4_tarski(E, F), k4_tarski(E, G)) &  (k8_group_1(A, H, k5_algstr_0(A, k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), E), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F)))=k8_group_1(A, I, k5_algstr_0(A, k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), E), k1_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G))) &  (k8_group_1(A, H, k5_algstr_0(A, k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), E), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F)))=k8_group_1(A, I, k5_algstr_0(A, k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), E), k2_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G))) & k8_group_1(A, H, k5_algstr_0(A, k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), E), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), F)))=k8_group_1(A, I, k5_algstr_0(A, k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), E), k3_mcart_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), G)))) ) )  =>  (r1_parsp_1(k9_parsp_1(A), B, C, B, D) |  (H=k4_struct_0(A) & I=k4_struct_0(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t93_mcart_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (! [G] :  (! [H] :  (k4_tarski(k4_tarski(A, B), k4_tarski(C, D))=k4_tarski(k4_tarski(E, F), k4_tarski(G, H)) =>  (A=E &  (B=F &  (C=G & D=H) ) ) ) ) ) ) ) ) ) ) ) ).
