% Mizar problem: t2_numbers,numbers,355,5 
fof(t2_numbers, conjecture, r2_xboole_0(k3_numbers, k1_numbers)).
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(asymmetry_r2_xboole_0, axiom,  (! [A, B] :  (r2_xboole_0(A, B) =>  ~ (r2_xboole_0(B, A)) ) ) ).
fof(cc10_card_1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A))  => v3_card_1(A, 1)) ) ).
fof(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(B)) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_ordinal1(A)) ) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc1_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (v3_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ) ).
fof(cc1_card_1, axiom,  (! [A] :  (v1_card_1(A) => v3_ordinal1(A)) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_card_1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(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_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_card_1(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc4_card_1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v1_finset_1(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc5_card_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_finset_1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_card_1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v1_finset_1(A))  => v7_ordinal1(A)) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc7_card_1, axiom,  (! [A] :  (v3_card_1(A, k5_ordinal1) => v1_xboole_0(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc8_card_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_card_1(A, k5_ordinal1)) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc9_card_1, axiom,  (! [A] :  (v3_card_1(A, 1) =>  ( ~ (v1_xboole_0(A))  & v1_zfmisc_1(A)) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k10_arytm_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_arytm_3) & m1_subset_1(B, k5_arytm_3))  => k10_arytm_3(A, B)=k10_arytm_3(B, A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(commutativity_k8_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => k8_ordinal3(A, B)=k8_ordinal3(B, A)) ) ).
fof(commutativity_k9_arytm_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_arytm_3) & m1_subset_1(B, k5_arytm_3))  => k9_arytm_3(A, B)=k9_arytm_3(B, A)) ) ).
fof(commutativity_k9_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => k9_ordinal3(A, B)=k9_ordinal3(B, A)) ) ).
fof(connectedness_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) | r1_ordinal1(B, A)) ) ) ).
fof(connectedness_r3_arytm_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_arytm_3) & m1_subset_1(B, k5_arytm_3))  =>  (r3_arytm_3(A, B) | r3_arytm_3(B, A)) ) ) ).
fof(d11_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) => k9_arytm_3(A, B)=k8_arytm_3(k8_ordinal3(k9_ordinal3(k6_arytm_3(A), k7_arytm_3(B)), k9_ordinal3(k6_arytm_3(B), k7_arytm_3(A))), k9_ordinal3(k7_arytm_3(A), k7_arytm_3(B)))) ) ) ) ).
fof(d12_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) => k10_arytm_3(A, B)=k8_arytm_3(k9_ordinal3(k6_arytm_3(A), k6_arytm_3(B)), k9_ordinal3(k7_arytm_3(A), k7_arytm_3(B)))) ) ) ) ).
fof(d13_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (r3_arytm_3(A, B) <=>  (? [C] :  (m1_subset_1(C, k5_arytm_3) & B=k9_arytm_3(A, C)) ) ) ) ) ) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d1_arytm_2, axiom, k1_arytm_2=k6_subset_1(a_0_0_arytm_2, k1_tarski(k5_arytm_3))).
fof(d1_arytm_3, axiom, k1_arytm_3=1).
fof(d1_numbers, axiom, k1_numbers=k6_subset_1(k2_xboole_0(k2_arytm_2, k2_zfmisc_1(k1_tarski(k5_ordinal1), k2_arytm_2)), k1_tarski(k4_tarski(k5_ordinal1, k5_ordinal1)))).
fof(d1_ordinal1, axiom,  (! [A] : k1_ordinal1(A)=k2_xboole_0(A, k1_tarski(A))) ).
fof(d1_relat_1, axiom,  (! [A] :  (v1_relat_1(A) <=>  (! [B] :  ~ ( (r2_hidden(B, A) &  (! [C] :  (! [D] :  ~ (B=k4_tarski(C, D)) ) ) ) ) ) ) ) ).
fof(d1_tarski, axiom,  (! [A] :  (! [B] :  (B=k1_tarski(A) <=>  (! [C] :  (r2_hidden(C, B) <=> C=A) ) ) ) ) ).
fof(d2_arytm_2, axiom, k2_arytm_2=k6_subset_1(k2_xboole_0(k5_arytm_3, k1_arytm_2), a_0_1_arytm_2)).
fof(d2_arytm_3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r1_arytm_3(A, B) <=>  (! [C] :  (v3_ordinal1(C) =>  (! [D] :  (v3_ordinal1(D) =>  (! [E] :  (v3_ordinal1(E) =>  ( (A=k11_ordinal2(C, D) & B=k11_ordinal2(C, E))  => C=1) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_tarski, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k2_tarski(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (D=A | D=B) ) ) ) ) ) ) ).
fof(d3_numbers, axiom, k3_numbers=k6_subset_1(k2_xboole_0(k5_arytm_3, k2_zfmisc_1(k1_tarski(k5_ordinal1), k5_arytm_3)), k1_tarski(k4_tarski(k5_ordinal1, k5_ordinal1)))).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
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(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d5_xboole_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k4_xboole_0(A, B) <=>  (! [D] :  (r2_hidden(D, C) <=>  (r2_hidden(D, A) &  ~ (r2_hidden(D, B)) ) ) ) ) ) ) ) ).
fof(d7_arytm_3, axiom, k5_arytm_3=k2_xboole_0(k6_subset_1(a_0_0_arytm_3, a_0_1_arytm_3), k4_ordinal1)).
fof(d8_xboole_0, axiom,  (! [A] :  (! [B] :  (r2_xboole_0(A, B) <=>  (r1_tarski(A, B) &  ~ (A=B) ) ) ) ) ).
fof(dt_k10_arytm_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_arytm_3) & m1_subset_1(B, k5_arytm_3))  => m1_subset_1(k10_arytm_3(A, B), k5_arytm_3)) ) ).
fof(dt_k10_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k10_ordinal2(A, B))) ) ).
fof(dt_k11_arytm_3, axiom, m1_subset_1(k11_arytm_3, k5_arytm_3)).
fof(dt_k11_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k11_ordinal2(A, B))) ) ).
fof(dt_k12_arytm_3, axiom,  ( ~ (v1_xboole_0(k12_arytm_3))  &  (v3_ordinal1(k12_arytm_3) & m1_subset_1(k12_arytm_3, k5_arytm_3)) ) ).
fof(dt_k1_arytm_2, axiom, m1_subset_1(k1_arytm_2, k1_zfmisc_1(k1_zfmisc_1(k5_arytm_3)))).
fof(dt_k1_arytm_3, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_ordinal1, axiom, $true).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_arytm_2, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k5_arytm_3, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k6_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => m1_subset_1(k6_arytm_3(A), k4_ordinal1)) ) ).
fof(dt_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k7_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => m1_subset_1(k7_arytm_3(A), k4_ordinal1)) ) ).
fof(dt_k8_arytm_3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => m1_subset_1(k8_arytm_3(A, B), k5_arytm_3)) ) ).
fof(dt_k8_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => v3_ordinal1(k8_ordinal3(A, B))) ) ).
fof(dt_k9_arytm_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k5_arytm_3) & m1_subset_1(B, k5_arytm_3))  => m1_subset_1(k9_arytm_3(A, B), k5_arytm_3)) ) ).
fof(dt_k9_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => v3_ordinal1(k9_ordinal3(A, B))) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc12_card_1, axiom,  (! [A] :  ( ~ (v1_finset_1(A))  =>  ~ (v1_finset_1(k1_zfmisc_1(A))) ) ) ).
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(fc16_card_1, axiom,  (! [A] : v3_card_1(k1_tarski(A), 1)) ).
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(fc1_arytm_2, axiom,  ~ (v1_xboole_0(k1_arytm_2)) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_ordinal1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_ordinal1(A))) ) ).
fof(fc1_ordinal3, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k2_xboole_0(A, B))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_arytm_2, axiom,  ~ (v1_xboole_0(k2_arytm_2)) ).
fof(fc2_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  ( ~ (v1_xboole_0(k1_ordinal1(A)))  & v3_ordinal1(k1_ordinal1(A))) ) ) ).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_arytm_3, axiom,  ~ (v1_xboole_0(k5_arytm_3)) ).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc4_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  =>  (v3_ordinal1(k11_ordinal2(A, B)) & v7_ordinal1(k11_ordinal2(A, B))) ) ) ).
fof(fc4_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(A, B))) ) ) ).
fof(fc5_ordinal2, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v3_ordinal1(k10_ordinal2(A, B)) & v7_ordinal1(k10_ordinal2(A, B))) ) ) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc5_xboole_0, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(A))  =>  ~ (v1_xboole_0(k2_xboole_0(B, A))) ) ) ).
fof(fc6_card_1, axiom, v1_card_1(k4_ordinal1)).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
fof(fc7_card_1, axiom, v2_card_1(k4_ordinal1)).
fof(fc7_ordinal1, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  => v7_ordinal1(k1_ordinal1(A))) ) ).
fof(fc7_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_card_1, axiom,  ~ (v1_finset_1(k4_ordinal1)) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fraenkel_a_0_0_arytm_2, axiom,  (! [A] :  (r2_hidden(A, a_0_0_arytm_2) <=>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k5_arytm_3)) &  (A=B &  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (r2_tarski(C, B) =>  ( (! [D] :  (m1_subset_1(D, k5_arytm_3) =>  (r3_arytm_3(D, C) => r2_tarski(D, B)) ) )  &  (? [D] :  (m1_subset_1(D, k5_arytm_3) &  (r2_tarski(D, B) &  ~ (r3_arytm_3(D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_0_0_arytm_3, axiom,  (! [A] :  (r2_hidden(A, a_0_0_arytm_3) <=>  (? [B, C] :  ( (m1_subset_1(B, k4_ordinal1) & m1_subset_1(C, k4_ordinal1))  &  (A=k4_tarski(B, C) &  (r1_arytm_3(B, C) &  ~ (C=k1_xboole_0) ) ) ) ) ) ) ).
fof(fraenkel_a_0_1_arytm_2, axiom,  (! [A] :  (r2_hidden(A, a_0_1_arytm_2) <=>  (? [B] :  (m1_subset_1(B, k5_arytm_3) &  (A=a_1_0_arytm_2(B) &  ~ (B=k11_arytm_3) ) ) ) ) ) ).
fof(fraenkel_a_0_1_arytm_3, axiom,  (! [A] :  (r2_hidden(A, a_0_1_arytm_3) <=>  (? [B] :  (m1_subset_1(B, k4_ordinal1) & A=k4_tarski(B, 1)) ) ) ) ).
fof(fraenkel_a_0_1_numbers, axiom,  (! [A] :  (r2_hidden(A, a_0_1_numbers) <=>  (? [B, C] :  ( (m1_subset_1(B, k4_ordinal1) & m1_subset_1(C, k4_ordinal1))  &  (A=k4_tarski(B, C) &  (r1_arytm_3(B, C) &  ~ (C=k11_arytm_3) ) ) ) ) ) ) ).
fof(fraenkel_a_0_2_numbers, axiom,  (! [A] :  (r2_hidden(A, a_0_2_numbers) <=>  (? [B] :  (m1_subset_1(B, k4_ordinal1) & A=k4_tarski(B, 1)) ) ) ) ).
fof(fraenkel_a_0_3_numbers, axiom,  (! [A] :  (r2_hidden(A, a_0_3_numbers) <=>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(k5_arytm_3)) &  (A=B &  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (r2_tarski(C, B) =>  ( (! [D] :  (m1_subset_1(D, k5_arytm_3) =>  (r3_arytm_3(D, C) => r2_tarski(D, B)) ) )  &  (? [D] :  (m1_subset_1(D, k5_arytm_3) &  (r2_tarski(D, B) &  ~ (r3_arytm_3(D, C)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(fraenkel_a_0_4_numbers, axiom,  (! [A] :  (r2_hidden(A, a_0_4_numbers) <=>  (? [B] :  (m1_subset_1(B, k4_ordinal1) & A=k4_tarski(B, k12_arytm_3)) ) ) ) ).
fof(fraenkel_a_0_6_numbers, axiom,  (! [A] :  (r2_hidden(A, a_0_6_numbers) <=>  (? [B] :  (m1_subset_1(B, k5_arytm_3) &  (A=a_1_1_numbers(B) &  ~ (B=k5_numbers) ) ) ) ) ) ).
fof(fraenkel_a_1_0_arytm_2, axiom,  (! [A, B] :  (m1_subset_1(B, k5_arytm_3) =>  (r2_hidden(A, a_1_0_arytm_2(B)) <=>  (? [C] :  (m1_subset_1(C, k5_arytm_3) &  (A=C &  ~ (r3_arytm_3(B, C)) ) ) ) ) ) ) ).
fof(fraenkel_a_1_0_numbers, axiom,  (! [A, B] :  ( (v3_ordinal1(B) & m1_subset_1(B, k5_arytm_3))  =>  (r2_hidden(A, a_1_0_numbers(B)) <=>  (? [C] :  (m1_subset_1(C, k5_arytm_3) &  (A=C &  ~ (r3_arytm_3(B, k10_arytm_3(C, C))) ) ) ) ) ) ) ).
fof(fraenkel_a_1_1_numbers, axiom,  (! [A, B] :  (m1_subset_1(B, k5_arytm_3) =>  (r2_hidden(A, a_1_1_numbers(B)) <=>  (? [C] :  (m1_subset_1(C, k5_arytm_3) &  (A=C &  ~ (r3_arytm_3(B, C)) ) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(irreflexivity_r2_xboole_0, axiom,  (! [A, B] :  ~ (r2_xboole_0(A, A)) ) ).
fof(l13_numbers, axiom, r1_tarski(k3_numbers, k1_numbers)).
fof(l14_numbers, axiom,  (! [A] :  ( (v3_ordinal1(A) & m1_subset_1(A, k5_arytm_3))  =>  (! [B] :  ( (v3_ordinal1(B) & m1_subset_1(B, k5_arytm_3))  =>  ~ ( (r2_tarski(A, B) & r3_arytm_3(B, A)) ) ) ) ) ) ).
fof(l15_numbers, axiom,  (! [A] :  ( (v3_ordinal1(A) & m1_subset_1(A, k5_arytm_3))  =>  (! [B] :  ( (v3_ordinal1(B) & m1_subset_1(B, k5_arytm_3))  =>  (r1_ordinal1(A, B) => r3_arytm_3(A, B)) ) ) ) ) ).
fof(l16_numbers, axiom, 2=k2_tarski(k5_numbers, 1)).
fof(l17_numbers, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  =>  (! [B] :  ( (v3_ordinal1(B) & v7_ordinal1(B))  =>  ~ ( (k9_ordinal3(A, A)=k9_ordinal3(2, B) &  (! [C] :  ( (v3_ordinal1(C) & v7_ordinal1(C))  =>  ~ (A=k9_ordinal3(2, C)) ) ) ) ) ) ) ) ) ).
fof(l18_numbers, axiom, k9_arytm_3(k12_arytm_3, k12_arytm_3)=2).
fof(l19_numbers, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (A=2 => k9_arytm_3(B, B)=k10_arytm_3(A, B)) ) ) ) ) ).
fof(l1_numbers, axiom, r1_tarski(k4_ordinal1, k2_xboole_0(k6_subset_1(a_0_1_numbers, a_0_2_numbers), k4_ordinal1))).
fof(rc10_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_card_1(B)) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_arytm_3, axiom,  (? [A] :  (m1_subset_1(A, k5_arytm_3) &  ( ~ (v1_xboole_0(A))  & v3_ordinal1(A)) ) ) ).
fof(rc1_card_1, axiom,  (? [A] : v1_card_1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_arytm_3, axiom,  (? [A] :  (m1_subset_1(A, k5_arytm_3) & v1_xboole_0(A)) ) ).
fof(rc2_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v1_finset_1(A) & v1_card_1(A)) ) ) ) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc3_card_1, axiom,  (? [A] :  ~ (v1_finset_1(A)) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc4_card_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc5_card_1, axiom,  (? [A] :  (v1_ordinal1(A) &  (v2_ordinal1(A) &  (v3_ordinal1(A) &  (v7_ordinal1(A) &  ( ~ (v8_ordinal1(A))  & v1_card_1(A)) ) ) ) ) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_card_1, axiom,  (! [A] :  (v1_card_1(A) =>  (? [B] : v3_card_1(B, A)) ) ) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(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(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(redefinition_k11_arytm_3, axiom, k11_arytm_3=k1_xboole_0).
fof(redefinition_k12_arytm_3, axiom, k12_arytm_3=k1_arytm_3).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k8_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => k8_ordinal3(A, B)=k10_ordinal2(A, B)) ) ).
fof(redefinition_k9_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => k9_ordinal3(A, B)=k11_ordinal2(A, B)) ) ).
fof(redefinition_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_ordinal1(A, B) <=> r1_tarski(A, B)) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_ordinal1, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => r1_ordinal1(A, A)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(rqSucc__k1_ordinal1__r1_r2, axiom, k1_ordinal1(1)=2).
fof(s7_domain_1__e3_20__numbers, axiom,  (! [A] :  ( (v3_ordinal1(A) & m1_subset_1(A, k5_arytm_3))  => m1_subset_1(a_1_0_numbers(A), k1_zfmisc_1(k5_arytm_3))) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(symmetry_r1_arytm_3, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  =>  (r1_arytm_3(A, B) => r1_arytm_3(B, A)) ) ) ).
fof(t14_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ~ ( ( ~ (r2_tarski(A, B))  &  ( ~ (A=B)  &  ~ (r2_tarski(B, A)) ) ) ) ) ) ) ) ).
fof(t19_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  (! [D] :  (v3_ordinal1(D) =>  (r2_tarski(A, B) =>  ( ( ~ ( (r1_ordinal1(C, D) &  ~ (D=k1_xboole_0) ) )  &  ~ (r2_tarski(C, D)) )  | r2_tarski(k11_ordinal2(A, C), k11_ordinal2(B, D))) ) ) ) ) ) ) ) ) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t29_enumset1, axiom,  (! [A] : k2_tarski(A, A)=k1_tarski(A)) ).
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(t31_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ~ ( (k11_ordinal2(A, B)=k1_xboole_0 &  ( ~ (A=k1_xboole_0)  &  ~ (B=k1_xboole_0) ) ) ) ) ) ) ) ).
fof(t32_zfmisc_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (r1_tarski(k2_tarski(A, B), C) <=>  (r2_hidden(A, C) & r2_hidden(B, C)) ) ) ) ) ).
fof(t33_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  (k11_ordinal2(B, A)=k11_ordinal2(C, A) =>  (A=k1_xboole_0 | B=C) ) ) ) ) ) ) ) ).
fof(t34_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => r1_arytm_3(k6_arytm_3(A), k7_arytm_3(A))) ) ).
fof(t35_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  ~ (k7_arytm_3(A)=k1_xboole_0) ) ) ).
fof(t39_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (k11_ordinal2(1, A)=A & k11_ordinal2(A, 1)=A) ) ) ).
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(t40_arytm_3, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  =>  (! [B] :  ( (v3_ordinal1(B) & v7_ordinal1(B))  =>  (k8_arytm_3(k1_xboole_0, B)=k1_xboole_0 & k8_arytm_3(A, 1)=A) ) ) ) ) ).
fof(t45_arytm_3, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  =>  (! [B] :  ( (v3_ordinal1(B) & v7_ordinal1(B))  =>  (! [C] :  ( (v3_ordinal1(C) & v7_ordinal1(C))  =>  (! [D] :  ( (v3_ordinal1(D) & v7_ordinal1(D))  =>  ~ ( ( ~ (C=k1_xboole_0)  &  ( ~ (A=k1_xboole_0)  &  ~ ( (k8_arytm_3(B, C)=k8_arytm_3(D, A) <=> k9_ordinal3(B, A)=k9_ordinal3(C, D)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t48_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => k10_arytm_3(A, k11_arytm_3)=k11_arytm_3) ) ).
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(t50_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => k9_arytm_3(A, k11_arytm_3)=A) ) ).
fof(t50_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) => k11_ordinal2(k11_ordinal2(A, B), C)=k11_ordinal2(A, k11_ordinal2(B, C))) ) ) ) ) ) ).
fof(t51_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) => k9_arytm_3(k9_arytm_3(A, B), C)=k9_arytm_3(A, k9_arytm_3(B, C))) ) ) ) ) ) ).
fof(t52_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) => k10_arytm_3(k10_arytm_3(A, B), C)=k10_arytm_3(A, k10_arytm_3(B, C))) ) ) ) ) ) ).
fof(t53_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => k10_arytm_3(A, k12_arytm_3)=A) ) ).
fof(t54_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  ~ ( ( ~ (A=k11_arytm_3)  &  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ~ (k10_arytm_3(A, B)=1) ) ) ) ) ) ) ).
fof(t55_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ~ ( ( ~ (A=k11_arytm_3)  &  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  ~ (B=k10_arytm_3(A, C)) ) ) ) ) ) ) ) ) ).
fof(t57_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) => k10_arytm_3(A, k9_arytm_3(B, C))=k9_arytm_3(k10_arytm_3(A, B), k10_arytm_3(A, C))) ) ) ) ) ) ).
fof(t59_arytm_3, axiom,  (! [A] :  ( (v3_ordinal1(A) & m1_subset_1(A, k5_arytm_3))  =>  (! [B] :  ( (v3_ordinal1(B) & m1_subset_1(B, k5_arytm_3))  => k10_arytm_3(A, B)=k9_ordinal3(A, B)) ) ) ) ).
fof(t5_ordinal1, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(B, A) & r1_tarski(A, B)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t62_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (k9_arytm_3(B, C)=k9_arytm_3(A, C) => B=A) ) ) ) ) ) ) ).
fof(t63_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (k9_arytm_3(A, B)=k11_arytm_3 => A=k11_arytm_3) ) ) ) ) ).
fof(t64_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) => r3_arytm_3(k11_arytm_3, A)) ) ).
fof(t66_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ( (r3_arytm_3(A, B) & r3_arytm_3(B, A))  => A=B) ) ) ) ) ).
fof(t67_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  ( (r3_arytm_3(A, B) & r3_arytm_3(B, C))  => r3_arytm_3(A, C)) ) ) ) ) ) ) ).
fof(t68_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ( ~ (r3_arytm_3(B, A))  <=>  (r3_arytm_3(A, B) &  ~ (A=B) ) ) ) ) ) ) ).
fof(t69_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  ~ ( ( ( ( ~ (r3_arytm_3(B, A))  & r3_arytm_3(B, C))  |  (r3_arytm_3(A, B) &  ~ (r3_arytm_3(C, B)) ) )  & r3_arytm_3(C, A)) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_ordinal1, axiom,  (! [A] : r2_tarski(A, k1_ordinal1(A))) ).
fof(t70_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  ~ ( ( ~ (r3_arytm_3(B, A))  &  ( ~ (r3_arytm_3(C, B))  & r3_arytm_3(C, A)) ) ) ) ) ) ) ) ) ).
fof(t76_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (r3_arytm_3(k9_arytm_3(B, C), k9_arytm_3(A, C)) <=> r3_arytm_3(B, A)) ) ) ) ) ) ) ).
fof(t78_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ~ ( (k10_arytm_3(A, B)=k11_arytm_3 &  ( ~ (A=k11_arytm_3)  &  ~ (B=k11_arytm_3) ) ) ) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_xboole_1, axiom,  (! [A] :  (! [B] : r1_tarski(A, k2_xboole_0(A, B))) ) ).
fof(t80_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (r3_arytm_3(k10_arytm_3(B, C), k10_arytm_3(A, C)) =>  (C=k11_arytm_3 | r3_arytm_3(B, A)) ) ) ) ) ) ) ) ).
fof(t82_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (r3_arytm_3(B, A) => r3_arytm_3(k10_arytm_3(B, C), k10_arytm_3(A, C))) ) ) ) ) ) ) ).
fof(t83_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  (! [D] :  (m1_subset_1(D, k5_arytm_3) =>  ~ ( (k10_arytm_3(A, B)=k10_arytm_3(C, D) &  ( ~ (r3_arytm_3(A, C))  &  ~ (r3_arytm_3(B, D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t84_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  (A=k11_arytm_3 <=> k9_arytm_3(A, B)=B) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t92_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ~ ( (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  ( ~ (k9_arytm_3(A, C)=B)  &  ~ (k9_arytm_3(B, C)=A) ) ) ) ) ) ) ) ) ).
fof(t93_arytm_3, axiom,  (! [A] :  (m1_subset_1(A, k5_arytm_3) =>  (! [B] :  (m1_subset_1(B, k5_arytm_3) =>  ~ ( ( ~ (r3_arytm_3(B, A))  &  (! [C] :  (m1_subset_1(C, k5_arytm_3) =>  ~ ( ( ~ (r3_arytm_3(C, A))  &  ~ (r3_arytm_3(B, C)) ) ) ) ) ) ) ) ) ) ) ).
