% Mizar problem: t6_arytm_1,arytm_1,99,5 
fof(t6_arytm_1, conjecture,  (! [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)) ) ) ) ) ).
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_k5_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_arytm_2) & m1_subset_1(B, k1_arytm_2))  => k5_arytm_2(A, B)=k5_arytm_2(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(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(d8_arytm_2, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) =>  (! [B] :  (m1_subset_1(B, k2_arytm_2) =>  ( (B=k11_arytm_3 => k7_arytm_2(A, B)=A)  &  ( (A=k11_arytm_3 => k7_arytm_2(A, B)=B)  &  ~ ( ( ~ (B=k11_arytm_3)  &  ( ~ (A=k11_arytm_3)  &  ~ (k7_arytm_2(A, B)=k4_arytm_2(k5_arytm_2(k3_arytm_2(A), k3_arytm_2(B)))) ) ) ) ) ) ) ) ) ) ).
fof(dt_k11_arytm_3, axiom, m1_subset_1(k11_arytm_3, k5_arytm_3)).
fof(dt_k1_arytm_2, axiom, m1_subset_1(k1_arytm_2, k1_zfmisc_1(k1_zfmisc_1(k5_arytm_3)))).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_arytm_2, axiom, $true).
fof(dt_k3_arytm_2, axiom,  (! [A] :  (m1_subset_1(A, k2_arytm_2) => m2_subset_1(k3_arytm_2(A), k1_zfmisc_1(k5_arytm_3), k1_arytm_2)) ) ).
fof(dt_k4_arytm_2, axiom,  (! [A] :  (m1_subset_1(A, k1_arytm_2) => m1_subset_1(k4_arytm_2(A), k2_arytm_2)) ) ).
fof(dt_k5_arytm_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_arytm_2) & m1_subset_1(B, k1_arytm_2))  => m2_subset_1(k5_arytm_2(A, B), k1_zfmisc_1(k5_arytm_3), k1_arytm_2)) ) ).
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_m1_subset_1, axiom, $true).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (? [C] : m2_subset_1(C, A, B)) ) ) ).
fof(redefinition_k11_arytm_3, axiom, k11_arytm_3=k1_xboole_0).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  & m1_subset_1(B, k1_zfmisc_1(A))) )  =>  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
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(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
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(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
