% Mizar problem: t1_bvfunc_2,bvfunc_2,69,5 
fof(t1_bvfunc_2, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_partit1(A))) =>  (! [C] :  (m1_subset_1(C, A) =>  (? [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) &  (r2_tarski(C, D) &  (? [E] :  ( (v1_relat_1(E) & v1_funct_1(E))  &  (? [F] :  (m1_subset_1(F, k1_zfmisc_1(k1_zfmisc_1(A))) &  (k9_xtuple_0(E)=B &  (k10_xtuple_0(E)=F &  ( (! [G] :  (r2_tarski(G, B) => r2_tarski(k1_funct_1(E, G), G)) )  &  (D=k8_setfam_1(A, F) &  ~ (D=k1_xboole_0) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_margrel1, axiom,  (! [A] :  (v1_xboole_0(A) => v2_card_3(A)) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) ) ) ).
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_relset_1, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v4_relat_1(C, A) & v5_relat_1(C, 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_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_xboole_0(C)) ) ) ) ).
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_relset_1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(B, A))) => v1_xboole_0(C)) ) ) ) ).
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(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d1_setfam_1, axiom,  (! [A] :  (! [B] :  ( ( ~ (A=k1_xboole_0)  =>  (B=k1_setfam_1(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (! [D] :  (r2_tarski(D, A) => r2_hidden(C, D)) ) ) ) ) )  &  (A=k1_xboole_0 =>  (B=k1_setfam_1(A) <=> B=k1_xboole_0) ) ) ) ) ).
fof(d3_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (B=k10_xtuple_0(A) <=>  (! [C] :  (r2_hidden(C, B) <=>  (? [D] :  (r2_hidden(D, k9_xtuple_0(A)) & C=k1_funct_1(A, D)) ) ) ) ) ) ) ) ).
fof(d3_partit1, axiom,  (! [A] :  (! [B] :  (B=k1_partit1(A) <=>  (! [C] :  (r2_tarski(C, B) <=> m1_eqrel_1(C, A)) ) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(d6_eqrel_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, A) =>  (! [C] :  (m1_eqrel_1(C, A) =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  (D=k12_eqrel_1(A, B, C) <=>  (r2_tarski(B, D) & r2_tarski(D, C)) ) ) ) ) ) ) ) ) ) ).
fof(d6_partfun1, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (! [C] :  (r2_hidden(C, k9_xtuple_0(B)) => k7_partfun1(A, B, C)=k1_funct_1(B, C)) ) ) ) ) ).
fof(d9_setfam_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) =>  ( ( ~ (B=k1_xboole_0)  => k8_setfam_1(A, B)=k6_setfam_1(A, B))  &  (B=k1_xboole_0 => k8_setfam_1(A, B)=A) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k12_eqrel_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_eqrel_1(C, A)) )  => m1_subset_1(k12_eqrel_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k15_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_eqrel_1(C, A)) )  => m1_bvfunc_1(k15_bvfunc_1(A, B, C), A, C)) ) ).
fof(dt_k1_bvfunc_2, axiom,  (! [A] :  (v1_eqrel_1(k1_bvfunc_2(A), A) & m1_subset_1(k1_bvfunc_2(A), k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A))))) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_partit1, axiom, $true).
fof(dt_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => m1_subset_1(k1_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k1_setfam_1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => m1_subset_1(k2_relset_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k6_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k6_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k7_partfun1, axiom,  (! [A, B, C] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  => m1_subset_1(k7_partfun1(A, B, C), A)) ) ).
fof(dt_k8_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k8_setfam_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k9_setfam_1, axiom,  (! [A] : m1_subset_1(k9_setfam_1(A), k1_zfmisc_1(k1_zfmisc_1(A)))) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(dt_m1_bvfunc_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  =>  (! [C] :  (m1_bvfunc_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(A))) ) ) ) ).
fof(dt_m1_bvfunc_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_eqrel_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A))))) )  =>  (! [C] :  (m1_bvfunc_2(C, A, B) => m1_eqrel_1(C, 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(existence_m1_bvfunc_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  =>  (? [C] : m1_bvfunc_1(C, A, B)) ) ) ).
fof(existence_m1_bvfunc_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_eqrel_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A))))) )  =>  (? [C] : m1_bvfunc_2(C, A, B)) ) ) ).
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(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_partit1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_partit1(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(fc8_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, B), C))) => v1_relat_1(k9_xtuple_0(D))) ) ).
fof(fc9_relset_1, axiom,  (! [A, B, C, D] :  (m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k2_zfmisc_1(B, C)))) => v1_relat_1(k10_xtuple_0(D))) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ) ).
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_eqrel_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) & v1_eqrel_1(B, 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(rc4_eqrel_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) &  ( ~ (v1_xboole_0(B))  & v1_eqrel_1(B, A)) ) ) ) ).
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(redefinition_k15_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, A) & m1_eqrel_1(C, A)) )  => k15_bvfunc_1(A, B, C)=k12_eqrel_1(A, B, C)) ) ).
fof(redefinition_k1_bvfunc_2, axiom,  (! [A] : k1_bvfunc_2(A)=k1_partit1(A)) ).
fof(redefinition_k1_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  => k1_relset_1(A, B)=k9_xtuple_0(B)) ) ).
fof(redefinition_k2_relset_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  => k2_relset_1(A, B)=k10_xtuple_0(B)) ) ).
fof(redefinition_k6_setfam_1, axiom,  (! [A, B] :  (m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(A))) => k6_setfam_1(A, B)=k1_setfam_1(B)) ) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(A)) ).
fof(redefinition_m1_bvfunc_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_eqrel_1(B, A))  =>  (! [C] :  (m1_bvfunc_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_m1_bvfunc_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(B))  &  (v1_eqrel_1(B, A) & m1_subset_1(B, k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A))))) )  =>  (! [C] :  (m1_bvfunc_2(C, A, B) <=> m1_subset_1(C, 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(s2_partfun2__e1_3__bvfunc_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(B, k1_zfmisc_1(k1_partit1(A))) & m1_subset_1(C, A)) )  =>  (? [D] :  ( (v1_funct_1(D) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(k1_bvfunc_2(A), k9_setfam_1(A)))))  &  ( (! [E] :  (m1_subset_1(E, k1_bvfunc_2(A)) =>  (r2_tarski(E, k1_relset_1(k1_bvfunc_2(A), D)) <=> r2_tarski(E, B)) ) )  &  (! [E] :  (m1_subset_1(E, k1_bvfunc_2(A)) =>  (r2_tarski(E, k1_relset_1(k1_bvfunc_2(A), D)) => k7_partfun1(k9_setfam_1(A), D, E)=k15_bvfunc_1(A, C, E)) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
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(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
