% Mizar problem: t37_normform,normform,655,29 
fof(t37_normform, conjecture,  (! [A] :  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  (! [C] :  (m1_subset_1(C, k5_finsub_1(k7_normform(A))) =>  (r2_tarski(B, k9_normform(A, C)) => r2_tarski(B, C)) ) ) ) ) ) ).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(symmetry_r1_xboole_0, axiom,  (! [A, B] :  (r1_xboole_0(A, B) => r1_xboole_0(B, A)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(cc2_finsub_1, axiom,  (! [A] :  ( (v1_finsub_1(A) & v3_finsub_1(A))  => v4_finsub_1(A)) ) ).
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(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_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(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(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
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(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_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_k8_normform, axiom,  (! [A] : m1_subset_1(k8_normform(A), k1_zfmisc_1(k5_finsub_1(k7_normform(A))))) ).
fof(cc1_finsub_1, axiom,  (! [A] :  (v4_finsub_1(A) =>  (v1_finsub_1(A) & v3_finsub_1(A)) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
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_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
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_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
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(fc10_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_xboole_0(k2_zfmisc_1(A, B))) ) ) ).
fof(fc1_finsub_1, axiom,  (! [A] : v4_finsub_1(k1_zfmisc_1(A))) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc3_normform, axiom,  (! [A] :  ~ (v1_xboole_0(k8_normform(A))) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(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(rc2_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(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)) ) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => 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_2_0_normform, axiom,  (! [A, B, C] :  (m1_subset_1(C, k5_finsub_1(k7_normform(B))) =>  (r2_hidden(A, a_2_0_normform(B, C)) <=>  (? [D] :  (m2_subset_1(D, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) &  (A=D &  (! [E] :  (m2_subset_1(E, k2_zfmisc_1(k5_finsub_1(B), k5_finsub_1(B)), k7_normform(B)) =>  ( (r2_tarski(E, C) & r1_normform(k5_finsub_1(B), k5_finsub_1(B), E, D))  <=> E=D) ) ) ) ) ) ) ) ) ).
fof(d9_normform, axiom,  (! [A] : k8_normform(A)=a_1_1_normform(A)) ).
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(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
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(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(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k5_finsub_1, axiom,  (! [A] : v4_finsub_1(k5_finsub_1(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_k9_normform, axiom,  (! [A, B] :  (m1_subset_1(B, k5_finsub_1(k7_normform(A))) => m2_subset_1(k9_normform(A, B), k5_finsub_1(k7_normform(A)), k8_normform(A))) ) ).
fof(dt_m1_subset_1, axiom, $true).
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(cc3_finsub_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k5_finsub_1(A)) => v1_finset_1(B)) ) ) ).
fof(fc2_finsub_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(k5_finsub_1(A)))  & v4_finsub_1(k5_finsub_1(A))) ) ).
fof(fc2_normform, axiom,  (! [A] :  ~ (v1_xboole_0(k7_normform(A))) ) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(d8_normform, axiom,  (! [A] : k7_normform(A)=a_1_0_normform(A)) ).
fof(d10_normform, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, k5_finsub_1(k7_normform(A))) => k9_normform(A, B)=a_2_0_normform(A, B)) ) ) ).
fof(d1_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)) =>  (r1_normform(A, B, C, D) <=>  (r1_tarski(k2_domain_1(A, B, C), k2_domain_1(A, B, D)) & r1_tarski(k3_domain_1(A, B, C), k3_domain_1(A, B, D))) ) ) ) ) ) ) ) ) ) ).
fof(t36_normform, axiom,  (! [A] :  (! [B] :  (m2_subset_1(B, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  (! [C] :  (m2_subset_1(C, k2_zfmisc_1(k5_finsub_1(A), k5_finsub_1(A)), k7_normform(A)) =>  (! [D] :  (m1_subset_1(D, k5_finsub_1(k7_normform(A))) =>  (r2_tarski(B, k9_normform(A, D)) =>  (r2_tarski(B, D) &  ( (r2_tarski(C, D) & r1_normform(k5_finsub_1(A), k5_finsub_1(A), C, B))  => C=B) ) ) ) ) ) ) ) ) ) ).
