% Mizar problem: t4_arytm_3,arytm_3,81,5 
fof(t4_arytm_3, conjecture,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  =>  (! [B] :  ( (v3_ordinal1(B) & v7_ordinal1(B))  =>  ~ ( ( ~ ( (A=k1_xboole_0 & B=k1_xboole_0) )  &  (! [C] :  ( (v3_ordinal1(C) & v7_ordinal1(C))  =>  (! [D] :  ( (v3_ordinal1(D) & v7_ordinal1(D))  =>  (! [E] :  ( (v3_ordinal1(E) & v7_ordinal1(E))  =>  ~ ( (r1_arytm_3(D, E) &  (A=k9_ordinal3(C, D) & B=k9_ordinal3(C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_ordinal1(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(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_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(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_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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
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_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(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(d12_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) <=> r2_hidden(A, k4_ordinal1)) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
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(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
fof(dt_k11_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k11_ordinal2(A, B))) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_ordinal1, axiom, $true).
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(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
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(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(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(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(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(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(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_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
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_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
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(s1_ordinal1__e4_5__arytm_3, axiom,  ( (? [A] :  (v3_ordinal1(A) &  (? [B] :  (v3_ordinal1(B) &  (r1_tarski(B, A) &  (r2_tarski(A, k4_ordinal1) &  ( ~ (A=k1_xboole_0)  &  (! [C] :  ( (v3_ordinal1(C) & v7_ordinal1(C))  =>  (! [D] :  ( (v3_ordinal1(D) & v7_ordinal1(D))  =>  (! [E] :  ( (v3_ordinal1(E) & v7_ordinal1(E))  =>  ~ ( (r1_arytm_3(D, E) &  (A=k9_ordinal3(C, D) & B=k9_ordinal3(C, E)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )  =>  (? [A] :  (v3_ordinal1(A) &  ( (? [F] :  (v3_ordinal1(F) &  (r1_tarski(F, A) &  (r2_tarski(A, k4_ordinal1) &  ( ~ (A=k1_xboole_0)  &  (! [G] :  ( (v3_ordinal1(G) & v7_ordinal1(G))  =>  (! [H] :  ( (v3_ordinal1(H) & v7_ordinal1(H))  =>  (! [I] :  ( (v3_ordinal1(I) & v7_ordinal1(I))  =>  ~ ( (r1_arytm_3(H, I) &  (A=k9_ordinal3(G, H) & F=k9_ordinal3(G, I)) ) ) ) ) ) ) ) ) ) ) ) ) )  &  (! [J] :  (v3_ordinal1(J) =>  ( (? [K] :  (v3_ordinal1(K) &  (r1_tarski(K, J) &  (r2_tarski(J, k4_ordinal1) &  ( ~ (J=k1_xboole_0)  &  (! [L] :  ( (v3_ordinal1(L) & v7_ordinal1(L))  =>  (! [M] :  ( (v3_ordinal1(M) & v7_ordinal1(M))  =>  (! [N] :  ( (v3_ordinal1(N) & v7_ordinal1(N))  =>  ~ ( (r1_arytm_3(M, N) &  (J=k9_ordinal3(L, M) & K=k9_ordinal3(L, N)) ) ) ) ) ) ) ) ) ) ) ) ) )  => r1_ordinal1(A, J)) ) ) ) ) ) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, 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(t12_ordinal1, axiom,  (! [A] :  (v1_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  ( (r1_tarski(A, B) & r2_tarski(B, C))  => r2_tarski(A, C)) ) ) ) ) ) ) ).
fof(t14_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ~ ( ( ~ (r2_tarski(A, B))  &  ( ~ (A=B)  &  ~ (r2_tarski(B, A)) ) ) ) ) ) ) ) ).
fof(t14_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (r2_tarski(A, 1) => A=k1_xboole_0) ) ) ).
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_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(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t35_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) => k11_ordinal2(k5_ordinal1, A)=k5_ordinal1) ) ).
fof(t35_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) =>  (r1_ordinal1(k11_ordinal2(B, A), k11_ordinal2(C, A)) =>  (A=k1_xboole_0 | r1_ordinal1(B, C)) ) ) ) ) ) ) ) ).
fof(t36_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  ( ~ (B=k1_xboole_0)  =>  (r1_ordinal1(A, k11_ordinal2(A, B)) & r1_ordinal1(A, k11_ordinal2(B, A))) ) ) ) ) ) ).
fof(t38_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) => k11_ordinal2(A, k5_ordinal1)=k5_ordinal1) ) ).
fof(t39_ordinal2, axiom,  (! [A] :  (v3_ordinal1(A) =>  (k11_ordinal2(1, A)=A & k11_ordinal2(A, 1)=A) ) ) ).
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(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(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(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)) ) ) ) ) ).
