% Mizar problem: t30_bvfunc25,bvfunc25,513,5 
fof(t30_bvfunc25, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  ( (r2_funct_2(A, k5_margrel1, k9_bvfunc_1(A, B, C), k12_bvfunc_1(A)) & r2_funct_2(A, k5_margrel1, k9_bvfunc_1(A, C, B), k12_bvfunc_1(A)))  <=> r2_funct_2(A, k5_margrel1, B, C)) ) ) ) ) ) ) ).
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_2, axiom,  (! [A, B] :  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_partfun1(C, A) => v1_funct_2(C, A, 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_xboolean, axiom,  (! [A] :  (v1_xboolean(A) => v7_ordinal1(A)) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc2_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => v1_xboolean(A)) ) ).
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(cc3_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ) ) ).
fof(cc3_margrel1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1))) =>  ( (v1_funct_1(B) & v1_funct_2(B, A, k5_margrel1))  =>  (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & v1_margrel1(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(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) =>  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ) ).
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(cc5_funct_2, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A, A), A))) =>  (v1_funct_2(B, k2_zfmisc_1(A, A), A) => v1_partfun1(B, k2_zfmisc_1(A, A))) ) ) ) ).
fof(cc9_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) =>  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
fof(commutativity_k10_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k10_bvfunc_1(A, B, C)=k10_bvfunc_1(A, C, B)) ) ).
fof(commutativity_k8_bvfunc_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_margrel1(B)) ) )  => k8_bvfunc_1(A, B)=k8_bvfunc_1(B, A)) ) ).
fof(dt_k10_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  =>  (v1_funct_1(k10_bvfunc_1(A, B, C)) &  (v1_funct_2(k10_bvfunc_1(A, B, C), A, k5_margrel1) & m1_subset_1(k10_bvfunc_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ) ).
fof(dt_k12_bvfunc_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (v1_funct_1(k12_bvfunc_1(A)) &  (v1_funct_2(k12_bvfunc_1(A), A, k5_margrel1) & m1_subset_1(k12_bvfunc_1(A), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k5_margrel1, axiom, $true).
fof(dt_k7_bvfunc_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_margrel1(B)) ) )  =>  (v1_relat_1(k7_bvfunc_1(A, B)) & v1_funct_1(k7_bvfunc_1(A, B))) ) ) ).
fof(dt_k8_bvfunc_1, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) )  &  (v1_relat_1(B) &  (v1_funct_1(B) & v1_margrel1(B)) ) )  =>  (v1_relat_1(k8_bvfunc_1(A, B)) & v1_funct_1(k8_bvfunc_1(A, B))) ) ) ).
fof(dt_k9_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  =>  (v1_funct_1(k9_bvfunc_1(A, B, C)) &  (v1_funct_2(k9_bvfunc_1(A, B, C), A, k5_margrel1) & m1_subset_1(k9_bvfunc_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
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(fc2_margrel1, axiom,  ~ (v1_xboole_0(k5_margrel1)) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ) ).
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_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xboolean, axiom,  (? [A] : v1_xboolean(A)) ).
fof(rc2_margrel1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v1_margrel1(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rd1_bvfunc25, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k9_bvfunc_1(A, k9_bvfunc_1(A, B, C), k9_bvfunc_1(A, C, B))=k9_bvfunc_1(A, C, B)) ) ).
fof(redefinition_k10_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k10_bvfunc_1(A, B, C)=k8_bvfunc_1(B, C)) ) ).
fof(redefinition_k9_bvfunc_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  &  (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) )  => k9_bvfunc_1(A, B, C)=k7_bvfunc_1(B, C)) ) ).
fof(redefinition_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) <=> C=D) ) ) ).
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_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  => r2_funct_2(A, B, C, C)) ) ).
fof(symmetry_r2_funct_2, axiom,  (! [A, B, C, D] :  ( ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  &  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) )  =>  (r2_funct_2(A, B, C, D) => r2_funct_2(A, B, D, C)) ) ) ).
fof(t10_bvfunc_4, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  (r2_funct_2(A, k5_margrel1, k10_bvfunc_1(A, B, C), k12_bvfunc_1(A)) <=>  (r2_funct_2(A, k5_margrel1, k9_bvfunc_1(A, B, C), k12_bvfunc_1(A)) & r2_funct_2(A, k5_margrel1, k9_bvfunc_1(A, C, B), k12_bvfunc_1(A))) ) ) ) ) ) ) ) ).
fof(t17_bvfunc_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( (v1_funct_1(B) &  (v1_funct_2(B, A, k5_margrel1) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, A, k5_margrel1) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  (r2_funct_2(A, k5_margrel1, k10_bvfunc_1(A, B, C), k12_bvfunc_1(A)) <=> r2_funct_2(A, k5_margrel1, B, C)) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
