% Mizar problem: t12_bvfunc_4,bvfunc_4,189,5 
fof(t12_bvfunc_4, 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)))) )  =>  (! [D] :  ( (v1_funct_1(D) &  (v1_funct_2(D, A, k5_margrel1) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) )  =>  (! [E] :  ( (v1_funct_1(E) &  (v1_funct_2(E, A, k5_margrel1) & m1_subset_1(E, 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, k10_bvfunc_1(A, D, E), k12_bvfunc_1(A)))  => r2_funct_2(A, k5_margrel1, k10_bvfunc_1(A, k2_bvfunc_1(A, B, D), k2_bvfunc_1(A, C, E)), k12_bvfunc_1(A))) ) ) ) ) ) ) ) ) ) ) ).
fof(cc1_margrel1, axiom,  (! [A] :  (v1_xboole_0(A) => v2_card_3(A)) ) ).
fof(cc1_xboolean, axiom,  (! [A] :  (v1_xboolean(A) => v7_ordinal1(A)) ) ).
fof(cc2_margrel1, axiom,  (! [A] :  (m1_subset_1(A, k5_margrel1) => v1_xboolean(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(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_k13_margrel1, 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)) ) )  => k13_margrel1(A, B)=k13_margrel1(B, A)) ) ).
fof(commutativity_k2_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)))) ) ) )  => k2_bvfunc_1(A, B, C)=k2_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_k13_margrel1, 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(k13_margrel1(A, B)) &  (v1_funct_1(k13_margrel1(A, B)) & v1_margrel1(k13_margrel1(A, B))) ) ) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_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(k2_bvfunc_1(A, B, C)) &  (v1_funct_2(k2_bvfunc_1(A, B, C), A, k5_margrel1) & m1_subset_1(k2_bvfunc_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(A, k5_margrel1)))) ) ) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k5_margrel1, axiom, $true).
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_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc2_margrel1, axiom,  ~ (v1_xboole_0(k5_margrel1)) ).
fof(idempotence_k13_margrel1, 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)) ) )  => k13_margrel1(A, A)=A) ) ).
fof(idempotence_k2_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)))) ) ) )  => k2_bvfunc_1(A, B, B)=B) ) ).
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(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_k2_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)))) ) ) )  => k2_bvfunc_1(A, B, C)=k13_margrel1(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(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(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)) ) ) ) ) ) ) ).
