% Mizar problem: l49_mod_2,mod_2,774,5 
fof(l49_mod_2, conjecture,  (! [A] :  (m1_subset_1(A, k1_enumset1(k5_numbers, 1, 2)) =>  (! [B] :  (m1_subset_1(B, k1_enumset1(k5_numbers, 1, 2)) =>  (! [C] :  (m1_subset_1(C, k1_enumset1(k5_numbers, 1, 2)) =>  (! [D] :  (m1_subset_1(D, k1_enumset1(k5_numbers, 1, 2)) =>  (D=k5_numbers =>  (k11_mod_2(A, k10_mod_2(A))=D &  (k11_mod_2(A, D)=A & k11_mod_2(k11_mod_2(A, B), C)=k11_mod_2(A, k11_mod_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(d12_mod_2, axiom,  (! [A] :  (m1_subset_1(A, k1_enumset1(k5_numbers, 1, 2)) =>  ( (A=k5_numbers => k10_mod_2(A)=k5_numbers)  &  ( (A=1 => k10_mod_2(A)=2)  &  (A=2 => k10_mod_2(A)=1) ) ) ) ) ).
fof(d13_mod_2, axiom,  (! [A] :  (m1_subset_1(A, k1_enumset1(k5_numbers, 1, 2)) =>  (! [B] :  (m1_subset_1(B, k1_enumset1(k5_numbers, 1, 2)) =>  ( (A=k5_numbers => k11_mod_2(A, B)=B)  &  ( (B=k5_numbers => k11_mod_2(A, B)=A)  &  ( ( (A=1 & B=1)  => k11_mod_2(A, B)=2)  &  ( ( (A=1 & B=2)  => k11_mod_2(A, B)=k5_numbers)  &  ( ( (A=2 & B=1)  => k11_mod_2(A, B)=k5_numbers)  &  ( (A=2 & B=2)  => k11_mod_2(A, B)=1) ) ) ) ) ) ) ) ) ) ).
fof(d13_ordinal1, axiom, k5_ordinal1=k1_xboole_0).
fof(d1_enumset1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (D=k1_enumset1(A, B, C) <=>  (! [E] :  (r2_hidden(E, D) <=>  ~ ( ( ~ (E=A)  &  ( ~ (E=B)  &  ~ (E=C) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k10_mod_2, axiom,  (! [A] :  (m1_subset_1(A, k1_enumset1(k5_numbers, 1, 2)) => m1_subset_1(k10_mod_2(A), k1_enumset1(k5_numbers, 1, 2))) ) ).
fof(dt_k11_mod_2, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_enumset1(k5_numbers, 1, 2)) & m1_subset_1(B, k1_enumset1(k5_numbers, 1, 2)))  => m1_subset_1(k11_mod_2(A, B), k1_enumset1(k5_numbers, 1, 2))) ) ).
fof(dt_k1_enumset1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc2_subset_1, axiom,  (! [A, B, C] :  ~ (v1_xboole_0(k1_enumset1(A, B, C))) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
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(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_tarski(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
