% Mizar problem: t120_group_9,group_9,11701,73 
fof(t120_group_9, conjecture,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (A=k6_relat_1(k10_xtuple_0(A), B) <=> k2_relat_1(A)=k5_relat_1(k2_relat_1(B), k9_xtuple_0(k2_relat_1(A)))) ) ) ) ) ).
fof(involutiveness_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k2_relat_1(k2_relat_1(A))=A) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => v1_relat_1(k2_relat_1(A))) ) ).
fof(dt_k5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k5_relat_1(A, B))) ) ).
fof(dt_k6_relat_1, axiom,  (! [A, B] :  (v1_relat_1(B) => v1_relat_1(k6_relat_1(A, B))) ) ).
fof(dt_k9_xtuple_0, axiom, $true).
fof(rd4_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k5_relat_1(A, k9_xtuple_0(A))=A) ) ).
fof(rd5_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => k5_relat_1(k5_relat_1(A, B), B)=k5_relat_1(A, B)) ) ).
fof(rd6_relat_1, axiom,  (! [A] :  (v1_relat_1(A) => k6_relat_1(k10_xtuple_0(A), A)=A) ) ).
fof(rd7_relat_1, axiom,  (! [A, B] :  (v1_relat_1(B) => k6_relat_1(A, k6_relat_1(A, B))=k6_relat_1(A, B)) ) ).
fof(l167_group_9, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (v1_relat_1(B) =>  (A=k6_relat_1(k10_xtuple_0(A), B) <=> k2_relat_1(A)=k5_relat_1(k2_relat_1(B), k9_xtuple_0(k2_relat_1(A)))) ) ) ) ) ).
