% Mizar problem: t28_grcat_1,grcat_1,966,5 
fof(t28_grcat_1, conjecture,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (r2_tarski(B, A) & r1_grcat_1(B, k3_algstr_0)) ) ) ) ).
fof(abstractness_v8_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v8_algstr_0(A) => A=g2_algstr_0(u1_struct_0(A), u1_algstr_0(A), u2_struct_0(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_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v14_algstr_0(A) =>  (v12_algstr_0(A) & v13_algstr_0(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_algstr_0, axiom,  (! [A] :  ( (v12_algstr_0(A) & l2_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v9_algstr_0(B, 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_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(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v2_algstr_0(B, A) & v3_algstr_0(B, A))  => v4_algstr_0(B, A)) ) ) ) ) ).
fof(cc1_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) ) ) ) ) ).
fof(cc1_classes2, axiom,  (! [A] :  (v2_classes1(A) => v1_classes1(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_midsp_2, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v2_midsp_2(A))  =>  ( ~ (v2_struct_0(A))  & v12_vectsp_1(A)) ) ) ) ).
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(cc2_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v4_algstr_0(B, A) =>  (v2_algstr_0(B, A) & v3_algstr_0(B, A)) ) ) ) ) ) ).
fof(cc2_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v2_algstr_1(A) & v3_algstr_1(A)) ) ) )  =>  ( ~ (v2_struct_0(A))  & v4_algstr_1(A)) ) ) ) ).
fof(cc2_classes2, axiom,  (! [A] :  (v1_classes2(A) =>  (v1_ordinal1(A) & v2_classes1(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(cc3_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  ( (v5_algstr_0(A) & v6_algstr_0(A))  => v7_algstr_0(A)) ) ) ).
fof(cc3_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  & v4_algstr_1(A))  =>  ( ~ (v2_struct_0(A))  & v2_algstr_1(A)) ) ) ) ).
fof(cc3_classes2, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_classes1(A))  => v1_classes2(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(cc4_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) =>  (v7_algstr_0(A) =>  (v5_algstr_0(A) & v6_algstr_0(A)) ) ) ) ).
fof(cc4_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( ( ~ (v2_struct_0(A))  &  (v13_algstr_0(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) )  =>  ( ~ (v2_struct_0(A))  &  (v1_algstr_1(A) & v4_algstr_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(cc5_algstr_0, axiom,  (! [A] :  ( (v5_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v2_algstr_0(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(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(A)) ) ) ) ) ).
fof(cc6_algstr_0, axiom,  (! [A] :  ( (v6_algstr_0(A) & l1_algstr_0(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) => v3_algstr_0(B, A)) ) ) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  ( (v9_algstr_0(B, A) & v10_algstr_0(B, A))  => v11_algstr_0(B, A)) ) ) ) ) ).
fof(cc7_algstr_1, axiom,  (! [A] :  (l2_algstr_0(A) =>  (v13_struct_0(A, 1) =>  (v13_struct_0(A, 1) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) & v4_rlvect_1(A)) ) ) ) ) ) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (v11_algstr_0(B, A) =>  (v9_algstr_0(B, A) & v10_algstr_0(B, A)) ) ) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_algstr_0, axiom,  (! [A] :  (l2_algstr_0(A) =>  ( (v12_algstr_0(A) & v13_algstr_0(A))  => v14_algstr_0(A)) ) ) ).
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(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d1_algstr_1, axiom,  (! [A] : k1_algstr_1(A)=A) ).
fof(d23_grcat_1, axiom,  (! [A] :  (! [B] :  (r1_grcat_1(A, B) <=>  (? [C] :  (? [D] :  (? [E] :  (? [F] :  (A=k6_xtuple_0(C, D, E, F) &  (? [G] :  ( ( ~ (v2_struct_0(G))  &  (v8_algstr_0(G) &  (v13_algstr_0(G) &  (v3_rlvect_1(G) &  (v4_rlvect_1(G) & l2_algstr_0(G)) ) ) ) )  &  (B=G &  (C=u1_struct_0(G) &  (D=u1_algstr_0(G) &  (E=k4_vectsp_1(G) & F=k4_struct_0(G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] : k3_xtuple_0(A, B, C)=k4_tarski(k4_tarski(A, B), C)) ) ) ).
fof(d6_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => k4_struct_0(A)=u2_struct_0(A)) ) ).
fof(d8_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k6_xtuple_0(A, B, C, D)=k4_tarski(k3_xtuple_0(A, B, C), D)) ) ) ) ).
fof(d9_algstr_0, axiom, k3_algstr_0=g2_algstr_0(k1_tarski(k5_ordinal1), k9_funct_5, k5_funct_5)).
fof(dt_g2_algstr_0, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A))  =>  (v8_algstr_0(g2_algstr_0(A, B, C)) & l2_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(dt_k1_algstr_1, axiom,  (! [A] : m1_subset_1(k1_algstr_1(A), k1_tarski(A))) ).
fof(dt_k1_classes2, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  & m1_subset_1(B, A))  => m1_subset_1(k1_classes2(A, B), A)) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_algstr_0, axiom, l2_algstr_0(k3_algstr_0)).
fof(dt_k3_xtuple_0, axiom, $true).
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_vectsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_algstr_0(A))  =>  (v1_funct_1(k4_vectsp_1(A)) &  (v1_funct_2(k4_vectsp_1(A), u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(k4_vectsp_1(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ) ) ).
fof(dt_k5_funct_5, axiom, m1_subset_1(k5_funct_5, k1_tarski(k5_ordinal1))).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_funct_5, axiom, $true).
fof(dt_k6_xtuple_0, axiom, $true).
fof(dt_k7_funct_5, axiom, $true).
fof(dt_k8_funct_5, axiom,  (v1_funct_1(k8_funct_5) &  (v1_funct_2(k8_funct_5, k1_tarski(k5_ordinal1), k1_tarski(k5_ordinal1)) & m1_subset_1(k8_funct_5, k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_ordinal1), k1_tarski(k5_ordinal1))))) ) ).
fof(dt_k9_funct_5, axiom,  (v1_funct_1(k9_funct_5) &  (v1_funct_2(k9_funct_5, k2_zfmisc_1(k1_tarski(k5_ordinal1), k1_tarski(k5_ordinal1)), k1_tarski(k5_ordinal1)) & m1_subset_1(k9_funct_5, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_ordinal1), k1_tarski(k5_ordinal1)), k1_tarski(k5_ordinal1))))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(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_m1_subset_1, axiom, $true).
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_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_l2_algstr_0, axiom,  (? [A] : l2_algstr_0(A)) ).
fof(existence_l2_struct_0, axiom,  (? [A] : l2_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc10_algstr_0, axiom, v7_algstr_0(k3_algstr_0)).
fof(fc10_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_struct_0(A), A)) ) ).
fof(fc11_algstr_0, axiom, v14_algstr_0(k3_algstr_0)).
fof(fc1_algstr_1, axiom,  (v3_rlvect_1(k3_algstr_0) &  (v4_rlvect_1(k3_algstr_0) &  (v1_algstr_1(k3_algstr_0) & v4_algstr_1(k3_algstr_0)) ) ) ).
fof(fc1_grcat_1, axiom, v2_midsp_2(k3_algstr_0)).
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_algstr_1, axiom, v2_rlvect_1(k3_algstr_0)).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc6_algstr_0, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A)) )  =>  ( ~ (v2_struct_0(g2_algstr_0(A, B, C)))  & v8_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_algstr_0, axiom,  (! [A, B, C] :  ( (v1_zfmisc_1(A) &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A)) )  =>  (v7_struct_0(g2_algstr_0(A, B, C)) & v8_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_algstr_0, axiom,  (! [A, B, C] :  ( ( ~ (v1_zfmisc_1(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A)) )  =>  ( ~ (v7_struct_0(g2_algstr_0(A, B, C)))  & v8_algstr_0(g2_algstr_0(A, B, C))) ) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_algstr_0, axiom,  (v13_struct_0(k3_algstr_0, 1) & v8_algstr_0(k3_algstr_0)) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(free_g2_algstr_0, axiom,  (! [A, B, C] :  ( ( (v1_funct_1(B) &  (v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A)))) )  & m1_subset_1(C, A))  =>  (! [D, E, F] :  (g2_algstr_0(A, B, C)=g2_algstr_0(D, E, F) =>  (A=D &  (B=E & C=F) ) ) ) ) ) ).
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_algstr_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v8_algstr_0(A) &  (v4_rlvect_1(A) &  (v1_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ).
fof(rc1_classes2, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_classes2(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_midsp_2, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v8_algstr_0(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) & v2_midsp_2(A)) ) ) ) ) ) ) ) ).
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_xboole_0, axiom,  (? [A] : v1_xboole_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_algstr_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v7_algstr_0(A) &  (v8_algstr_0(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc2_classes2, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_algstr_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  &  (v5_algstr_0(A) &  (v6_algstr_0(A) &  (v7_algstr_0(A) &  (v8_algstr_0(A) &  (v13_algstr_0(A) &  (v2_rlvect_1(A) &  (v3_rlvect_1(A) &  (v4_rlvect_1(A) &  (v1_algstr_1(A) &  (v2_algstr_1(A) &  (v3_algstr_1(A) & v4_algstr_1(A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc4_algstr_0, axiom,  (? [A] :  (l2_algstr_0(A) & v8_algstr_0(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(rc5_algstr_0, axiom,  (? [A] :  (l2_algstr_0(A) &  (v13_struct_0(A, 1) & v8_algstr_0(A)) ) ) ).
fof(rc6_algstr_0, axiom,  (? [A] :  (l2_algstr_0(A) &  (v13_struct_0(A, 1) &  (v7_algstr_0(A) &  (v8_algstr_0(A) & v14_algstr_0(A)) ) ) ) ) ).
fof(redefinition_k1_classes2, axiom,  (! [A, B] :  ( ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  & m1_subset_1(B, A))  => k1_classes2(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k5_funct_5, axiom, k5_funct_5=k5_ordinal1).
fof(redefinition_k8_funct_5, axiom, k8_funct_5=k6_funct_5).
fof(redefinition_k9_funct_5, axiom, k9_funct_5=k7_funct_5).
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_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, A) =>  (r2_hidden(k3_xtuple_0(B, C, D), A) & r2_hidden(k6_xtuple_0(B, C, D, E), A)) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_tarski, axiom, $true).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_grcat_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  =>  (r2_tarski(k1_tarski(k1_xboole_0), A) &  (r2_hidden(k4_tarski(k1_tarski(k1_xboole_0), k1_tarski(k1_xboole_0)), A) &  (r2_tarski(k2_zfmisc_1(k1_tarski(k1_xboole_0), k1_tarski(k1_xboole_0)), A) &  (r2_tarski(k9_funct_5, A) & r2_tarski(k8_funct_5, A)) ) ) ) ) ) ).
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(t56_classes2, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_classes2(A))  => r2_tarski(k1_xboole_0, A)) ) ).
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(t6_grcat_1, axiom, r1_funct_2(u1_struct_0(k3_algstr_0), u1_struct_0(k3_algstr_0), k1_tarski(k5_ordinal1), k1_tarski(k5_ordinal1), k4_vectsp_1(k3_algstr_0), k8_funct_5)).
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)) ) ) ) ) ).
