% Mizar problem: t85_mcart_1,mcart_1,1320,17 
fof(t85_mcart_1, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (k13_mcart_1(k4_tarski(k4_tarski(A, B), C))=A &  (k14_mcart_1(k4_tarski(k4_tarski(A, B), C))=B &  (k15_mcart_1(k4_tarski(F, k4_tarski(D, E)))=D & k16_mcart_1(k4_tarski(F, k4_tarski(D, E)))=E) ) ) ) ) ) ) ) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc7_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(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(dt_k13_mcart_1, axiom, $true).
fof(dt_k14_mcart_1, axiom, $true).
fof(dt_k15_mcart_1, axiom, $true).
fof(dt_k16_mcart_1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(d14_mcart_1, axiom,  (! [A] : k13_mcart_1(A)=k1_xtuple_0(k1_xtuple_0(A))) ).
fof(d15_mcart_1, axiom,  (! [A] : k14_mcart_1(A)=k2_xtuple_0(k1_xtuple_0(A))) ).
fof(d16_mcart_1, axiom,  (! [A] : k15_mcart_1(A)=k1_xtuple_0(k2_xtuple_0(A))) ).
fof(d17_mcart_1, axiom,  (! [A] : k16_mcart_1(A)=k2_xtuple_0(k2_xtuple_0(A))) ).
fof(d5_tarski, axiom,  (! [A] :  (! [B] : k4_tarski(A, B)=k2_tarski(k2_tarski(A, B), k1_tarski(A))) ) ).
