% Mizar problem: t22_pasch,pasch,1643,5 
fof(t22_pasch, conjecture,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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, E, C, D) & r2_analoaf(A, B, C, E, D)) ) ) ) ) ) ) ) ) ) ) ).
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(d3_diraf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(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_diraf(A, B, C, D) <=> r2_analoaf(A, B, C, C, D)) ) ) ) ) ) ) ) ) ).
fof(d5_analoaf, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_analoaf(A))  =>  (v2_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)) =>  (r2_analoaf(A, B, C, D, D) &  ( (r2_analoaf(A, B, C, C, B) => B=C)  &  ( ( (r2_analoaf(A, B, C, F, G) & r2_analoaf(A, B, C, H, I))  =>  (B=C | r2_analoaf(A, F, G, H, I)) )  &  ( (r2_analoaf(A, B, C, D, E) => r2_analoaf(A, C, B, E, D))  &  ( (r2_analoaf(A, B, C, C, D) => r2_analoaf(A, B, C, B, D))  &  ~ ( (r2_analoaf(A, B, C, B, D) &  ( ~ (r2_analoaf(A, B, C, C, D))  &  ~ (r2_analoaf(A, B, D, D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  &  ( (? [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)) ) ) ) ) ) ) ) ) )  &  ( (! [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, D, C, E) &  ~ (C=E) ) ) ) ) ) ) ) ) ) )  &  (! [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)) =>  ~ ( ( ~ (B=D)  &  (r2_analoaf(A, D, B, B, E) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( (r2_analoaf(A, C, B, B, F) & r2_analoaf(A, C, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t13_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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_diraf(A, B, C, D) &  ~ (C=D) ) ) ) ) ) ) ) ) ) ).
fof(t19_pasch, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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_diraf(A, E, D, C) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( (r1_diraf(A, E, F, B) & r2_analoaf(A, C, B, D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t20_pasch, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  ~ ( ( ~ (E=C)  &  (r1_diraf(A, E, C, D) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( (r1_diraf(A, E, B, F) & r2_analoaf(A, C, B, D, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t21_pasch, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  ~ ( ( ~ (r3_diraf(A, E, B, C))  &  (r1_diraf(A, E, D, C) &  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  ~ ( (r1_diraf(A, E, F, B) & r2_analoaf(A, B, C, F, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t28_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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_diraf(A, B, C, D) => r3_diraf(A, B, C, D)) ) ) ) ) ) ) ) ) ).
fof(t29_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  ~ ( (r3_diraf(A, B, C, D) &  ( ~ (r1_diraf(A, B, C, D))  &  ( ~ (r1_diraf(A, C, B, D))  &  ~ (r1_diraf(A, B, D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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, C, B, E, D) &  (r2_analoaf(A, D, E, B, C) & r2_analoaf(A, E, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t30_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  (r3_diraf(A, B, C, D) =>  (r3_diraf(A, B, D, C) &  (r3_diraf(A, C, B, D) &  (r3_diraf(A, C, D, B) &  (r3_diraf(A, D, B, C) & r3_diraf(A, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t31_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r3_diraf(A, B, B, C) &  (r3_diraf(A, B, C, C) & r3_diraf(A, B, C, B)) ) ) ) ) ) ) ) ).
fof(t32_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  ( (r3_diraf(A, B, C, D) &  (r3_diraf(A, B, C, E) & r3_diraf(A, B, C, F)) )  =>  (B=C | r3_diraf(A, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  ( (r2_analoaf(A, B, C, D, E) & r2_analoaf(A, D, E, F, G))  =>  (D=E | r2_analoaf(A, B, C, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t4_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  (r2_analoaf(A, B, B, C, D) & r2_analoaf(A, C, D, B, B)) ) ) ) ) ) ) ) ) ).
fof(t6_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  (r2_analoaf(A, B, C, B, D) <=>  (r2_analoaf(A, B, C, C, D) | r2_analoaf(A, B, D, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(t7_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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)) =>  (r2_analoaf(A, B, C, B, D) <=>  (r1_diraf(A, B, C, D) | r1_diraf(A, B, D, C)) ) ) ) ) ) ) ) ) ) ).
fof(t8_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(A) & l1_analoaf(A)) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_diraf(A, B, C, B) => B=C) ) ) ) ) ) ) ).
fof(t9_diraf, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  &  (v2_analoaf(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_diraf(A, B, C, D) => r1_diraf(A, D, C, B)) ) ) ) ) ) ) ) ) ).
