% Mizar problem: t27_xxreal_3,xxreal_3,790,5 
fof(t27_xxreal_3, conjecture,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (k2_xxreal_3(k1_xxreal_3(k2_xxreal_3(A), B))=k3_xxreal_3(A, B) & k2_xxreal_3(k1_xxreal_3(k2_xxreal_3(A), B))=k1_xxreal_3(A, k2_xxreal_3(B))) ) ) ) ) ).
fof(commutativity_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k1_xxreal_3(A, B)=k1_xxreal_3(B, A)) ) ).
fof(d4_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) => k3_xxreal_3(A, B)=k1_xxreal_3(A, k2_xxreal_3(B))) ) ) ) ).
fof(dt_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k1_xxreal_3(A, B))) ) ).
fof(dt_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => v1_xxreal_0(k2_xxreal_3(A))) ) ).
fof(dt_k3_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k3_xxreal_3(A, B))) ) ).
fof(involutiveness_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k2_xxreal_3(k2_xxreal_3(A))=A) ) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(t25_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) => k2_xxreal_3(k1_xxreal_3(A, B))=k3_xxreal_3(k2_xxreal_3(B), A)) ) ) ) ).
