% Mizar problem: t21_heyting1,heyting1,843,5 
fof(t21_heyting1, conjecture,  (! [A] :  (! [B] :  (m2_subset_1(B, k5_finsub_1(k7_normform(A)), k8_normform(A)) => k10_normform(A, B, k6_heyting1(A, B))=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(cc10_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) => v4_funct_1(C)) ) ) ).
fof(cc1_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_finset_1(A)) ) ).
fof(cc1_finsub_1, axiom,  (! [A] :  (v4_finsub_1(A) =>  (v1_finsub_1(A) & v3_finsub_1(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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(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_finset_1, axiom,  (! [A] :  (v1_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_finset_1(B)) ) ) ) ).
fof(cc2_finsub_1, axiom,  (! [A] :  ( (v1_finsub_1(A) & v3_finsub_1(A))  => v4_finsub_1(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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(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_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) =>  (! [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_funct_2(C, A, B) & v1_finset_1(C)) ) ) ) ) ) ) ).
fof(cc3_finsub_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k5_finsub_1(A)) => v1_finset_1(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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
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_finset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) => v1_finset_1(A)) ) ).
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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(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(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(B, A)) ) ) ) ) ).
fof(cc5_finset_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_zfmisc_1(A)) ) ) ).
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(cc5_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v4_relat_1(C, A)) ) ) ) ).
fof(cc5_subset_1, axiom,  (! [A] :  (v1_zfmisc_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_zfmisc_1(B)) ) ) ) ).
fof(cc6_finset_1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_finset_1(A)) ) ).
fof(cc6_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(B)) => v5_relat_1(C, A)) ) ) ) ).
fof(cc7_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_finset_1(B)) ) ) ) ).
fof(cc7_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v4_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v4_relat_1(B, A)) ) ) ) ) ) ).
fof(cc8_finset_1, axiom,  (! [A] :  (v5_finset_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_finset_1(B)) ) ) ) ).
fof(cc8_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  ( (v1_relat_1(B) & v5_relat_1(B, A))  =>  (v1_xboole_0(B) &  (v1_relat_1(B) & v5_relat_1(B, A)) ) ) ) ) ) ).
fof(cc9_finset_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_finset_1(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_k1_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k1_finsub_1(A, B, C)=k1_finsub_1(A, C, B)) ) ).
fof(commutativity_k1_normform, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  ( ( ~ (v1_xboole_0(B))  & v4_finsub_1(B))  &  (m1_subset_1(C, k2_zfmisc_1(A, B)) & m1_subset_1(D, k2_zfmisc_1(A, B))) ) )  => k1_normform(A, B, C, D)=k1_normform(A, B, D, C)) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k3_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k3_finsub_1(A, B, C)=k3_finsub_1(A, C, B)) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k5_setwiseo, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k5_finsub_1(A)) & m1_subset_1(C, k5_finsub_1(A)))  => k5_setwiseo(A, B, C)=k5_setwiseo(A, C, B)) ) ).
fof(commutativity_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, C)=k8_subset_1(A, C, B)) ) ).
fof(d11_normform, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k5_finsub_1(k7_normform(A))) =>  (! [C] :  (m1_subset_1(C, k5_finsub_1(k7_normform(A))) => k10_normform(A, B, C)=k8_subset_1(k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A), a_3_0_normform(A, B, C))) ) ) ) ) ).
fof(d2_normform, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  =>  (! [B] :  ( ( ~ (v1_xboole_0(B))  & v4_finsub_1(B))  =>  (! [C] :  (m1_subset_1(C, k2_zfmisc_1(A, B)) =>  (! [D] :  (m1_subset_1(D, k2_zfmisc_1(A, B)) => k1_normform(A, B, C, D)=k1_domain_1(A, B, k1_finsub_1(A, k2_domain_1(A, B, C), k2_domain_1(A, B, D)), k1_finsub_1(B, k3_domain_1(A, B, C), k3_domain_1(A, B, D)))) ) ) ) ) ) ) ) ).
fof(d3_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) | r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d4_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k3_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) & r2_hidden(D, B)) ) ) ) ) ) ) ).
fof(d6_heyting1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k5_finsub_1(k7_normform(A))) => k6_heyting1(A, B)=k8_subset_1(k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A), a_2_0_heyting1(A, B))) ) ) ).
fof(d7_xboole_0, axiom,  (! [A] :  (! [B] :  (r1_xboole_0(A, B) <=> k3_xboole_0(A, B)=k1_xboole_0) ) ) ).
fof(d8_normform, axiom,  (! [A] : k7_normform(A)=a_1_0_normform(A)) ).
fof(d9_normform, axiom,  (! [A] : k8_normform(A)=a_1_1_normform(A)) ).
fof(dt_k10_normform, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k5_finsub_1(k7_normform(A))) & m1_subset_1(C, k5_finsub_1(k7_normform(A))))  => m1_subset_1(k10_normform(A, B, C), k5_finsub_1(k7_normform(A)))) ) ).
fof(dt_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => m1_subset_1(k1_domain_1(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => m1_subset_1(k1_finsub_1(A, B, C), A)) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_heyting1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_heyting1(A))) ) ).
fof(dt_k1_normform, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  ( ( ~ (v1_xboole_0(B))  & v4_finsub_1(B))  &  (m1_subset_1(C, k2_zfmisc_1(A, B)) & m1_subset_1(D, k2_zfmisc_1(A, B))) ) )  => m1_subset_1(k1_normform(A, B, C, D), k2_zfmisc_1(A, B))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => m1_subset_1(k2_domain_1(A, B, C), A)) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => m1_subset_1(k3_domain_1(A, B, C), B)) ) ).
fof(dt_k3_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => m1_subset_1(k3_finsub_1(A, B, C), A)) ) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => m1_subset_1(k3_funct_2(A, B, C, D), B)) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_finsub_1, axiom,  (! [A] : v4_finsub_1(k5_finsub_1(A))) ).
fof(dt_k5_setwiseo, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k5_finsub_1(A)) & m1_subset_1(C, k5_finsub_1(A)))  => m1_subset_1(k5_setwiseo(A, B, C), k5_finsub_1(A))) ) ).
fof(dt_k6_heyting1, axiom,  (! [A, B] :  (m1_subset_1(B, k5_finsub_1(k7_normform(A))) => m1_subset_1(k6_heyting1(A, B), k5_finsub_1(k7_normform(A)))) ) ).
fof(dt_k7_normform, axiom,  (! [A] : m1_subset_1(k7_normform(A), k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A))))) ).
fof(dt_k8_normform, axiom,  (! [A] : m1_subset_1(k8_normform(A), k1_zfmisc_1(k5_finsub_1(k7_normform(A))))) ).
fof(dt_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k8_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(dt_o_2_11_heyting1, axiom,  (! [A, B] :  (m2_subset_1(B, k5_finsub_1(k7_normform(A)), k8_normform(A)) => m1_subset_1(o_2_11_heyting1(A, B), k10_normform(A, B, k6_heyting1(A, B)))) ) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(fc10_finset_1, axiom,  (! [A, B] :  (v1_finset_1(B) => v1_finset_1(k3_xboole_0(A, B))) ) ).
fof(fc10_funct_2, axiom,  (! [A, B] : v4_funct_1(k1_funct_2(A, B))) ).
fof(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc11_finset_1, axiom,  (! [A, B] :  (v1_finset_1(A) => v1_finset_1(k3_xboole_0(A, B))) ) ).
fof(fc14_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_zfmisc_1(A, B))) ) ).
fof(fc17_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc1_finsub_1, axiom,  (! [A] : v4_finsub_1(k1_zfmisc_1(A))) ).
fof(fc1_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  =>  ~ (v1_xboole_0(k1_funct_2(A, B))) ) ) ).
fof(fc1_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k3_xboole_0(A, B))) ) ).
fof(fc1_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  &  (v1_relat_1(C) & v4_relat_1(C, A)) )  => v4_relat_1(k2_xboole_0(B, C), 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(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc2_finsub_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(k5_finsub_1(A)))  & v4_finsub_1(k5_finsub_1(A))) ) ).
fof(fc2_funct_2, axiom,  (! [A] :  ~ (v1_xboole_0(k1_funct_2(A, A))) ) ).
fof(fc2_normform, axiom,  (! [A] :  ~ (v1_xboole_0(k7_normform(A))) ) ).
fof(fc2_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc31_finset_1, axiom,  (! [A] :  (v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A))) ) ).
fof(fc33_finset_1, axiom,  (! [A, B] :  ( (v5_finset_1(A) & v5_finset_1(B))  => v5_finset_1(k2_xboole_0(A, B))) ) ).
fof(fc35_finset_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) )  => v1_finset_1(k1_funct_1(A, B))) ) ).
fof(fc3_funct_2, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & v1_xboole_0(B))  => v1_xboole_0(k1_funct_2(A, B))) ) ).
fof(fc3_normform, axiom,  (! [A] :  ~ (v1_xboole_0(k8_normform(A))) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc4_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  &  (v1_relat_1(C) & v5_relat_1(C, A)) )  => v5_relat_1(k2_xboole_0(B, C), A)) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k3_xboole_0(B, C), A)) ) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc9_finset_1, axiom,  (! [A, B] :  ( (v1_finset_1(A) & v1_finset_1(B))  => v1_finset_1(k2_xboole_0(A, B))) ) ).
fof(fraenkel_a_1_0_normform, axiom,  (! [A, B] :  (r2_hidden(A, a_1_0_normform(B)) <=>  (? [C] :  (m1_subset_1(C, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B))) &  (A=C & r1_xboole_0(k2_domain_1(k5_finsub_1(B), k5_finsub_1(B), C), k3_domain_1(k5_finsub_1(B), k5_finsub_1(B), C))) ) ) ) ) ).
fof(fraenkel_a_1_1_normform, axiom,  (! [A, B] :  (r2_hidden(A, a_1_1_normform(B)) <=>  (? [C] :  (m1_subset_1(C, k5_finsub_1(k7_normform(B))) &  (A=C &  (! [D] :  (m2_subset_1(D, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) =>  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) =>  ( (r2_tarski(D, C) &  (r2_tarski(E, C) & r1_normform(k5_finsub_1(B), k5_finsub_1(B), D, E)) )  => D=E) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_heyting1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k5_finsub_1(k7_normform(B))) =>  (r2_hidden(A, a_2_0_heyting1(B, C)) <=>  (? [D] :  (m2_funct_2(D, k7_normform(B), k1_heyting1(B), k9_funct_2(k7_normform(B), k1_heyting1(B))) &  (A=k4_tarski(a_3_0_heyting1(B, C, D), a_3_1_heyting1(B, C, D)) &  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) =>  (r2_tarski(E, C) => r2_tarski(k3_funct_2(k7_normform(B), k1_heyting1(B), D, E), k5_setwiseo(B, k2_domain_1(k5_finsub_1(B), k5_finsub_1(B), E), k3_domain_1(k5_finsub_1(B), k5_finsub_1(B), E)))) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_heyting1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k5_finsub_1(k7_normform(B))) & m2_funct_2(D, k7_normform(B), k1_heyting1(B), k9_funct_2(k7_normform(B), k1_heyting1(B))))  =>  (r2_hidden(A, a_3_0_heyting1(B, C, D)) <=>  (? [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) &  (A=k3_funct_2(k7_normform(B), k1_heyting1(B), D, E) &  (r2_tarski(k3_funct_2(k7_normform(B), k1_heyting1(B), D, E), k3_domain_1(k5_finsub_1(B), k5_finsub_1(B), E)) & r2_tarski(E, C)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_0_normform, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k5_finsub_1(k7_normform(B))) & m1_subset_1(D, k5_finsub_1(k7_normform(B))))  =>  (r2_hidden(A, a_3_0_normform(B, C, D)) <=>  (? [E, F] :  ( (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) & m2_subset_1(F, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)))  &  (A=k1_normform(k5_finsub_1(B), k5_finsub_1(B), E, F) &  (r2_tarski(E, C) & r2_tarski(F, D)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_1_heyting1, axiom,  (! [A, B, C, D] :  ( (m1_subset_1(C, k5_finsub_1(k7_normform(B))) & m2_funct_2(D, k7_normform(B), k1_heyting1(B), k9_funct_2(k7_normform(B), k1_heyting1(B))))  =>  (r2_hidden(A, a_3_1_heyting1(B, C, D)) <=>  (? [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) &  (A=k3_funct_2(k7_normform(B), k1_heyting1(B), D, E) &  (r2_tarski(k3_funct_2(k7_normform(B), k1_heyting1(B), D, E), k2_domain_1(k5_finsub_1(B), k5_finsub_1(B), E)) & r2_tarski(E, C)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_5_heyting1, axiom,  (! [A, B, C, D] :  ( (m2_subset_1(C, k5_finsub_1(k7_normform(B)), k8_normform(B)) & m2_funct_2(D, k7_normform(B), k1_heyting1(B), k9_funct_2(k7_normform(B), k1_heyting1(B))))  =>  (r2_hidden(A, a_3_5_heyting1(B, C, D)) <=>  (? [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) &  (A=k3_funct_2(k7_normform(B), k1_heyting1(B), D, E) &  (r2_tarski(k3_funct_2(k7_normform(B), k1_heyting1(B), D, E), k3_domain_1(k5_finsub_1(B), k5_finsub_1(B), E)) & r2_tarski(E, C)) ) ) ) ) ) ) ).
fof(fraenkel_a_3_6_heyting1, axiom,  (! [A, B, C, D] :  ( (m2_subset_1(C, k5_finsub_1(k7_normform(B)), k8_normform(B)) & m2_funct_2(D, k7_normform(B), k1_heyting1(B), k9_funct_2(k7_normform(B), k1_heyting1(B))))  =>  (r2_hidden(A, a_3_6_heyting1(B, C, D)) <=>  (? [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) &  (A=k3_funct_2(k7_normform(B), k1_heyting1(B), D, E) &  (r2_tarski(k3_funct_2(k7_normform(B), k1_heyting1(B), D, E), k2_domain_1(k5_finsub_1(B), k5_finsub_1(B), E)) & r2_tarski(E, C)) ) ) ) ) ) ) ).
fof(idempotence_k1_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k1_finsub_1(A, B, B)=B) ) ).
fof(idempotence_k1_normform, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  ( ( ~ (v1_xboole_0(B))  & v4_finsub_1(B))  &  (m1_subset_1(C, k2_zfmisc_1(A, B)) & m1_subset_1(D, k2_zfmisc_1(A, B))) ) )  => k1_normform(A, B, C, C)=C) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(idempotence_k3_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k3_finsub_1(A, B, B)=B) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k5_setwiseo, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k5_finsub_1(A)) & m1_subset_1(C, k5_finsub_1(A)))  => k5_setwiseo(A, B, B)=B) ) ).
fof(idempotence_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, B)=B) ) ).
fof(rc10_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finset_1(A)) ) ) ) ).
fof(rc1_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ).
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_heyting1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k8_normform(A)) &  ~ (v1_xboole_0(B)) ) ) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
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(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_finset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_finset_1(B)) ) ) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(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_finset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc3_relat_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(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(rc5_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc6_finset_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ).
fof(rc6_subset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc7_finset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_finset_1(C)) ) ) ) ) ) ) ) ).
fof(rc8_finset_1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ( ~ (v1_zfmisc_1(B))  & v1_finset_1(B)) ) ) ) ) ).
fof(rc9_finset_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) & v5_finset_1(A)) ) ) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(redefinition_k1_domain_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  (m1_subset_1(C, A) & m1_subset_1(D, B)) ) )  => k1_domain_1(A, B, C, D)=k4_tarski(C, D)) ) ).
fof(redefinition_k1_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k1_finsub_1(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k2_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => k2_domain_1(A, B, C)=k1_xtuple_0(C)) ) ).
fof(redefinition_k3_domain_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(C, k2_zfmisc_1(A, B))) )  => k3_domain_1(A, B, C)=k2_xtuple_0(C)) ) ).
fof(redefinition_k3_finsub_1, axiom,  (! [A, B, C] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  (m1_subset_1(B, A) & m1_subset_1(C, A)) )  => k3_finsub_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( (v1_funct_1(C) &  (v1_funct_2(C, A, B) & m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) )  & m1_subset_1(D, A)) )  => k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ) ).
fof(redefinition_k5_setwiseo, axiom,  (! [A, B, C] :  ( (m1_subset_1(B, k5_finsub_1(A)) & m1_subset_1(C, k5_finsub_1(A)))  => k5_setwiseo(A, B, C)=k2_xboole_0(B, C)) ) ).
fof(redefinition_k8_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k8_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(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_normform, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v1_xboole_0(A))  & v4_finsub_1(A))  &  ( ( ~ (v1_xboole_0(B))  & v4_finsub_1(B))  &  (m1_subset_1(C, k2_zfmisc_1(A, B)) & m1_subset_1(D, k2_zfmisc_1(A, B))) ) )  => r1_normform(A, B, C, C)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(t11_heyting1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k5_finsub_1(k7_normform(A))) =>  (! [C] :  (m2_subset_1(C, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  ~ ( (r2_tarski(C, k6_heyting1(A, B)) &  (! [D] :  (m2_funct_2(D, k7_normform(A), k1_heyting1(A), k9_funct_2(k7_normform(A), k1_heyting1(A))) =>  ~ ( ( (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  (r2_tarski(E, B) => r2_tarski(k3_funct_2(k7_normform(A), k1_heyting1(A), D, E), k5_setwiseo(A, k2_domain_1(k5_finsub_1(A), k5_finsub_1(A), E), k3_domain_1(k5_finsub_1(A), k5_finsub_1(A), E)))) ) )  & C=k4_tarski(a_3_0_heyting1(A, B, D), a_3_1_heyting1(A, B, D))) ) ) ) ) ) ) ) ) ) ) ).
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(t25_normform, axiom,  (! [A] :  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) => r1_xboole_0(k2_domain_1(k5_finsub_1(A), k5_finsub_1(A), B), k3_domain_1(k5_finsub_1(A), k5_finsub_1(A), B))) ) ) ).
fof(t2_boole, axiom,  (! [A] : k3_xboole_0(A, k1_xboole_0)=k1_xboole_0) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t34_normform, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A))) =>  (! [C] :  (m1_subset_1(C, k5_finsub_1(k7_normform(A))) =>  (! [D] :  (m1_subset_1(D, k5_finsub_1(k7_normform(A))) =>  ~ ( (r2_tarski(B, k10_normform(A, C, D)) &  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  (! [F] :  (m2_subset_1(F, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  ~ ( (r2_tarski(E, C) &  (r2_tarski(F, D) & B=k1_normform(k5_finsub_1(A), k5_finsub_1(A), E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
fof(t9_setwiseo, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k5_finsub_1(A)) =>  (! [C] :  (r2_tarski(C, B) => m1_subset_1(C, A)) ) ) ) ) ) ).
