% Mizar problem: t37_orders_2,orders_2,1103,5 
fof(t37_orders_2, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (! [B] :  (m2_orders_1(B, k1_orders_1(u1_struct_0(A)), k6_partfun1(k1_orders_1(u1_struct_0(A)))) =>  (! [C] :  (m2_orders_2(C, A, B) => r2_tarski(k1_funct_1(B, u1_struct_0(A)), 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(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ( ~ (v2_struct_0(A))  & v7_struct_0(A))  => v13_struct_0(A, 1)) ) ) ).
fof(cc11_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_card_1(A))  =>  (! [B] :  (v3_card_1(B, A) =>  ~ (v1_xboole_0(B)) ) ) ) ) ).
fof(cc11_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, 1) =>  ( ~ (v2_struct_0(A))  & v7_struct_0(A)) ) ) ) ).
fof(cc17_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(A)) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (v3_orders_2(A) => v2_orders_2(A)) ) ) ).
fof(cc1_partfun1, axiom,  (! [A, B] :  (v1_xboole_0(A) =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_partfun1(C, A)) ) ) ) ).
fof(cc1_relat_2, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) &  (v1_relat_2(A) &  (v2_relat_2(A) &  (v3_relat_2(A) &  (v4_relat_2(A) &  (v5_relat_2(A) &  (v6_relat_2(A) &  (v7_relat_2(A) & v8_relat_2(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v7_struct_0(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_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (v1_xboole_0(B) => v6_orders_2(B, A)) ) ) ) ) ).
fof(cc2_partfun1, 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_partfun1(C, A)) ) ) ) ) ).
fof(cc2_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(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(cc2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v7_struct_0(A))  =>  ~ (v2_struct_0(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(cc3_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_partfun1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v1_relat_2(A)) ) ) ).
fof(cc3_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_2(A) & v8_relat_2(A)) )  =>  (v1_relat_1(A) & v5_relat_2(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_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_2(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) & v4_relat_2(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_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) =>  (v2_struct_0(A) & v8_struct_0(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(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_relat_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v7_relat_2(A))  =>  (v1_relat_1(A) &  (v1_relat_2(A) & v6_relat_2(A)) ) ) ) ).
fof(cc5_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ( ~ (v2_struct_0(A))  &  ~ (v8_struct_0(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_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v7_struct_0(A) => v8_struct_0(A)) ) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  ( ~ (v8_struct_0(A))  =>  ~ (v7_struct_0(A)) ) ) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v2_struct_0(A) => v13_struct_0(A, k5_ordinal1)) ) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_struct_0, axiom,  (! [A] :  (l1_struct_0(A) =>  (v13_struct_0(A, k5_ordinal1) => v2_struct_0(A)) ) ) ).
fof(commutativity_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, B)=k3_xboole_0(B, A)) ).
fof(commutativity_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k9_subset_1(A, C, B)) ) ).
fof(d10_orders_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) => k3_orders_2(A, B, C)=k9_subset_1(u1_struct_0(A), k2_orders_2(A, k6_domain_1(u1_struct_0(A), C)), B)) ) ) ) ) ) ).
fof(d12_orders_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (! [B] :  (m2_orders_1(B, k1_orders_1(u1_struct_0(A)), k6_partfun1(k1_orders_1(u1_struct_0(A)))) =>  (! [C] :  ( (v6_orders_2(C, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))  =>  (m2_orders_2(C, A, B) <=>  ( ~ (C=k1_xboole_0)  &  (r2_wellord1(u1_orders_2(A), C) &  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (r2_tarski(D, C) => k1_funct_1(B, k1_orders_2(A, k3_orders_2(A, C, D)))=D) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d2_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => k1_struct_0(A)=k1_xboole_0) ) ).
fof(d3_orders_1, axiom,  (! [A] : k1_orders_1(A)=k7_subset_1(k1_zfmisc_1(A), k9_setfam_1(A), k1_tarski(k1_xboole_0))) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, 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(d5_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r1_orders_2(A, B, C) <=> r2_hidden(k4_tarski(B, C), u1_orders_2(A))) ) ) ) ) ) ) ).
fof(d5_wellord1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (r2_wellord1(A, B) <=>  (r1_relat_2(A, B) &  (r8_relat_2(A, B) &  (r4_relat_2(A, B) &  (r6_relat_2(A, B) & r1_wellord1(A, B)) ) ) ) ) ) ) ) ).
fof(d6_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (r2_orders_2(A, B, C) <=>  (r1_orders_2(A, B, C) &  ~ (B=C) ) ) ) ) ) ) ) ) ).
fof(d8_orders_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => k1_orders_2(A, B)=a_2_0_orders_2(A, B)) ) ) ) ).
fof(d9_orders_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => k2_orders_2(A, B)=a_2_1_orders_2(A, B)) ) ) ) ).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_orders_1, axiom, $true).
fof(dt_k1_orders_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k1_orders_2(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => m1_subset_1(k1_struct_0(A), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_orders_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k2_orders_2(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  &  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) )  => m1_subset_1(k3_orders_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k3_xboole_0, axiom, $true).
fof(dt_k4_relat_1, axiom,  (! [A] : v1_relat_1(k4_relat_1(A))) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) ) ).
fof(dt_k6_partfun1, axiom,  (! [A] :  (v1_partfun1(k6_partfun1(A), A) & m1_subset_1(k6_partfun1(A), k1_zfmisc_1(k2_zfmisc_1(A, A)))) ) ).
fof(dt_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A, B, C), 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_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A, B, C), k1_zfmisc_1(A))) ) ).
fof(dt_l1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_orders_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (! [B] :  (m1_orders_1(B, A) =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_orders_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m2_orders_1(C, A, B) =>  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v1_funct_1(C) & v1_partfun1(C, A)) ) ) ) ) ) ) ).
fof(dt_m2_orders_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  & m1_orders_1(B, k6_partfun1(k1_orders_1(u1_struct_0(A)))))  =>  (! [C] :  (m2_orders_2(C, A, B) =>  (v6_orders_2(C, A) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) ) ) ) ) ).
fof(dt_o_4_0_orders_2, axiom,  (! [A, B, C, D] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  &  (m2_orders_1(B, k1_orders_1(u1_struct_0(A)), k6_partfun1(k1_orders_1(u1_struct_0(A)))) &  (m2_orders_2(C, A, B) & m1_subset_1(D, u1_struct_0(A))) ) )  => m1_subset_1(o_4_0_orders_2(A, B, C, D), k9_subset_1(u1_struct_0(A), k2_orders_2(A, k6_domain_1(u1_struct_0(A), D)), C))) ) ).
fof(dt_u1_orders_2, axiom,  (! [A] :  (l1_orders_2(A) => m1_subset_1(u1_orders_2(A), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A))))) ) ).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_orders_2, axiom,  (? [A] : l1_orders_2(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_orders_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_funct_1(A))  =>  (? [B] : m1_orders_1(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_orders_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (? [C] : m2_orders_1(C, A, B)) ) ) ).
fof(existence_m2_orders_2, axiom,  (! [A, B] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  & m1_orders_1(B, k6_partfun1(k1_orders_1(u1_struct_0(A)))))  =>  (? [C] : m2_orders_2(C, 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_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_relat_2(A))  &  (v1_relat_1(B) & v3_relat_2(B)) )  => v3_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
fof(fc12_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v3_relat_2(A))  &  (v1_relat_1(B) & v3_relat_2(B)) )  => v3_relat_2(k4_xboole_0(A, B))) ) ).
fof(fc13_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(A, B))) ) ) ).
fof(fc14_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_finset_1(A))  &  ~ (v1_xboole_0(B)) )  =>  ~ (v1_finset_1(k2_zfmisc_1(B, A))) ) ) ).
fof(fc14_relat_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v5_relat_2(B)) )  => v5_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc15_relat_2, axiom,  (! [A, B] :  ( (v1_relat_1(A) &  (v1_relat_1(B) & v5_relat_2(B)) )  => v5_relat_2(k3_xboole_0(B, A))) ) ).
fof(fc16_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
fof(fc16_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v5_relat_2(A))  & v1_relat_1(B))  => v5_relat_2(k4_xboole_0(A, B))) ) ).
fof(fc18_card_1, axiom,  (! [A, B] :  ( ( ~ (v1_zfmisc_1(A))  &  (v3_card_1(B, 1) & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  ~ (v1_xboole_0(k4_xboole_0(A, B))) ) ) ).
fof(fc18_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_relat_2(A))  & v1_relat_1(B))  => v4_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc19_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_relat_2(A))  & v1_relat_1(B))  => v4_relat_2(k3_xboole_0(B, A))) ) ).
fof(fc19_struct_0, axiom,  (! [A, B] :  ( (v1_card_1(A) &  (v13_struct_0(B, A) & l1_struct_0(B)) )  => v3_card_1(u1_struct_0(B), A)) ) ).
fof(fc1_relat_2, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v3_relat_2(k4_relat_1(A)) &  (v4_relat_2(k4_relat_1(A)) & v8_relat_2(k4_relat_1(A))) ) ) ) ).
fof(fc1_struct_0, axiom,  (! [A] :  ( (v2_struct_0(A) & l1_struct_0(A))  => v1_xboole_0(u1_struct_0(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(fc20_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v4_relat_2(A))  & v1_relat_1(B))  => v4_relat_2(k4_xboole_0(A, B))) ) ).
fof(fc22_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v8_relat_2(A))  &  (v1_relat_1(B) & v8_relat_2(B)) )  => v8_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc2_orders_2, axiom,  (! [A] :  ( (v2_orders_2(A) & l1_orders_2(A))  => v1_partfun1(u1_orders_2(A), u1_struct_0(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(fc2_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_xboole_0(u1_struct_0(A))) ) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_orders_2, axiom,  (! [A] :  ( (v3_orders_2(A) & l1_orders_2(A))  => v1_relat_2(u1_orders_2(A))) ) ).
fof(fc3_partfun1, axiom,  (! [A] :  (v1_relat_1(k4_relat_1(A)) &  (v3_relat_2(k4_relat_1(A)) &  (v4_relat_2(k4_relat_1(A)) & v8_relat_2(k4_relat_1(A))) ) ) ) ).
fof(fc3_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v4_relat_1(B, A))  & v1_relat_1(C))  => v4_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc3_struct_0, axiom,  (! [A] :  (l1_struct_0(A) => v1_xboole_0(k1_struct_0(A))) ) ).
fof(fc4_orders_2, axiom,  (! [A] :  ( (v2_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) )  => v4_relat_2(u1_orders_2(A))) ) ).
fof(fc5_orders_2, axiom,  (! [A] :  ( (v4_orders_2(A) & l1_orders_2(A))  => v8_relat_2(u1_orders_2(A))) ) ).
fof(fc5_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v1_relat_2(A))  &  (v1_relat_1(B) & v1_relat_2(B)) )  => v1_relat_2(k3_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(fc6_relset_1, axiom,  (! [A, B, C] :  ( ( (v1_relat_1(B) & v5_relat_1(B, A))  & v1_relat_1(C))  => v5_relat_1(k4_xboole_0(B, C), A)) ) ).
fof(fc6_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(fc7_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_relat_2(A))  &  (v1_relat_1(B) & v2_relat_2(B)) )  => v2_relat_2(k3_xboole_0(A, B))) ) ).
fof(fc7_relset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  ( ~ (v1_xboole_0(k4_relat_1(A)))  & v1_relat_1(k4_relat_1(A))) ) ) ).
fof(fc7_struct_0, axiom,  (! [A] :  ( (v7_struct_0(A) & l1_struct_0(A))  => v1_zfmisc_1(u1_struct_0(A))) ) ).
fof(fc8_relat_2, axiom,  (! [A, B] :  ( ( (v1_relat_1(A) & v2_relat_2(A))  & v1_relat_1(B))  => v2_relat_2(k4_xboole_0(A, B))) ) ).
fof(fc8_struct_0, axiom,  (! [A] :  ( (v8_struct_0(A) & l1_struct_0(A))  => v1_finset_1(u1_struct_0(A))) ) ).
fof(fc9_struct_0, axiom,  (! [A] :  ( ( ~ (v8_struct_0(A))  & l1_struct_0(A))  =>  ~ (v1_finset_1(u1_struct_0(A))) ) ) ).
fof(fraenkel_a_2_0_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v3_orders_2(B) &  (v4_orders_2(B) &  (v5_orders_2(B) & l1_orders_2(B)) ) ) )  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))  =>  (r2_hidden(A, a_2_0_orders_2(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=D &  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (r2_tarski(E, C) => r2_orders_2(B, E, D)) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_2_1_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(B))  &  (v3_orders_2(B) &  (v4_orders_2(B) &  (v5_orders_2(B) & l1_orders_2(B)) ) ) )  & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))))  =>  (r2_hidden(A, a_2_1_orders_2(B, C)) <=>  (? [D] :  (m1_subset_1(D, u1_struct_0(B)) &  (A=D &  (! [E] :  (m1_subset_1(E, u1_struct_0(B)) =>  (r2_tarski(E, C) => r2_orders_2(B, D, E)) ) ) ) ) ) ) ) ) ).
fof(idempotence_k3_xboole_0, axiom,  (! [A, B] : k3_xboole_0(A, A)=A) ).
fof(idempotence_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, B)=B) ) ).
fof(irreflexivity_r2_orders_2, axiom,  (! [A, B, C] :  ( (l1_orders_2(A) &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  ~ (r2_orders_2(A, B, B)) ) ) ).
fof(l5_orders_2, axiom,  (! [A] :  (! [B] :  ( ( ~ (v2_struct_0(B))  &  (v3_orders_2(B) &  (v4_orders_2(B) &  (v5_orders_2(B) & l1_orders_2(B)) ) ) )  =>  (! [C] :  (m1_subset_1(C, k1_zfmisc_1(u1_struct_0(B))) =>  (r2_tarski(A, C) => m1_subset_1(A, u1_struct_0(B))) ) ) ) ) ) ).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_partfun1, 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)) ) ) ) ) ) ).
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(rc21_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ( ~ (v1_xboole_0(B))  & v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc22_struct_0, axiom,  (! [A] :  ( ( ~ (v7_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_zfmisc_1(B)) ) ) ) ) ).
fof(rc23_struct_0, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (l1_struct_0(B) & v13_struct_0(B, A)) ) ) ) ).
fof(rc2_partfun1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(A, A))) &  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v5_relat_1(B, A) &  (v1_relat_2(B) &  (v3_relat_2(B) &  (v4_relat_2(B) &  (v8_relat_2(B) & v1_partfun1(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_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_orders_2, axiom,  (! [A] :  (l1_orders_2(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & v6_orders_2(B, A)) ) ) ) ).
fof(rc3_partfun1, 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_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) &  ~ (v1_xboole_0(C)) ) ) ) ) ) ) ) ) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc4_struct_0, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  & l1_struct_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_finset_1(B)) ) ) ) ) ).
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_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc8_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (v1_relat_1(B) &  (v1_funct_1(B) & v3_card_1(B, A)) ) ) ) ) ).
fof(rc9_card_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v3_card_1(B, 1)) ) ) ) ).
fof(redefinition_k6_domain_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  & m1_subset_1(B, A))  => k6_domain_1(A, B)=k1_tarski(B)) ) ).
fof(redefinition_k6_partfun1, axiom,  (! [A] : k6_partfun1(A)=k4_relat_1(A)) ).
fof(redefinition_k7_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(B, k1_zfmisc_1(A)) => k7_subset_1(A, B, C)=k4_xboole_0(B, C)) ) ).
fof(redefinition_k9_setfam_1, axiom,  (! [A] : k9_setfam_1(A)=k1_zfmisc_1(A)) ).
fof(redefinition_k9_subset_1, axiom,  (! [A, B, C] :  (m1_subset_1(C, k1_zfmisc_1(A)) => k9_subset_1(A, B, C)=k3_xboole_0(B, C)) ) ).
fof(redefinition_m2_orders_1, axiom,  (! [A, B] :  ( (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) & v1_partfun1(B, A)) ) )  =>  (! [C] :  (m2_orders_1(C, A, B) <=> m1_orders_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(redefinition_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  =>  (r3_orders_2(A, B, C) <=> r1_orders_2(A, B, C)) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r3_orders_2, axiom,  (! [A, B, C] :  ( ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) & l1_orders_2(A)) )  &  (m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) )  => r3_orders_2(A, B, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(t14_orders_2, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v3_orders_2(A) &  (v4_orders_2(A) &  (v5_orders_2(A) & l1_orders_2(A)) ) ) )  => k1_orders_2(A, k1_struct_0(A))=u1_struct_0(A)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_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(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
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(t5_wellord1, axiom,  (! [A] :  (! [B] :  (v1_relat_1(B) =>  (r2_wellord1(B, A) =>  (! [C] :  ~ ( (r1_tarski(C, A) &  ( ~ (C=k1_xboole_0)  &  (! [D] :  ~ ( (r2_hidden(D, C) &  (! [E] :  (r2_hidden(E, C) => r2_hidden(k4_tarski(D, E), B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_orders_2, axiom,  (! [A] :  ( (v5_orders_2(A) & l1_orders_2(A))  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  ~ ( (r1_orders_2(A, B, C) & r2_orders_2(A, C, B)) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
