% Mizar problem: t9_altcat_3,altcat_3,330,5 
fof(t9_altcat_3, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v11_altcat_1(A) & l2_altcat_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)) =>  ~ ( ( ~ (k1_altcat_1(A, B, C)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, C, D)=k1_xboole_0)  &  (? [E] :  (m1_subset_1(E, k1_altcat_1(A, B, C)) &  (? [F] :  (m1_subset_1(F, k1_altcat_1(A, C, D)) &  (v4_altcat_3(E, A, B, C) &  (v4_altcat_3(F, A, C, D) &  ~ (v4_altcat_3(k5_altcat_1(A, B, C, D, E, F), A, B, 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(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_zfmisc_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_zfmisc_1(A)) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc2_zfmisc_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_setfam_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v2_setfam_1(A)) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (v4_funct_1(A) =>  (! [B] :  (m1_subset_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(d2_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) =>  (v2_altcat_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)) =>  ~ ( ( ~ (k1_altcat_1(A, B, C)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, C, D)=k1_xboole_0)  & k1_altcat_1(A, B, D)=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_altcat_3, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l2_altcat_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, k1_altcat_1(A, B, C)) =>  (v4_altcat_3(D, A, B, C) <=>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  ( ~ (k1_altcat_1(A, E, B)=k1_xboole_0)  =>  (! [F] :  (m1_subset_1(F, k1_altcat_1(A, E, B)) =>  (! [G] :  (m1_subset_1(G, k1_altcat_1(A, E, B)) =>  (k5_altcat_1(A, E, B, C, F, D)=k5_altcat_1(A, E, B, C, G, D) => F=G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_altcat_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k5_altcat_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ( ~ (v2_struct_0(A))  & l2_altcat_1(A))  &  (m1_subset_1(B, u1_struct_0(A)) &  (m1_subset_1(C, u1_struct_0(A)) &  (m1_subset_1(D, u1_struct_0(A)) &  (m1_subset_1(E, k1_altcat_1(A, B, C)) & m1_subset_1(F, k1_altcat_1(A, C, D))) ) ) ) )  => m1_subset_1(k5_altcat_1(A, B, C, D, E, F), k1_altcat_1(A, B, D))) ) ).
fof(dt_l1_altcat_1, axiom,  (! [A] :  (l1_altcat_1(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_l2_altcat_1, axiom,  (! [A] :  (l2_altcat_1(A) => l1_altcat_1(A)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_altcat_1, axiom,  (? [A] : l1_altcat_1(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_l2_altcat_1, axiom,  (? [A] : l2_altcat_1(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_zfmisc_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_setfam_1, axiom,  (? [A] :  ~ (v2_setfam_1(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_zfmisc_1, axiom,  (? [A] :  ~ (v1_zfmisc_1(A)) ) ).
fof(rc3_setfam_1, axiom,  (! [A] :  ( ~ (v2_setfam_1(A))  =>  (? [B] :  (m1_subset_1(B, A) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t21_altcat_1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_altcat_1(A) &  (v11_altcat_1(A) & l2_altcat_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)) =>  ~ ( ( ~ (k1_altcat_1(A, B, C)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, C, D)=k1_xboole_0)  &  ( ~ (k1_altcat_1(A, D, E)=k1_xboole_0)  &  ~ ( (! [F] :  (m1_subset_1(F, k1_altcat_1(A, B, C)) =>  (! [G] :  (m1_subset_1(G, k1_altcat_1(A, C, D)) =>  (! [H] :  (m1_subset_1(H, k1_altcat_1(A, D, E)) => k5_altcat_1(A, B, D, E, k5_altcat_1(A, B, C, D, F, G), H)=k5_altcat_1(A, B, C, E, F, k5_altcat_1(A, C, D, E, G, H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
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)) ) ) ) ) ).
