% Mizar problem: l4_homothet,homothet,329,5 
fof(l4_homothet, conjecture,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (v7_aff_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(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)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ( (r5_aff_1(A, B, C) &  (r5_aff_1(A, B, D) &  (r2_tarski(E, B) &  (r2_tarski(F, B) &  (r2_tarski(G, C) &  (r2_tarski(H, C) &  (r2_tarski(I, D) &  (r2_tarski(J, D) &  (r2_analoaf(A, E, G, F, H) & r2_analoaf(A, E, I, F, J)) ) ) ) ) ) ) ) )  =>  (B=C |  (B=D | r2_analoaf(A, G, I, H, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(A)) ) ) ).
fof(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_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(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(d11_aff_2, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (v11_aff_2(A) <=>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(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)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ( (r5_aff_1(A, B, C) &  (r5_aff_1(A, B, D) &  (r2_hidden(E, B) &  (r2_hidden(H, B) &  (r2_hidden(F, C) &  (r2_hidden(I, C) &  (r2_hidden(G, D) &  (r2_hidden(J, D) &  (v1_aff_1(B, A) &  (v1_aff_1(C, A) &  (v1_aff_1(D, A) &  (r2_analoaf(A, E, F, H, I) & r2_analoaf(A, E, G, H, J)) ) ) ) ) ) ) ) ) ) ) )  =>  (B=C |  (B=D | r2_analoaf(A, F, G, I, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_l1_analoaf, axiom,  (! [A] :  (l1_analoaf(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_analoaf, axiom,  (? [A] : l1_analoaf(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_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(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(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(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(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r5_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (r5_aff_1(A, B, C) <=> r3_aff_1(A, B, C)) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(symmetry_r5_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  =>  (r5_aff_1(A, B, C) => r5_aff_1(A, C, B)) ) ) ).
fof(t14_aff_2, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (v7_aff_2(A) => v11_aff_2(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(t36_aff_1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))) =>  (r3_aff_1(A, B, C) =>  (v1_aff_1(B, A) & v1_aff_1(C, 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(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)) ) ) ) ) ).
