% Mizar problem: t31_rewrite1,rewrite1,809,30 
fof(t31_rewrite1, conjecture,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (! [C] :  (r2_rewrite1(A, B, C) => r2_rewrite1(A, C, B)) ) ) ) ) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(A))) ) ).
fof(dt_k2_xboole_0, axiom, $true).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(d4_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (! [C] :  (r2_rewrite1(A, B, C) <=> r1_rewrite1(k2_xboole_0(A, k2_relat_1(A)), B, C)) ) ) ) ) ).
fof(l33_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (! [C] :  (r2_rewrite1(A, B, C) => r2_rewrite1(A, C, B)) ) ) ) ) ).
