% Mizar problem: t75_mcart_1,mcart_1,1051,5 
fof(t75_mcart_1, conjecture,  (! [A] :  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  ( ~ (v1_xboole_0(E))  =>  (! [F] :  (m1_subset_1(F, k4_zfmisc_1(B, C, D, E)) =>  ( (! [G] :  (m1_subset_1(G, B) =>  (! [H] :  (m1_subset_1(H, C) =>  (! [I] :  (m1_subset_1(I, D) =>  (! [J] :  (m1_subset_1(J, E) =>  (F=k6_xtuple_0(G, H, I, J) => A=G) ) ) ) ) ) ) ) )  => A=k4_mcart_1(B, C, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ).
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_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(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(cc3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ~ (v1_xboole_0(D)) ) ) )  =>  (! [E] :  (m1_subset_1(E, k4_zfmisc_1(A, B, C, D)) => v3_xtuple_0(E)) ) ) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(A)) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(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_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => m1_subset_1(k4_mcart_1(A, B, C, D, E), A)) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_zfmisc_1, axiom, $true).
fof(dt_k5_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => m1_subset_1(k5_mcart_1(A, B, C, D, E), B)) ) ).
fof(dt_k5_xtuple_0, axiom, $true).
fof(dt_k6_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => m1_subset_1(k6_mcart_1(A, B, C, D, E), C)) ) ).
fof(dt_k6_xtuple_0, axiom, $true).
fof(dt_k7_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => m1_subset_1(k7_mcart_1(A, B, C, D, E), D)) ) ).
fof(dt_k7_xtuple_0, axiom, $true).
fof(dt_k8_xtuple_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc12_subset_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ~ (v1_xboole_0(D)) ) ) )  =>  ~ (v1_xboole_0(k4_zfmisc_1(A, B, C, D))) ) ) ).
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(fc7_relat_1, axiom,  (! [A, B, C, D] : v1_relat_1(k2_tarski(k4_tarski(A, B), k4_tarski(C, D)))) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_xtuple_0, axiom,  (? [A] : v1_xtuple_0(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(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_k4_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => k4_mcart_1(A, B, C, D, E)=k7_xtuple_0(E)) ) ).
fof(redefinition_k5_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => k5_mcart_1(A, B, C, D, E)=k8_xtuple_0(E)) ) ).
fof(redefinition_k6_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => k6_mcart_1(A, B, C, D, E)=k5_xtuple_0(E)) ) ).
fof(redefinition_k7_mcart_1, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  & m1_subset_1(E, k4_zfmisc_1(A, B, C, D))) ) ) )  => k7_mcart_1(A, B, C, D, E)=k2_xtuple_0(E)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(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)) ) ) ) ) ).
