% Mizar problem: t33_midsp_2,midsp_2,921,5 
fof(t33_midsp_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  ( (v4_midsp_2(B, A) & l1_midsp_2(B, 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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(u1_midsp_2(A, B))) =>  (k9_midsp_2(A, B, C, C)=k11_midsp_2(A, B) &  ( (k9_midsp_2(A, B, C, D)=k11_midsp_2(A, B) => C=D)  &  (k9_midsp_2(A, B, C, D)=k4_algstr_0(u1_midsp_2(A, B), k9_midsp_2(A, B, D, C)) &  ( (k9_midsp_2(A, B, C, D)=k9_midsp_2(A, B, E, F) => k9_midsp_2(A, B, D, C)=k9_midsp_2(A, B, F, E))  &  ( (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(u1_midsp_2(A, B))) =>  (? [J] :  (m1_subset_1(J, u1_struct_0(A)) & k9_midsp_2(A, B, J, H)=I) ) ) ) ) )  &  ( (k9_midsp_2(A, B, D, C)=k9_midsp_2(A, B, E, C) => D=E)  &  ( (k3_midsp_1(A, C, D)=E => k9_midsp_2(A, B, C, E)=k9_midsp_2(A, B, E, D))  &  ( (k9_midsp_2(A, B, C, E)=k9_midsp_2(A, B, E, D) => k3_midsp_1(A, C, D)=E)  &  ( (k3_midsp_1(A, C, D)=k3_midsp_1(A, E, F) => k9_midsp_2(A, B, C, F)=k9_midsp_2(A, B, E, D))  &  ( (k9_midsp_2(A, B, C, F)=k9_midsp_2(A, B, E, D) => k3_midsp_1(A, C, D)=k3_midsp_1(A, E, F))  &  ( (k9_midsp_2(A, B, C, D)=G => k10_midsp_2(A, B, C, G)=D)  &  (k10_midsp_2(A, B, C, G)=D => k9_midsp_2(A, B, C, D)=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_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_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_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_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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(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_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_midsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_midsp_1(A, B, C)=k3_midsp_1(A, C, B)) ) ).
fof(d12_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_midsp_1(A))  =>  (! [B] :  (l1_midsp_2(B, A) =>  (v4_midsp_2(B, A) <=>  (v2_midsp_2(u1_midsp_2(A, B)) &  (v3_rlvect_1(u1_midsp_2(A, B)) &  (v4_rlvect_1(u1_midsp_2(A, B)) &  (v13_algstr_0(u1_midsp_2(A, B)) &  (v2_rlvect_1(u1_midsp_2(A, B)) &  (v1_midsp_2(u2_midsp_2(A, B), A, u1_midsp_2(A, B)) & r1_midsp_2(u1_struct_0(A), u1_midsp_2(A, B), u2_midsp_2(A, B))) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  (l1_midsp_2(B, A) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => k9_midsp_2(A, B, C, D)=k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(u1_midsp_2(A, B)), u2_midsp_2(A, B), C, D)) ) ) ) ) ) ) ) ).
fof(d14_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  (l1_midsp_2(B, A) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(u1_midsp_2(A, B))) => k10_midsp_2(A, B, C, D)=k2_midsp_2(u1_struct_0(A), u1_midsp_2(A, B), u2_midsp_2(A, B), C, D)) ) ) ) ) ) ) ) ).
fof(d15_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  ( (v4_midsp_2(B, A) & l1_midsp_2(B, A))  => k11_midsp_2(A, B)=k4_struct_0(u1_midsp_2(A, B))) ) ) ) ).
fof(d3_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(B))))) )  =>  (r1_midsp_2(A, B, C) <=>  ( (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (? [F] :  (m1_subset_1(F, A) & k2_binop_1(A, A, u1_struct_0(B), C, D, F)=E) ) ) ) ) )  &  ( (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, A) =>  (! [F] :  (m1_subset_1(F, A) =>  (k2_binop_1(A, A, u1_struct_0(B), C, D, E)=k2_binop_1(A, A, u1_struct_0(B), C, D, F) => E=F) ) ) ) ) ) )  &  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, A) =>  (! [F] :  (m1_subset_1(F, A) => k1_algstr_0(B, k2_binop_1(A, A, u1_struct_0(B), C, D, E), k2_binop_1(A, A, u1_struct_0(B), C, E, F))=k2_binop_1(A, A, u1_struct_0(B), C, D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(B))))) )  =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (r1_midsp_2(A, B, C) =>  (! [F] :  (m1_subset_1(F, A) =>  (F=k2_midsp_2(A, B, C, D, E) <=> k2_binop_1(A, A, u1_struct_0(B), C, D, F)=E) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_midsp_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (l1_midsp_2(B, A) &  (m1_subset_1(C, u1_struct_0(A)) & m1_subset_1(D, u1_struct_0(u1_midsp_2(A, B)))) ) )  => m1_subset_1(k10_midsp_2(A, B, C, D), u1_struct_0(A))) ) ).
fof(dt_k11_midsp_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (v4_midsp_2(B, A) & l1_midsp_2(B, A)) )  => m1_subset_1(k11_midsp_2(A, B), u1_struct_0(u1_midsp_2(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_binop_1, axiom, $true).
fof(dt_k1_midsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  & l1_midsp_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_midsp_1(A, B, C), u1_struct_0(A))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) ) ).
fof(dt_k2_midsp_2, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ( ~ (v2_struct_0(B))  & l2_algstr_0(B))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(B))))) )  &  (m1_subset_1(D, A) & m1_subset_1(E, u1_struct_0(B))) ) ) )  => m1_subset_1(k2_midsp_2(A, B, C, D, E), A)) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_midsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_midsp_1(A, B, C), u1_struct_0(A))) ) ).
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_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => m1_subset_1(k4_struct_0(A), u1_struct_0(A))) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k9_midsp_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (l1_midsp_2(B, A) &  (m1_subset_1(C, u1_struct_0(A)) & m1_subset_1(D, u1_struct_0(A))) ) )  => m1_subset_1(k9_midsp_2(A, B, C, D), u1_struct_0(u1_midsp_2(A, B)))) ) ).
fof(dt_l1_algstr_0, axiom,  (! [A] :  (l1_algstr_0(A) => l1_struct_0(A)) ) ).
fof(dt_l1_midsp_1, axiom,  (! [A] :  (l1_midsp_1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_midsp_2, axiom, $true).
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_midsp_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_midsp_1(A))  & l1_midsp_2(B, A))  =>  ( ~ (v2_struct_0(u1_midsp_2(A, B)))  & l2_algstr_0(u1_midsp_2(A, B))) ) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(dt_u2_midsp_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  & l1_midsp_1(A))  & l1_midsp_2(B, A))  =>  (v1_funct_1(u2_midsp_2(A, B)) &  (v1_funct_2(u2_midsp_2(A, B), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(u1_midsp_2(A, B))) & m1_subset_1(u2_midsp_2(A, B), k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(u1_midsp_2(A, B)))))) ) ) ) ).
fof(existence_l1_algstr_0, axiom,  (? [A] : l1_algstr_0(A)) ).
fof(existence_l1_midsp_1, axiom,  (? [A] : l1_midsp_1(A)) ).
fof(existence_l1_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_midsp_1(A))  =>  (? [B] : l1_midsp_2(B, 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_struct_0, axiom,  (! [A] :  (l2_struct_0(A) => v9_struct_0(k4_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_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_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(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_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_midsp_1, axiom,  (? [A] :  (l1_midsp_1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (? [B] :  (l1_midsp_2(B, A) & v4_midsp_2(B, 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(rc9_vectsp_1, axiom,  (? [A] :  (l2_algstr_0(A) &  ( ~ (v2_struct_0(A))  & v12_vectsp_1(A)) ) ) ).
fof(redefinition_k2_binop_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C)))) )  &  (m1_subset_1(E, A) & m1_subset_1(F, B)) ) ) )  => k2_binop_1(A, B, C, D, E, F)=k1_binop_1(D, E, F)) ) ).
fof(redefinition_k3_midsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k3_midsp_1(A, B, C)=k1_midsp_1(A, B, C)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t13_midsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_midsp_1(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v2_rlvect_1(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(B))))) )  =>  ( (r1_midsp_2(u1_struct_0(A), B, C) & v1_midsp_2(C, A, B))  =>  (! [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)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (k1_midsp_1(A, D, E)=k1_midsp_1(A, F, G) <=> k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), C, D, G)=k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(B), C, F, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  ( ( ~ (v2_struct_0(C))  &  (v13_algstr_0(C) &  (v3_rlvect_1(C) &  (v4_rlvect_1(C) & l2_algstr_0(C)) ) ) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, k2_zfmisc_1(A, A), u1_struct_0(C)) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(C))))) )  =>  (r1_midsp_2(A, C, D) => k2_binop_1(A, A, u1_struct_0(C), D, B, B)=k4_struct_0(C)) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l2_algstr_0(D)) ) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(A, A), u1_struct_0(D)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(D))))) )  =>  ( (r1_midsp_2(A, D, E) & k2_binop_1(A, A, u1_struct_0(D), E, B, C)=k4_struct_0(D))  => B=C) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  ( ( ~ (v2_struct_0(D))  &  (v13_algstr_0(D) &  (v3_rlvect_1(D) &  (v4_rlvect_1(D) & l2_algstr_0(D)) ) ) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, k2_zfmisc_1(A, A), u1_struct_0(D)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(D))))) )  =>  (r1_midsp_2(A, D, E) => k2_binop_1(A, A, u1_struct_0(D), E, B, C)=k4_algstr_0(D, k2_binop_1(A, A, u1_struct_0(D), E, C, 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_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(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) =>  (! [F] :  ( ( ~ (v2_struct_0(F))  &  (v13_algstr_0(F) &  (v3_rlvect_1(F) &  (v4_rlvect_1(F) & l2_algstr_0(F)) ) ) )  =>  (! [G] :  ( (v1_funct_1(G) &  (v1_funct_2(G, k2_zfmisc_1(A, A), u1_struct_0(F)) & m1_subset_1(G, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(F))))) )  =>  ( (r1_midsp_2(A, F, G) & k2_binop_1(A, A, u1_struct_0(F), G, B, C)=k2_binop_1(A, A, u1_struct_0(F), G, D, E))  => k2_binop_1(A, A, u1_struct_0(F), G, C, B)=k2_binop_1(A, A, u1_struct_0(F), G, E, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v13_algstr_0(B) &  (v3_rlvect_1(B) &  (v4_rlvect_1(B) & l2_algstr_0(B)) ) ) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k2_zfmisc_1(A, A), u1_struct_0(B)) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(B))))) )  =>  (r1_midsp_2(A, B, C) =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (? [F] :  (m1_subset_1(F, A) & k2_binop_1(A, A, u1_struct_0(B), C, F, D)=E) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_midsp_2, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_subset_1(C, A) =>  (! [D] :  (m1_subset_1(D, A) =>  (! [E] :  ( ( ~ (v2_struct_0(E))  &  (v13_algstr_0(E) &  (v3_rlvect_1(E) &  (v4_rlvect_1(E) & l2_algstr_0(E)) ) ) )  =>  (! [F] :  ( (v1_funct_1(F) &  (v1_funct_2(F, k2_zfmisc_1(A, A), u1_struct_0(E)) & m1_subset_1(F, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), u1_struct_0(E))))) )  =>  ( (r1_midsp_2(A, E, F) & k2_binop_1(A, A, u1_struct_0(E), F, C, B)=k2_binop_1(A, A, u1_struct_0(E), F, D, B))  => C=D) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
