% Mizar problem: l32_homothet,homothet,1680,5 
fof(l32_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, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (r2_aff_1(A, B, C, D) &  ( ~ (r2_tarski(B, D))  &  (v7_aff_2(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))))) ) )  =>  ~ ( (! [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 <=>  ( (r2_tarski(F, D) & F=G)  |  ( ~ (r2_tarski(F, D))  &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (? [I] :  (m1_subset_1(I, u1_struct_0(A)) &  (r2_tarski(H, D) &  (r2_tarski(I, D) &  (r2_analoaf(A, H, B, I, F) &  (r2_analoaf(A, H, C, I, G) & r2_aff_1(A, F, G, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(l26_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, k1_zfmisc_1(u1_struct_0(A))) =>  (r2_aff_1(A, B, C, D) =>  (r2_tarski(B, D) |  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ~ ( (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( ~ ( (r2_tarski(E, D) & E=F) )  &  ~ ( ( ~ (r2_tarski(E, D))  &  (? [G] :  (m1_subset_1(G, u1_struct_0(A)) &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (r2_tarski(G, D) &  (r2_tarski(H, D) &  (r2_analoaf(A, G, B, H, E) &  (r2_analoaf(A, G, C, H, F) & r2_aff_1(A, E, F, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l27_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, k1_zfmisc_1(u1_struct_0(A))) =>  (r2_aff_1(A, B, C, D) =>  (r2_tarski(B, D) |  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ~ ( (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ( ~ ( (r2_tarski(F, D) & F=E) )  &  ~ ( ( ~ (r2_tarski(F, D))  &  (? [G] :  (m1_subset_1(G, u1_struct_0(A)) &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (r2_tarski(G, D) &  (r2_tarski(H, D) &  (r2_analoaf(A, G, B, H, F) &  (r2_analoaf(A, G, C, H, E) & r2_aff_1(A, F, E, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l30_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)) =>  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  (! [J] :  (m1_subset_1(J, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, k1_zfmisc_1(u1_struct_0(A))) =>  ( (r2_aff_1(A, B, C, K) &  (v7_aff_2(A) &  (r2_tarski(D, K) &  (r2_tarski(E, K) &  (r2_analoaf(A, D, B, E, I) &  (r2_analoaf(A, D, C, E, J) &  (r2_aff_1(A, I, J, K) &  (r2_tarski(F, K) &  (r2_tarski(G, K) &  (r2_analoaf(A, F, B, G, I) &  (r2_aff_1(A, I, H, K) & r2_analoaf(A, F, C, G, H)) ) ) ) ) ) ) ) ) ) )  =>  (r2_tarski(B, K) |  (r2_tarski(I, K) | H=J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l31_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, k1_zfmisc_1(u1_struct_0(A))) =>  ( (r2_aff_1(A, B, C, G) & v7_aff_2(A))  =>  (r2_tarski(B, G) |  ( ( ~ ( (r2_tarski(E, G) & E=F) )  &  ~ ( ( ~ (r2_tarski(E, G))  &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (? [I] :  (m1_subset_1(I, u1_struct_0(A)) &  (r2_tarski(H, G) &  (r2_tarski(I, G) &  (r2_analoaf(A, H, B, I, E) &  (r2_analoaf(A, H, C, I, F) & r2_aff_1(A, E, F, G)) ) ) ) ) ) ) ) ) ) )  |  ( ( ~ ( (r2_tarski(D, G) & D=F) )  &  ~ ( ( ~ (r2_tarski(D, G))  &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (? [I] :  (m1_subset_1(I, u1_struct_0(A)) &  (r2_tarski(H, G) &  (r2_tarski(I, G) &  (r2_analoaf(A, H, B, I, D) &  (r2_analoaf(A, H, C, I, F) & r2_aff_1(A, D, F, G)) ) ) ) ) ) ) ) ) ) )  | E=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(s1_transgeo__e8_29__homothet, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) & 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)) &  ( (r2_tarski(E, D) & E=F)  |  ( ~ (r2_tarski(E, D))  &  (? [G] :  (m1_subset_1(G, u1_struct_0(A)) &  (? [H] :  (m1_subset_1(H, u1_struct_0(A)) &  (r2_tarski(G, D) &  (r2_tarski(H, D) &  (r2_analoaf(A, G, B, H, E) &  (r2_analoaf(A, G, C, H, F) & r2_aff_1(A, E, F, D)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (? [F] :  (m1_subset_1(F, u1_struct_0(A)) &  ( (r2_tarski(F, D) & F=E)  |  ( ~ (r2_tarski(F, D))  &  (? [I] :  (m1_subset_1(I, u1_struct_0(A)) &  (? [J] :  (m1_subset_1(J, u1_struct_0(A)) &  (r2_tarski(I, D) &  (r2_tarski(J, D) &  (r2_analoaf(A, I, B, J, F) &  (r2_analoaf(A, I, C, J, E) & r2_aff_1(A, F, E, D)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  ( ( ( (r2_tarski(E, D) & E=F)  |  ( ~ (r2_tarski(E, D))  &  (? [L] :  (m1_subset_1(L, u1_struct_0(A)) &  (? [M] :  (m1_subset_1(M, u1_struct_0(A)) &  (r2_tarski(L, D) &  (r2_tarski(M, D) &  (r2_analoaf(A, L, B, M, E) &  (r2_analoaf(A, L, C, M, F) & r2_aff_1(A, E, F, D)) ) ) ) ) ) ) ) ) )  &  ( (r2_tarski(K, D) & K=F)  |  ( ~ (r2_tarski(K, D))  &  (? [N] :  (m1_subset_1(N, u1_struct_0(A)) &  (? [O] :  (m1_subset_1(O, u1_struct_0(A)) &  (r2_tarski(N, D) &  (r2_tarski(O, D) &  (r2_analoaf(A, N, B, O, K) &  (r2_analoaf(A, N, C, O, F) & r2_aff_1(A, K, F, D)) ) ) ) ) ) ) ) ) ) )  => E=K) ) ) ) ) ) )  &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  ( ( ( (r2_tarski(E, D) & E=F)  |  ( ~ (r2_tarski(E, D))  &  (? [P] :  (m1_subset_1(P, u1_struct_0(A)) &  (? [Q] :  (m1_subset_1(Q, u1_struct_0(A)) &  (r2_tarski(P, D) &  (r2_tarski(Q, D) &  (r2_analoaf(A, P, B, Q, E) &  (r2_analoaf(A, P, C, Q, F) & r2_aff_1(A, E, F, D)) ) ) ) ) ) ) ) ) )  &  ( (r2_tarski(E, D) & E=K)  |  ( ~ (r2_tarski(E, D))  &  (? [R] :  (m1_subset_1(R, u1_struct_0(A)) &  (? [S] :  (m1_subset_1(S, u1_struct_0(A)) &  (r2_tarski(R, D) &  (r2_tarski(S, D) &  (r2_analoaf(A, R, B, S, E) &  (r2_analoaf(A, R, C, S, K) & r2_aff_1(A, E, K, D)) ) ) ) ) ) ) ) ) ) )  => F=K) ) ) ) ) ) ) ) ) )  =>  (? [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))))) ) )  &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [K] :  (m1_subset_1(K, u1_struct_0(A)) =>  (k3_funct_2(u1_struct_0(A), u1_struct_0(A), E, F)=K <=>  ( (r2_tarski(F, D) & F=K)  |  ( ~ (r2_tarski(F, D))  &  (? [T] :  (m1_subset_1(T, u1_struct_0(A)) &  (? [U] :  (m1_subset_1(U, u1_struct_0(A)) &  (r2_tarski(T, D) &  (r2_tarski(U, D) &  (r2_analoaf(A, T, B, U, F) &  (r2_analoaf(A, T, C, U, K) & r2_aff_1(A, F, K, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_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)) ) ) ) ) ).
