% Mizar problem: t22_xtuple_0,xtuple_0,583,5 
fof(t22_xtuple_0, conjecture,  (! [A] :  (v3_xtuple_0(A) =>  (! [B] :  (v3_xtuple_0(B) =>  ( (k7_xtuple_0(A)=k7_xtuple_0(B) &  (k8_xtuple_0(A)=k8_xtuple_0(B) &  (k5_xtuple_0(A)=k5_xtuple_0(B) & k2_xtuple_0(A)=k2_xtuple_0(B)) ) )  => A=B) ) ) ) ) ).
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(cc1_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc2_xtuple_0, axiom,  (! [A] :  (v3_xtuple_0(A) => v2_xtuple_0(A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(d10_xtuple_0, axiom,  (! [A] : k7_xtuple_0(A)=k1_xtuple_0(k1_xtuple_0(k1_xtuple_0(A)))) ).
fof(d11_xtuple_0, axiom,  (! [A] : k8_xtuple_0(A)=k2_xtuple_0(k1_xtuple_0(k1_xtuple_0(A)))) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(d4_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] : k3_xtuple_0(A, B, C)=k4_tarski(k4_tarski(A, B), C)) ) ) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
fof(d7_xtuple_0, axiom,  (! [A] : k5_xtuple_0(A)=k2_xtuple_0(k1_xtuple_0(A))) ).
fof(d8_xtuple_0, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k6_xtuple_0(A, B, C, D)=k4_tarski(k3_xtuple_0(A, B, C), D)) ) ) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k5_xtuple_0, axiom, $true).
fof(dt_k6_xtuple_0, axiom, $true).
fof(dt_k7_xtuple_0, axiom, $true).
fof(dt_k8_xtuple_0, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc2_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(fc3_xboole_0, axiom,  (! [A, B] :  ~ (v1_xboole_0(k2_tarski(A, B))) ) ).
fof(fc3_xtuple_0, axiom,  (! [A, B, C, D] : v3_xtuple_0(k6_xtuple_0(A, B, C, D))) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc3_xtuple_0, axiom,  (? [A] : v3_xtuple_0(A)) ).
fof(rd10_xtuple_0, axiom,  (! [A, B, C, D] : k5_xtuple_0(k6_xtuple_0(A, B, C, D))=C) ).
fof(rd11_xtuple_0, axiom,  (! [A, B, C, D] : k2_xtuple_0(k6_xtuple_0(A, B, C, D))=D) ).
fof(rd12_xtuple_0, axiom,  (! [A] :  (v3_xtuple_0(A) => k6_xtuple_0(k7_xtuple_0(A), k8_xtuple_0(A), k5_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(rd1_xtuple_0, axiom,  (! [A, B] : k1_xtuple_0(k4_tarski(A, B))=A) ).
fof(rd2_xtuple_0, axiom,  (! [A, B] : k2_xtuple_0(k4_tarski(A, B))=B) ).
fof(rd3_xtuple_0, axiom,  (! [A] :  (v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(rd5_xtuple_0, axiom,  (! [A, B, C] : k5_xtuple_0(k3_xtuple_0(A, B, C))=B) ).
fof(rd6_xtuple_0, axiom,  (! [A, B, C] : k2_xtuple_0(k3_xtuple_0(A, B, C))=C) ).
fof(rd8_xtuple_0, axiom,  (! [A, B, C, D] : k7_xtuple_0(k6_xtuple_0(A, B, C, D))=A) ).
fof(rd9_xtuple_0, axiom,  (! [A, B, C, D] : k8_xtuple_0(k6_xtuple_0(A, B, C, D))=B) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(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)) ) ) ) ) ).
