% Mizar problem: t4_pasch,pasch,239,5 
fof(t4_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)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  ( (r3_diraf(A, G, C, D) &  (r3_diraf(A, G, B, E) &  (r3_diraf(A, G, B, F) &  (r2_diraf(A, B, C, D, E) & r2_diraf(A, B, C, D, F)) ) ) )  =>  (r3_diraf(A, G, B, C) | E=F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(d5_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)) =>  (r3_diraf(A, B, C, D) <=> r2_diraf(A, B, C, B, D)) ) ) ) ) ) ) ) ) ).
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(t22_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_diraf(A, B, C, D, E) =>  (r2_diraf(A, B, C, E, D) &  (r2_diraf(A, C, B, D, E) &  (r2_diraf(A, C, B, E, D) &  (r2_diraf(A, D, E, B, C) &  (r2_diraf(A, D, E, C, B) &  (r2_diraf(A, E, D, B, C) & r2_diraf(A, E, D, C, B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_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)) =>  ~ ( ( ~ (B=C)  &  ( ~ ( ( ~ ( (r2_diraf(A, B, C, D, E) & r2_diraf(A, B, C, F, G)) )  &  ( ~ ( (r2_diraf(A, B, C, D, E) & r2_diraf(A, F, G, B, C)) )  &  ( ~ ( (r2_diraf(A, D, E, B, C) & r2_diraf(A, F, G, B, C)) )  &  ~ ( (r2_diraf(A, D, E, B, C) & r2_diraf(A, B, C, F, G)) ) ) ) ) )  &  ~ (r2_diraf(A, D, E, F, G)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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(t33_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)) =>  ( (r3_diraf(A, B, C, D) & r2_diraf(A, B, C, D, E))  =>  (B=C | r3_diraf(A, B, C, E)) ) ) ) ) ) ) ) ) ) ) ) ).
