% Mizar problem: l20_connsp_3,connsp_3,448,8 
fof(l20_connsp_3, conjecture,  (! [A] :  (l1_pre_topc(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) &  ( (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (r2_tarski(C, B) => v3_connsp_1(C, A)) ) )  & k1_struct_0(A)=k5_setfam_1(u1_struct_0(A), B)) ) ) ) ) ).
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(cc1_connsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v3_connsp_1(B, A) => v2_connsp_1(B, A)) ) ) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_connsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v2_connsp_1(B, A)) ) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(d2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k1_struct_0(A)=k1_xboole_0) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k1_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_l1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_pre_topc, axiom,  (? [A] : l1_pre_topc(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => v1_xboole_0(k1_struct_0(A))) ) ).
fof(rc1_connsp_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B)) ) ) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(redefinition_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A, B)=k3_tarski(B)) ) ).
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(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_xboole_1, axiom,  (! [A] : r1_tarski(k1_xboole_0, A)) ).
fof(t2_zfmisc_1, axiom, k3_tarski(k1_xboole_0)=k1_xboole_0).
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(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(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)) ) ) ) ) ).
