% Mizar problem: t61_mcart_1,mcart_1,858,5 
fof(t61_mcart_1, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k4_zfmisc_1(k1_tarski(A), k1_tarski(B), k1_tarski(C), k1_tarski(D))=k1_tarski(k6_xtuple_0(A, B, C, D))) ) ) ) ).
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(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(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_k2_tarski, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k3_zfmisc_1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_zfmisc_1, axiom, $true).
fof(dt_k6_xtuple_0, axiom, $true).
fof(fc1_xtuple_0, axiom,  (! [A, B] : v1_xtuple_0(k4_tarski(A, B))) ).
fof(fc2_xtuple_0, axiom,  (! [A, B, C] : v2_xtuple_0(k3_xtuple_0(A, B, C))) ).
fof(fc3_xtuple_0, axiom,  (! [A, B, C, D] : v3_xtuple_0(k6_xtuple_0(A, B, C, D))) ).
fof(fc5_relat_1, axiom,  (! [A, B] : v1_relat_1(k1_tarski(k4_tarski(A, B)))) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(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(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc3_xtuple_0, axiom,  (? [A] : v3_xtuple_0(A)) ).
fof(t29_zfmisc_1, axiom,  (! [A] :  (! [B] : k2_zfmisc_1(k1_tarski(A), k1_tarski(B))=k1_tarski(k4_tarski(A, B))) ) ).
fof(t35_mcart_1, axiom,  (! [A] :  (! [B] :  (! [C] : k3_zfmisc_1(k1_tarski(A), k1_tarski(B), k1_tarski(C))=k1_tarski(k3_xtuple_0(A, B, C))) ) ) ).
fof(t50_mcart_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] : k3_zfmisc_1(k2_zfmisc_1(A, B), C, D)=k4_zfmisc_1(A, B, C, D)) ) ) ) ).
