% Mizar problem: t16_taxonom2,taxonom2,963,5 
fof(t16_taxonom2, conjecture,  (! [A] :  (! [B] :  ( (v3_abian(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  (v5_taxonom2(B, A) & m1_taxonom2(B, A)) )  =>  (v6_taxonom2(B, A) =>  (r2_tarski(k1_xboole_0, B) |  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(A)) =>  (! [D] :  ( (v4_taxonom2(D) & m1_subset_1(D, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( (r2_tarski(C, D) &  (r1_tarski(D, B) &  (! [E] :  ( (v4_taxonom2(E) & m1_subset_1(E, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( (r2_tarski(C, E) &  (r1_tarski(E, B) & r1_tarski(D, E)) )  => D=E) ) ) ) )  => m1_eqrel_1(D, A)) ) ) ) ) ) ) ) ) ) ).
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_eqrel_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_eqrel_1(B, A) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc2_eqrel_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_eqrel_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
fof(cc3_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_eqrel_1(B, A) => v1_setfam_1(B)) ) ) ).
fof(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_eqrel_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_eqrel_1(B, A) => v1_xboole_0(B)) ) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d1_xboole_0, axiom,  (! [A] :  (v1_xboole_0(A) <=>  (! [B] :  ~ (r2_hidden(B, A)) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d4_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (m1_eqrel_1(B, A) <=>  (k5_setfam_1(A, B)=A &  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(A)) =>  (r2_tarski(C, B) =>  ( ~ (C=k1_xboole_0)  &  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  ~ ( (r2_tarski(D, B) &  ( ~ (C=D)  &  ~ (r1_xboole_0(C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d4_tarski, axiom,  (! [A] :  (! [B] :  (B=k3_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(C, D) & r2_hidden(D, A)) ) ) ) ) ) ) ).
fof(d4_taxonom2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (m1_taxonom2(B, A) <=> v3_taxonom2(B)) ) ) ) ).
fof(d5_taxonom2, axiom,  (! [A] :  (v4_taxonom2(A) <=>  (! [B] :  (! [C] :  ( (r2_tarski(B, A) & r2_tarski(C, A))  =>  (B=C | r1_xboole_0(B, C)) ) ) ) ) ) ).
fof(d6_taxonom2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (v5_taxonom2(B, A) <=>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(A)) =>  (r2_tarski(C, B) =>  (! [D] :  (m1_subset_1(D, A) =>  ~ ( ( ~ (r2_tarski(D, C))  &  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(A)) =>  ~ ( (r2_tarski(D, E) &  (r2_tarski(E, B) & r1_xboole_0(C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d8_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) <=>  (! [B] :  (! [C] :  ( (r2_tarski(B, A) & r2_tarski(C, A))  => r3_xboole_0(B, C)) ) ) ) ) ).
fof(d9_xboole_0, axiom,  (! [A] :  (! [B] :  (r3_xboole_0(A, B) <=>  (r1_tarski(A, B) | r1_tarski(B, A)) ) ) ) ).
fof(dt_k1_setfam_1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k3_tarski, axiom, $true).
fof(dt_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_m1_eqrel_1, axiom,  (! [A] :  (! [B] :  (m1_eqrel_1(B, A) => m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m1_taxonom2, axiom,  (! [A] :  (! [B] :  (m1_taxonom2(B, A) => m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A)))) ) ) ).
fof(existence_m1_eqrel_1, axiom,  (! [A] :  (? [B] : m1_eqrel_1(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m1_taxonom2, axiom,  (! [A] :  (? [B] : m1_taxonom2(B, A)) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_taxonom2, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) & v4_taxonom2(B)) ) ) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
fof(rc4_taxonom2, axiom,  (! [A] :  (? [B] :  (m1_taxonom2(B, A) &  (v3_abian(B, k1_zfmisc_1(k1_zfmisc_1(A))) & v5_taxonom2(B, A)) ) ) ) ).
fof(redefinition_k5_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A, B)=k3_tarski(B)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r3_xboole_0, axiom,  (! [A, B] : r3_xboole_0(A, A)) ).
fof(s1_xfamily__e8_29_1_1_1__taxonom2, axiom,  (! [A, B, C] :  ( (v3_abian(B, k1_zfmisc_1(k1_zfmisc_1(A))) &  (v5_taxonom2(B, A) & m1_taxonom2(B, A)) )  =>  (? [D] :  (! [E] :  (r2_tarski(E, D) <=>  (r2_tarski(E, B) & r2_hidden(C, E)) ) ) ) ) ) ).
fof(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(symmetry_r3_xboole_0, axiom,  (! [A, B] :  (r3_xboole_0(A, B) => r3_xboole_0(B, A)) ) ).
fof(t12_taxonom2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (! [C] :  ( (v4_taxonom2(C) & m1_subset_1(C, k1_zfmisc_1(k1_zfmisc_1(A))))  =>  ( (! [D] :  (r2_tarski(D, C) =>  (r1_xboole_0(B, D) &  ~ (A=k1_xboole_0) ) ) )  =>  ( (v4_taxonom2(k2_xboole_0(C, k1_tarski(B))) & m1_subset_1(k2_xboole_0(C, k1_tarski(B)), k1_zfmisc_1(k1_zfmisc_1(A))))  &  ~ ( ( ~ (B=k1_xboole_0)  & k3_tarski(k2_xboole_0(C, k1_tarski(B)))=k5_setfam_1(A, C)) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t1_zfmisc_1, axiom, k1_zfmisc_1(k1_xboole_0)=k1_tarski(k1_xboole_0)).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t33_zfmisc_1, axiom,  (! [A] :  (! [B] :  (r1_tarski(B, k1_tarski(A)) <=>  (B=k1_xboole_0 | B=k1_tarski(A)) ) ) ) ).
fof(t3_setfam_1, axiom,  (! [A] :  (! [B] :  (r2_tarski(B, A) => r1_tarski(k1_setfam_1(A), B)) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t3_xboole_0, axiom,  (! [A] :  (! [B] :  ( ~ ( ( ~ (r1_xboole_0(A, B))  &  (! [C] :  ~ ( (r2_hidden(C, A) & r2_hidden(C, B)) ) ) ) )  &  ~ ( ( (? [C] :  (r2_hidden(C, A) & r2_hidden(C, B)) )  & r1_xboole_0(A, B)) ) ) ) ) ).
fof(t45_eqrel_1, axiom, m1_eqrel_1(k1_xboole_0, k1_xboole_0)).
fof(t4_abian, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  (v3_abian(B, k1_zfmisc_1(k1_zfmisc_1(A))) <=> k5_setfam_1(A, B)=A) ) ) ) ).
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(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_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(A, k2_xboole_0(A, B))) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_xboole_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r1_tarski(A, C) & r1_tarski(B, C))  => r1_tarski(k2_xboole_0(A, B), C)) ) ) ) ).
