% Mizar problem: t11_arytm_3,arytm_3,273,5 
fof(t11_arytm_3, conjecture,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  =>  (! [B] :  ( (v3_ordinal1(B) & v7_ordinal1(B))  =>  (! [C] :  ( (v3_ordinal1(C) & v7_ordinal1(C))  =>  ( (r2_arytm_3(A, B) & r2_arytm_3(A, k8_ordinal3(B, C)))  => r2_arytm_3(A, C)) ) ) ) ) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(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_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(d3_arytm_3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (r2_arytm_3(A, B) <=>  (? [C] :  (v3_ordinal1(C) & B=k11_ordinal2(A, C)) ) ) ) ) ) ) ).
fof(dt_k10_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k10_ordinal2(A, B))) ) ).
fof(dt_k11_ordinal2, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k11_ordinal2(A, B))) ) ).
fof(dt_k5_ordinal3, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => v3_ordinal1(k5_ordinal3(A, B))) ) ).
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_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  => v3_ordinal1(k9_ordinal3(A, B))) ) ).
fof(fc3_ordinal3, axiom,  (! [A, B] :  ( ( (v3_ordinal1(A) & v7_ordinal1(A))  &  (v3_ordinal1(B) & v7_ordinal1(B)) )  =>  (v3_ordinal1(k5_ordinal3(A, B)) & v7_ordinal1(k5_ordinal3(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(fc5_ordinal2, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v3_ordinal1(k10_ordinal2(A, B)) & v7_ordinal1(k10_ordinal2(A, B))) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
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(reflexivity_r2_arytm_3, axiom,  (! [A, B] :  ( (v3_ordinal1(A) & v3_ordinal1(B))  => r2_arytm_3(A, A)) ) ).
fof(t52_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) => k5_ordinal3(k10_ordinal2(A, B), A)=B) ) ) ) ).
fof(t5_arytm_3, axiom,  (! [A] :  ( (v3_ordinal1(A) & v7_ordinal1(A))  =>  (! [B] :  ( (v3_ordinal1(B) & v7_ordinal1(B))  =>  (r2_arytm_3(A, B) <=>  (? [C] :  ( (v3_ordinal1(C) & v7_ordinal1(C))  & B=k9_ordinal3(A, C)) ) ) ) ) ) ) ).
fof(t63_ordinal3, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (v3_ordinal1(B) =>  (! [C] :  (v3_ordinal1(C) => k5_ordinal3(k11_ordinal2(A, C), k11_ordinal2(B, C))=k11_ordinal2(k5_ordinal3(A, B), C)) ) ) ) ) ) ).
