% Mizar problem: t63_rewrite1,rewrite1,2490,5 
fof(t63_rewrite1, conjecture,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m2_rewrite1(B, A) => r12_rewrite1(A, B)) ) ) ) ).
fof(cc10_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_rewrite1(A))  =>  (v1_relat_1(A) & v4_rewrite1(A)) ) ) ).
fof(cc11_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_rewrite1(A) & v4_rewrite1(A)) )  =>  (v1_relat_1(A) & v8_rewrite1(A)) ) ) ).
fof(cc13_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_rewrite1(A) & v9_rewrite1(A)) )  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc14_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v10_rewrite1(A))  =>  (v1_relat_1(A) &  (v3_rewrite1(A) & v7_rewrite1(A)) ) ) ) ).
fof(cc15_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v3_rewrite1(A) & v7_rewrite1(A)) )  =>  (v1_relat_1(A) & v10_rewrite1(A)) ) ) ).
fof(cc2_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_rewrite1(A))  =>  (v1_relat_1(A) &  (v2_relat_2(A) & v1_rewrite1(A)) ) ) ) ).
fof(cc3_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v2_relat_2(A) & v1_rewrite1(A)) )  =>  (v1_relat_1(A) & v3_rewrite1(A)) ) ) ).
fof(cc5_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_rewrite1(A))  =>  (v1_relat_1(A) & v2_rewrite1(A)) ) ) ).
fof(cc6_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_rewrite1(A))  =>  (v1_relat_1(A) & v7_rewrite1(A)) ) ) ).
fof(cc7_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v7_rewrite1(A))  =>  (v1_relat_1(A) &  (v8_rewrite1(A) & v9_rewrite1(A)) ) ) ) ).
fof(cc9_rewrite1, axiom,  (! [A] :  ( (v1_relat_1(A) & v8_rewrite1(A))  =>  (v1_relat_1(A) & v5_rewrite1(A)) ) ) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(B, A)) ).
fof(d23_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (v8_rewrite1(A) <=>  (! [B] :  (! [C] :  (r2_rewrite1(A, B, C) => r5_rewrite1(A, B, C)) ) ) ) ) ) ).
fof(d26_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (r12_rewrite1(A, B) <=>  (! [C] :  (! [D] :  (r2_rewrite1(A, C, D) <=> r2_rewrite1(B, C, D)) ) ) ) ) ) ) ) ).
fof(d28_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  ( (v1_relat_1(B) & v10_rewrite1(B))  =>  (m2_rewrite1(B, A) <=>  (! [C] :  (! [D] :  (r2_rewrite1(A, C, D) <=> r5_rewrite1(B, C, D)) ) ) ) ) ) ) ) ).
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(d7_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (! [C] :  (r5_rewrite1(A, B, C) <=>  (? [D] :  (r1_rewrite1(A, B, D) & r1_rewrite1(A, C, D)) ) ) ) ) ) ) ).
fof(d8_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (! [C] :  (r6_rewrite1(A, B, C) <=>  (? [D] :  (r1_rewrite1(A, D, B) & r1_rewrite1(A, D, C)) ) ) ) ) ) ) ).
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(dt_m2_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m2_rewrite1(B, A) =>  (v1_relat_1(B) & v10_rewrite1(B)) ) ) ) ) ).
fof(existence_m2_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (? [B] : m2_rewrite1(B, A)) ) ) ).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(symmetry_r12_rewrite1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  =>  (r12_rewrite1(A, B) => r12_rewrite1(B, A)) ) ) ).
fof(t37_rewrite1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (! [C] :  ( (r5_rewrite1(A, B, C) | r6_rewrite1(A, B, C))  => r2_rewrite1(A, B, C)) ) ) ) ) ).
