% Mizar problem: t54_aff_4,aff_4,2113,5 
fof(t54_aff_4, conjecture,  (! [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)) =>  ~ ( ( ~ (r1_aff_1(A, B, C, D))  &  ( ~ (E=F)  &  (r2_analoaf(A, B, C, E, F) &  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( (r2_analoaf(A, B, D, E, G) & r2_analoaf(A, C, D, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(commutativity_k2_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k2_aff_1(A, B, C)=k2_aff_1(A, C, B)) ) ).
fof(d3_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))) =>  (v1_aff_1(B, A) <=>  (? [C] :  (m1_subset_1(C, u1_struct_0(A)) &  (? [D] :  (m1_subset_1(D, u1_struct_0(A)) &  ( ~ (C=D)  & B=k2_aff_1(A, C, D)) ) ) ) ) ) ) ) ) ) ).
fof(d3_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_aff_1(C, A) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  (D=k2_aff_4(A, B, C) <=>  (r2_tarski(B, D) & r5_aff_1(A, C, D)) ) ) ) ) ) ) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k1_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k1_aff_1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k2_aff_1(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_aff_4, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) )  => m1_subset_1(k2_aff_4(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
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(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
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(l70_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( ( ~ (r1_aff_1(A, B, C, D))  &  (r2_analoaf(A, B, C, E, F) &  (r2_tarski(B, G) &  (r2_tarski(C, G) &  (r2_tarski(D, G) &  (v1_aff_4(G, A) &  (r2_tarski(E, G) &  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ~ ( (r2_analoaf(A, B, D, E, H) & r2_analoaf(A, C, D, F, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(l9_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  (! [F] :  (m1_subset_1(F, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (r5_aff_1(A, E, F) &  (r2_tarski(B, E) &  (r2_tarski(D, E) &  (r2_tarski(C, F) &  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( (r2_tarski(G, F) & r2_analoaf(A, B, C, D, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_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(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
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_k2_aff_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) & l1_analoaf(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => k2_aff_1(A, B, C)=k1_aff_1(A, B, C)) ) ).
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(t15_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)) =>  (r2_tarski(B, k2_aff_1(A, B, C)) & r2_tarski(C, k2_aff_1(A, B, C))) ) ) ) ) ) ) ).
fof(t18_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, k1_zfmisc_1(u1_struct_0(A))) =>  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (v1_aff_1(D, A) &  (v1_aff_1(E, A) &  (r2_tarski(B, D) &  (r2_tarski(C, D) &  (r2_tarski(B, E) &  (r2_tarski(C, E) &  ( ~ (B=C)  &  ~ (D=E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v1_aff_4(D, A) &  (r2_tarski(B, D) & r2_tarski(C, D)) )  =>  (B=C | r1_tarski(k2_aff_1(A, B, C), D)) ) ) ) ) ) ) ) ) ) ).
fof(t1_aff_4, 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)) =>  ~ ( ( (r1_aff_1(A, E, B, D) | r1_aff_1(A, E, D, B))  &  ( ~ (E=B)  &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( (r1_aff_1(A, E, C, F) & r2_analoaf(A, B, C, D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t21_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) <=>  (? [E] :  (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) &  (v1_aff_1(E, A) &  (r2_tarski(B, E) &  (r2_tarski(C, E) & r2_tarski(D, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_aff_4, 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))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (v1_aff_4(D, A) &  (v1_aff_1(B, A) &  (v1_aff_1(C, A) &  (r1_tarski(B, D) &  (r1_tarski(C, D) &  ( ~ (r5_aff_1(A, B, C))  &  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ~ ( (r2_tarski(E, B) & r2_tarski(E, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v1_aff_4(E, A) &  (r2_tarski(B, E) &  (r1_tarski(C, E) & r2_tarski(B, D)) ) )  =>  ( ( ~ (r5_aff_1(A, C, D))  &  ~ (r5_aff_1(A, D, C)) )  | r1_tarski(D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_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, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v1_aff_1(E, A) &  (r2_tarski(B, E) &  (r2_tarski(C, E) & r1_aff_1(A, B, C, D)) ) )  =>  (B=C | r2_tarski(D, E)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  (! [F] :  (m1_subset_1(F, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v1_aff_4(E, A) &  (v1_aff_4(F, A) &  (r2_tarski(B, E) &  (r2_tarski(C, E) &  (r2_tarski(D, E) &  (r2_tarski(B, F) &  (r2_tarski(C, F) & r2_tarski(D, F)) ) ) ) ) ) )  =>  (r1_aff_1(A, B, C, D) | E=F) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t27_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_aff_1(C, A) => v1_aff_1(k2_aff_4(A, B, C), A)) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t37_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) <=>  (? [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)) &  ( ~ (D=E)  &  ( ~ (F=G)  &  (r2_analoaf(A, D, E, F, G) &  (B=k2_aff_1(A, D, E) & C=k2_aff_1(A, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_aff_4, 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, k1_zfmisc_1(u1_struct_0(A))) &  (r2_tarski(B, E) &  (r2_tarski(C, E) &  (r2_tarski(D, E) & v1_aff_4(E, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_aff_4, 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))) =>  ~ ( (r5_aff_1(A, B, C) &  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))) =>  ~ ( (r1_tarski(B, D) &  (r1_tarski(C, D) & v1_aff_4(D, A)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t49_aff_4, 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)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  (! [I] :  (m1_subset_1(I, k1_zfmisc_1(u1_struct_0(A))) =>  (! [J] :  (m1_subset_1(J, k1_zfmisc_1(u1_struct_0(A))) =>  (! [K] :  (m1_subset_1(K, k1_zfmisc_1(u1_struct_0(A))) =>  ( (r2_tarski(H, I) &  (r2_tarski(H, K) &  (r2_tarski(H, J) &  (r2_tarski(B, I) &  (r2_tarski(E, I) &  (r2_tarski(C, K) &  (r2_tarski(F, K) &  (r2_tarski(D, J) &  (r2_tarski(G, J) &  (v1_aff_1(I, A) &  (v1_aff_1(K, A) &  (v1_aff_1(J, A) &  (r2_analoaf(A, B, C, E, F) & r2_analoaf(A, B, D, E, G)) ) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  |  (H=B |  (H=C |  (H=D |  (I=K |  (I=J | r2_analoaf(A, C, D, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t51_aff_4, 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)) =>  (! [H] :  (m1_subset_1(H, k1_zfmisc_1(u1_struct_0(A))) =>  (! [I] :  (m1_subset_1(I, k1_zfmisc_1(u1_struct_0(A))) =>  (! [J] :  (m1_subset_1(J, k1_zfmisc_1(u1_struct_0(A))) =>  ( (r5_aff_1(A, H, J) &  (r5_aff_1(A, H, I) &  (r2_tarski(B, H) &  (r2_tarski(E, H) &  (r2_tarski(C, J) &  (r2_tarski(F, J) &  (r2_tarski(D, I) &  (r2_tarski(G, I) &  (v1_aff_1(H, A) &  (v1_aff_1(J, A) &  (v1_aff_1(I, A) &  (r2_analoaf(A, B, C, E, F) & r2_analoaf(A, B, D, E, G)) ) ) ) ) ) ) ) ) ) ) )  =>  ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  |  (H=J |  (H=I | r2_analoaf(A, C, D, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t53_aff_4, 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)) =>  ~ ( ( ( ~ (v7_struct_0(A))  &  (v1_diraf(A) &  (v2_diraf(A) & l1_analoaf(A)) ) )  &  ( ~ (r1_aff_1(A, B, C, D))  &  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ~ ( (r2_analoaf(A, B, D, E, G) & r2_analoaf(A, C, D, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t57_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, k1_zfmisc_1(u1_struct_0(A))) =>  ( (v1_aff_1(D, A) &  (r2_tarski(B, D) & r2_tarski(C, D)) )  =>  (B=C | D=k2_aff_1(A, B, 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_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)) ) ) ) ) ).
