% Mizar problem: t19_arytm_1,arytm_1,492,5 
fof(t19_arytm_1, conjecture,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  (A=k11_arytm_3 =>  (B=k11_arytm_3 | k2_arytm_1(A, B)=k4_tarski(k11_arytm_3, B)) ) ) ) ) ) ).
fof(connectedness_r1_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_arytm_2) & m1_subset_1(B, k2_arytm_2))  =>  (r1_arytm_2(A, B) | r1_arytm_2(B, A)) ) ) ).
fof(d2_arytm_1, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  ( (r1_arytm_2(B, A) => k2_arytm_1(A, B)=k1_arytm_1(A, B))  &  ( ~ (r1_arytm_2(B, A))  => k2_arytm_1(A, B)=k4_tarski(k11_arytm_3, k1_arytm_1(B, A))) ) ) ) ) ) ).
fof(dt_k11_arytm_3, axiom, m1_subset_1(k11_arytm_3, k5_arytm_3)).
fof(dt_k1_arytm_1, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_arytm_2) & m1_subset_1(B, k2_arytm_2))  => m1_subset_1(k1_arytm_1(A, B), k2_arytm_2)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_arytm_1, axiom, $true).
fof(dt_k2_arytm_2, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_arytm_3, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(l16_arytm_1, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  (A=k11_arytm_3 => k1_arytm_1(B, A)=B) ) ) ) ) ).
fof(redefinition_k11_arytm_3, axiom, k11_arytm_3=k1_xboole_0).
fof(t4_arytm_1, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  ( (r1_arytm_2(A, B) & r1_arytm_2(B, A))  => A=B) ) ) ) ) ).
fof(t6_arytm_1, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  (A=k11_arytm_3 => r1_arytm_2(A, B)) ) ) ) ) ).
