% Mizar problem: l19_homothet,homothet,1142,5 
fof(l19_homothet, conjecture,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, u1_struct_0(A), u1_struct_0(A)) &  (v3_funct_2(E, u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) )  =>  ( (r1_aff_1(A, D, B, C) &  (v4_aff_2(A) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (k3_funct_2(u1_struct_0(A), u1_struct_0(A), E, F)=G <=>  ( ( ~ (r1_aff_1(A, D, B, F))  &  (r1_aff_1(A, D, F, G) & r2_analoaf(A, B, F, C, G)) )  |  (r1_aff_1(A, D, B, F) &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (? [I] :  (m1_subset_1(I, u1_struct_0(A)) &  ( ~ (r1_aff_1(A, D, B, H))  &  (r1_aff_1(A, D, H, I) &  (r2_analoaf(A, B, H, C, I) &  (r2_analoaf(A, H, F, I, G) & r1_aff_1(A, D, B, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (D=B |  (v6_transgeo(E, A) &  (k3_funct_2(u1_struct_0(A), u1_struct_0(A), E, D)=D & k3_funct_2(u1_struct_0(A), u1_struct_0(A), E, B)=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(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(dt_k1_funct_1, 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_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
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(l16_homothet, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(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(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (v4_aff_2(A) &  (r1_aff_1(A, D, B, C) &  (r1_aff_1(A, D, F, G) &  (r2_analoaf(A, B, F, C, G) & r1_aff_1(A, D, B, H)) ) ) )  =>  (D=B |  (r1_aff_1(A, D, B, F) |  ( (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( ( ~ (r1_aff_1(A, D, B, I))  &  (r1_aff_1(A, D, I, J) &  (r2_analoaf(A, B, I, C, J) &  (r2_analoaf(A, I, H, J, E) & r1_aff_1(A, D, B, E)) ) ) ) ) ) ) ) )  | r2_analoaf(A, F, H, G, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l17_homothet, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(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(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (v4_aff_2(A) &  (r1_aff_1(A, D, B, C) &  (r1_aff_1(A, D, B, F) &  (r1_aff_1(A, D, H, E) & r2_analoaf(A, B, H, C, E)) ) ) )  =>  (D=B |  ( (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( ( ~ (r1_aff_1(A, D, B, I))  &  (r1_aff_1(A, D, I, J) &  (r2_analoaf(A, B, I, C, J) &  (r2_analoaf(A, I, F, J, G) & r1_aff_1(A, D, B, G)) ) ) ) ) ) ) ) )  |  (r1_aff_1(A, D, B, H) | r2_analoaf(A, F, H, G, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l18_homothet, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(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(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (r1_aff_1(A, D, B, F) & r1_aff_1(A, D, B, H))  =>  (D=B |  ( (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( ( ~ (r1_aff_1(A, D, B, I))  &  (r1_aff_1(A, D, I, J) &  (r2_analoaf(A, B, I, C, J) &  (r2_analoaf(A, I, F, J, G) & r1_aff_1(A, D, B, G)) ) ) ) ) ) ) ) )  |  ( (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  ~ ( ( ~ (r1_aff_1(A, D, B, I))  &  (r1_aff_1(A, D, I, J) &  (r2_analoaf(A, B, I, C, J) &  (r2_analoaf(A, I, H, J, E) & r1_aff_1(A, D, B, E)) ) ) ) ) ) ) ) )  | r2_analoaf(A, F, H, G, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l1_homothet, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (v4_aff_2(A) <=>  (! [B] :  (m1_subset_1(B, u1_struct_0(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(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (r1_aff_1(A, B, C, D) &  (r1_aff_1(A, B, E, F) &  (r1_aff_1(A, B, G, H) &  (r2_analoaf(A, C, E, D, F) & r2_analoaf(A, C, G, D, H)) ) ) )  =>  (r1_aff_1(A, B, C, E) |  (r1_aff_1(A, B, C, G) | r2_analoaf(A, E, G, F, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l9_homothet, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(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)) =>  (E=D =>  (D=B |  ( ( ~ ( ( ~ (r1_aff_1(A, D, B, E))  &  (r1_aff_1(A, D, E, F) & r2_analoaf(A, B, E, C, F)) ) )  &  ~ ( (r1_aff_1(A, D, B, E) &  (? [G] :  (m1_subset_1(G, u1_struct_0(A)) &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  ( ~ (r1_aff_1(A, D, B, G))  &  (r1_aff_1(A, D, G, H) &  (r2_analoaf(A, B, G, C, H) &  (r2_analoaf(A, G, E, H, F) & r1_aff_1(A, D, B, F)) ) ) ) ) ) ) ) ) ) )  | F=D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
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(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(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_aff_1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(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)) =>  (r2_analoaf(A, B, C, D, E) =>  (r2_analoaf(A, B, C, E, D) &  (r2_analoaf(A, C, B, D, E) &  (r2_analoaf(A, C, B, E, D) &  (r2_analoaf(A, D, E, B, C) &  (r2_analoaf(A, D, E, C, B) &  (r2_analoaf(A, E, D, B, C) & r2_analoaf(A, E, D, 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(t56_aff_1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(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(A)) =>  ( (r1_aff_1(A, F, B, C) &  (r1_aff_1(A, F, D, E) &  (r1_aff_1(A, F, D, G) &  (r2_analoaf(A, B, D, C, E) & r2_analoaf(A, B, D, C, G)) ) ) )  =>  (r1_aff_1(A, F, B, D) | E=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t68_transgeo, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, u1_struct_0(A), u1_struct_0(A)) &  (v3_funct_2(B, u1_struct_0(A), u1_struct_0(A)) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) )  =>  (v6_transgeo(B, A) <=>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) => r2_analoaf(A, C, D, k3_funct_2(u1_struct_0(A), u1_struct_0(A), B, C), k3_funct_2(u1_struct_0(A), u1_struct_0(A), B, D))) ) ) ) ) ) ) ) ) ).
fof(t6_aff_1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r1_aff_1(A, B, C, D) =>  (r1_aff_1(A, B, D, C) &  (r1_aff_1(A, C, B, D) &  (r1_aff_1(A, C, D, B) &  (r1_aff_1(A, D, B, C) & r1_aff_1(A, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_aff_1, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_aff_1(A, B, B, C) &  (r1_aff_1(A, B, C, C) & r1_aff_1(A, B, C, B)) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
