% Mizar problem: l22_arytm_1,arytm_1,305,5 
fof(l22_arytm_1, conjecture,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  (! [C] :  (m1_subset_1(C, k2_arytm_2) => k1_arytm_1(k1_arytm_1(B, C), A)=k1_arytm_1(k1_arytm_1(B, A), C)) ) ) ) ) ) ).
fof(commutativity_k7_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_arytm_2) & m1_subset_1(B, k2_arytm_2))  => k7_arytm_2(A, B)=k7_arytm_2(B, A)) ) ).
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_k2_arytm_2, axiom, $true).
fof(dt_k7_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_arytm_2) & m1_subset_1(B, k2_arytm_2))  => m1_subset_1(k7_arytm_2(A, B), k2_arytm_2)) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(l21_arytm_1, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  (! [C] :  (m1_subset_1(C, k2_arytm_2) => k1_arytm_1(k1_arytm_1(C, B), A)=k1_arytm_1(C, k7_arytm_2(A, B))) ) ) ) ) ) ).
