% Mizar problem: l10_arytm_1,arytm_1,134,5 
fof(l10_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) =>  (r1_arytm_2(k8_arytm_2(A, B), k8_arytm_2(A, C)) =>  (A=k11_arytm_3 | r1_arytm_2(B, C)) ) ) ) ) ) ) ) ).
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(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(commutativity_k8_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_arytm_2) & m1_subset_1(B, k2_arytm_2))  => k8_arytm_2(A, B)=k8_arytm_2(B, A)) ) ).
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(dt_k11_arytm_3, axiom, m1_subset_1(k11_arytm_3, k5_arytm_3)).
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_3, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k2_arytm_2, axiom, $true).
fof(dt_k5_arytm_3, 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_k8_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k2_arytm_2) & m1_subset_1(B, k2_arytm_2))  => m1_subset_1(k8_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(l2_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) =>  (k8_arytm_2(A, B)=k8_arytm_2(A, C) =>  (A=k11_arytm_3 | B=C) ) ) ) ) ) ) ) ).
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_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t12_arytm_2, 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) => k8_arytm_2(A, k8_arytm_2(B, C))=k8_arytm_2(k8_arytm_2(A, B), C)) ) ) ) ) ) ).
fof(t13_arytm_2, 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) => k8_arytm_2(A, k7_arytm_2(B, C))=k7_arytm_2(k8_arytm_2(A, B), k8_arytm_2(A, C))) ) ) ) ) ) ).
fof(t14_arytm_2, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  ~ ( ( ~ (A=k11_arytm_3)  &  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  ~ (k8_arytm_2(A, B)=k12_arytm_3) ) ) ) ) ) ) ).
fof(t15_arytm_2, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  (A=k12_arytm_3 => k8_arytm_2(A, B)=B) ) ) ) ) ).
fof(t19_arytm_2, 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) =>  (A=k7_arytm_2(B, C) => r1_arytm_2(C, A)) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t20_arytm_2, axiom,  (r2_tarski(k11_arytm_3, k2_arytm_2) & r2_tarski(k12_arytm_3, k2_arytm_2)) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t9_arytm_2, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  ~ ( (r1_arytm_2(A, B) &  (! [C] :  (m1_subset_1(C, k2_arytm_2) =>  ~ (k7_arytm_2(A, C)=B) ) ) ) ) ) ) ) ) ).
