% Mizar problem: t24_midsp_1,midsp_1,265,39 
fof(t24_midsp_1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (r2_midsp_1(A, B, C) =>  (r2_midsp_1(A, D, B) <=> r2_midsp_1(A, D, C)) ) ) ) ) ) ) ) ) ) ).
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(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_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(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(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(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(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
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(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(redefinition_k2_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => k2_domain_1(A, B, C)=k1_xtuple_0(C)) ) ).
fof(redefinition_k3_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => k3_domain_1(A, B, C)=k2_xtuple_0(C)) ) ).
fof(dt_k2_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => m1_subset_1(k2_domain_1(A, B, C), A)) ) ).
fof(dt_k3_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => m1_subset_1(k3_domain_1(A, B, C), B)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(cc1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc4_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(A)) ) ) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
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(symmetry_r2_midsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (m1_subset_1(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) & m1_subset_1(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) )  =>  (r2_midsp_1(A, B, C) => r2_midsp_1(A, C, B)) ) ) ).
fof(reflexivity_r2_midsp_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  &  (m1_subset_1(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) & m1_subset_1(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)))) )  => r2_midsp_1(A, B, B)) ) ).
fof(existence_l1_midsp_1, axiom,  (? [A] : l1_midsp_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_l1_midsp_1, axiom,  (! [A] :  (l1_midsp_1(A) => l1_struct_0(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(rc2_midsp_1, axiom,  (? [A] :  (l1_midsp_1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(d5_midsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (r2_midsp_1(A, B, C) <=> r1_midsp_1(A, k2_domain_1(u1_struct_0(A), u1_struct_0(A), B), k3_domain_1(u1_struct_0(A), u1_struct_0(A), B), k2_domain_1(u1_struct_0(A), u1_struct_0(A), C), k3_domain_1(u1_struct_0(A), u1_struct_0(A), C))) ) ) ) ) ) ) ).
fof(t21_midsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_midsp_1(A) & l1_midsp_1(A)) )  =>  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))) =>  ( (r2_midsp_1(A, B, C) & r2_midsp_1(A, B, D))  => r2_midsp_1(A, C, D)) ) ) ) ) ) ) ) ) ).
