% Mizar problem: t31_anproj_2,anproj_2,3232,5 
fof(t31_anproj_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  ~ ( (v4_collsp(k5_anproj_1(A)) &  (v3_anproj_2(k5_anproj_1(A)) &  ( (? [B] :  (m1_subset_1(B, u1_struct_0(k5_anproj_1(A))) &  (? [C] :  (m1_subset_1(C, u1_struct_0(k5_anproj_1(A))) &  (? [D] :  (m1_subset_1(D, u1_struct_0(k5_anproj_1(A))) &  ( ~ (r1_collsp(k5_anproj_1(A), B, C, D))  &  (! [E] :  (m1_subset_1(E, u1_struct_0(k5_anproj_1(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k5_anproj_1(A))) =>  (? [G] :  (m1_subset_1(G, u1_struct_0(k5_anproj_1(A))) &  (? [H] :  (m1_subset_1(H, u1_struct_0(k5_anproj_1(A))) &  (r1_collsp(k5_anproj_1(A), E, F, H) &  (r1_collsp(k5_anproj_1(A), C, D, G) & r1_collsp(k5_anproj_1(A), B, H, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v2_collsp(B) &  (v3_collsp(B) &  (v4_collsp(B) &  (v2_anproj_2(B) &  (v3_anproj_2(B) & l1_collsp(B)) ) ) ) ) )  =>  ~ ( (B=k5_anproj_1(A) & v8_anproj_2(B)) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_collsp, axiom,  (! [A] :  (l1_collsp(A) =>  (v1_collsp(A) => A=g1_collsp(u1_struct_0(A), u1_collsp(A))) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(d10_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_collsp(A))  =>  (v3_anproj_2(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)) &  ( ~ (B=D)  &  ( ~ (C=D)  & r1_collsp(A, B, C, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_collsp, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_collsp(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)) =>  (r1_collsp(A, B, C, D) <=> r2_tarski(k4_domain_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), B, C, D), u1_collsp(A))) ) ) ) ) ) ) ) ) ).
fof(d7_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_collsp(A))  =>  (v2_collsp(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)) =>  (r1_collsp(A, B, C, B) &  (r1_collsp(A, B, B, C) & r1_collsp(A, B, C, C)) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_collsp(A))  =>  (v3_collsp(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)) =>  ( (r1_collsp(A, B, C, D) &  (r1_collsp(A, B, C, E) & r1_collsp(A, B, C, F)) )  =>  (B=C | r1_collsp(A, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_collsp(A))  =>  (v2_anproj_2(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)) =>  ~ ( (r1_collsp(A, B, C, E) &  (r1_collsp(A, C, D, F) &  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( (r1_collsp(A, B, D, G) & r1_collsp(A, E, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_g1_collsp, axiom,  (! [A, B] :  (m1_collsp(B, A) =>  (v1_collsp(g1_collsp(A, B)) & l1_collsp(g1_collsp(A, B))) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k3_zfmisc_1, axiom, $true).
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_ordinal1, axiom, $true).
fof(dt_k5_anproj_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  (v1_collsp(k5_anproj_1(A)) & l1_collsp(k5_anproj_1(A))) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_collsp, axiom,  (! [A] :  (l1_collsp(A) => l1_struct_0(A)) ) ).
fof(dt_l1_rlvect_1, axiom,  (! [A] :  (l1_rlvect_1(A) => l2_algstr_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_m1_collsp, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_collsp, axiom,  (! [A] :  (l1_collsp(A) => m1_collsp(u1_collsp(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_collsp, axiom,  (? [A] : l1_collsp(A)) ).
fof(existence_l1_rlvect_1, axiom,  (? [A] : l1_rlvect_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_m1_collsp, axiom,  (! [A] :  (? [B] : m1_collsp(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc11_subset_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k3_zfmisc_1(A, B, C))) ) ) ).
fof(fc1_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  (v1_collsp(k5_anproj_1(A)) &  (v2_collsp(k5_anproj_1(A)) & v3_collsp(k5_anproj_1(A))) ) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_anproj_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  ( ~ (v2_struct_0(k5_anproj_1(A)))  & v1_collsp(k5_anproj_1(A))) ) ) ).
fof(fc2_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  (v1_collsp(k5_anproj_1(A)) & v2_anproj_2(k5_anproj_1(A))) ) ) ).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
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_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(free_g1_collsp, axiom,  (! [A, B] :  (m1_collsp(B, A) =>  (! [C, D] :  (g1_collsp(A, B)=g1_collsp(C, D) =>  (A=C & B=D) ) ) ) ) ).
fof(l89_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k5_anproj_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k5_anproj_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k5_anproj_1(A))) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(k5_anproj_1(A))) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(k5_anproj_1(A))) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(k5_anproj_1(A))) =>  ~ ( ( ~ (r1_collsp(k5_anproj_1(A), G, D, C))  &  (r1_collsp(k5_anproj_1(A), D, C, B) &  (r1_collsp(k5_anproj_1(A), G, E, D) &  (r1_collsp(k5_anproj_1(A), G, F, C) &  (! [H] :  (m1_subset_1(H, u1_struct_0(k5_anproj_1(A))) =>  ~ ( (r1_collsp(k5_anproj_1(A), E, F, H) & r1_collsp(k5_anproj_1(A), G, B, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc1_collsp, axiom,  (? [A] :  (l1_collsp(A) & v1_collsp(A)) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc20_struct_0, axiom,  (? [A] :  (l2_struct_0(A) &  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ).
fof(rc2_anproj_2, axiom,  (? [A] :  (l1_collsp(A) &  ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) & v3_anproj_2(A)) ) ) ) ) ) ) ).
fof(rc2_collsp, axiom,  (? [A] :  (l1_collsp(A) &  ( ~ (v2_struct_0(A))  & v1_collsp(A)) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_collsp, axiom,  (? [A] :  (l1_collsp(A) &  ( ~ (v2_struct_0(A))  &  (v1_collsp(A) &  (v2_collsp(A) & v3_collsp(A)) ) ) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_collsp, axiom,  (? [A] :  (l1_collsp(A) &  ( ~ (v2_struct_0(A))  &  (v1_collsp(A) &  (v2_collsp(A) &  (v3_collsp(A) & v4_collsp(A)) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
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_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(t12_collsp, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) & l1_collsp(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( ( ~ (B=C)  &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => r1_collsp(A, B, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t24_anproj_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  ( ~ (v7_struct_0(A))  &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v5_rlvect_1(A) &  (v6_rlvect_1(A) &  (v7_rlvect_1(A) &  (v8_rlvect_1(A) & l1_rlvect_1(A)) ) ) ) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(k5_anproj_1(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(k5_anproj_1(A))) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(k5_anproj_1(A))) =>  (r1_collsp(k5_anproj_1(A), B, C, D) =>  (r1_collsp(k5_anproj_1(A), B, D, C) &  (r1_collsp(k5_anproj_1(A), C, B, D) &  (r1_collsp(k5_anproj_1(A), D, C, B) &  (r1_collsp(k5_anproj_1(A), D, B, C) & r1_collsp(k5_anproj_1(A), C, D, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
