% Mizar problem: l27_latwal_1,latwal_1,1357,5 
fof(l27_latwal_1, conjecture,  (r2_hidden(2, k1_enumset1(k5_ordinal1, 1, 2)) &  (! [A] :  (m1_subset_1(A, k1_enumset1(k5_ordinal1, 1, 2)) =>  (! [B] :  (m1_subset_1(B, k1_enumset1(k5_ordinal1, 1, 2)) => r2_hidden(k4_xxreal_0(A, B), k1_enumset1(k5_ordinal1, 1, 2))) ) ) ) ) ).
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(cc3_latquasi, axiom,  (! [A] :  (m1_subset_1(A, k1_enumset1(k5_ordinal1, 1, 2)) => v1_xreal_0(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(commutativity_k4_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k4_xxreal_0(A, B)=k4_xxreal_0(B, A)) ) ).
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_k1_enumset1, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k4_xxreal_0(A, B))) ) ).
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_latquasi, axiom, v3_membered(k1_enumset1(k5_ordinal1, 1, 2))).
fof(fc2_subset_1, axiom,  (! [A, B, C] :  ~ (v1_xboole_0(k1_enumset1(A, B, C))) ) ).
fof(fc36_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k4_xxreal_0(A, B)) & v1_xreal_0(k4_xxreal_0(A, B))) ) ) ).
fof(idempotence_k4_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k4_xxreal_0(A, A)=A) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
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(t16_xxreal_0, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (k4_xxreal_0(A, B)=A | k4_xxreal_0(A, B)=B) ) ) ) ) ).
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)) ) ) ) ) ).
