% Mizar problem: t21_parsp_2,parsp_2,933,5 
fof(t21_parsp_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_parsp_1(A) &  (v1_parsp_2(A) & l1_parsp_1(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_parsp_2(A, B, C, D) & r1_parsp_1(A, B, C, D, E))  =>  (B=C | r1_parsp_1(A, B, D, C, E)) ) ) ) ) ) ) ) ) ) ) ) ).
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(d12_parsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_parsp_1(A))  =>  (v2_parsp_1(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)) =>  (r1_parsp_1(A, B, C, C, B) &  (r1_parsp_1(A, B, C, D, D) &  ( ~ ( (r1_parsp_1(A, B, C, F, G) &  (r1_parsp_1(A, B, C, H, I) &  ( ~ (r1_parsp_1(A, F, G, H, I))  &  ~ (B=C) ) ) ) )  &  ( (r1_parsp_1(A, B, C, B, D) => r1_parsp_1(A, C, B, C, D))  &  (? [J] :  (m1_subset_1(J, u1_struct_0(A)) &  (r1_parsp_1(A, B, C, D, J) & r1_parsp_1(A, B, D, C, J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_parsp_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_parsp_1(A) &  (v1_parsp_2(A) & l1_parsp_1(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_parsp_2(A, B, C, D) <=> r1_parsp_1(A, B, C, B, D)) ) ) ) ) ) ) ) ) ).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_l1_parsp_1, axiom,  (! [A] :  (l1_parsp_1(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_parsp_1, axiom,  (? [A] : l1_parsp_1(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(rc2_parsp_1, axiom,  (? [A] :  (l1_parsp_1(A) &  ~ (v2_struct_0(A)) ) ) ).
fof(t24_parsp_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_parsp_1(A) & l1_parsp_1(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_parsp_1(A, B, C, B, D) =>  (r1_parsp_1(A, B, D, B, C) &  (r1_parsp_1(A, C, B, B, D) &  (r1_parsp_1(A, B, C, D, B) &  (r1_parsp_1(A, B, D, C, B) &  (r1_parsp_1(A, C, B, D, B) &  (r1_parsp_1(A, D, B, B, C) &  (r1_parsp_1(A, D, B, C, B) &  (r1_parsp_1(A, C, B, C, D) &  (r1_parsp_1(A, B, C, C, D) &  (r1_parsp_1(A, C, B, D, C) &  (r1_parsp_1(A, C, D, C, B) &  (r1_parsp_1(A, B, C, D, C) &  (r1_parsp_1(A, D, C, C, B) &  (r1_parsp_1(A, C, D, B, C) &  (r1_parsp_1(A, D, C, B, C) &  (r1_parsp_1(A, D, B, D, C) &  (r1_parsp_1(A, B, D, D, C) &  (r1_parsp_1(A, D, B, C, D) &  (r1_parsp_1(A, B, D, C, D) &  (r1_parsp_1(A, D, C, D, B) &  (r1_parsp_1(A, C, D, D, B) &  (r1_parsp_1(A, D, C, B, D) & r1_parsp_1(A, C, D, B, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
