% Mizar problem: t83_mcart_1,mcart_1,1194,5 
fof(t83_mcart_1, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( ~ (v1_xboole_0(D))  =>  (! [E] :  ( ( ~ (v1_xboole_0(E))  & m1_subset_1(E, k1_zfmisc_1(A)))  =>  (! [F] :  ( ( ~ (v1_xboole_0(F))  & m1_subset_1(F, k1_zfmisc_1(B)))  =>  (! [G] :  ( ( ~ (v1_xboole_0(G))  & m1_subset_1(G, k1_zfmisc_1(C)))  =>  (! [H] :  ( ( ~ (v1_xboole_0(H))  & m1_subset_1(H, k1_zfmisc_1(D)))  =>  (! [I] :  (m1_subset_1(I, k4_zfmisc_1(A, B, C, D)) =>  (r2_tarski(I, k4_zfmisc_1(E, F, G, H)) =>  (r2_tarski(k4_mcart_1(A, B, C, D, I), E) &  (r2_tarski(k5_mcart_1(A, B, C, D, I), F) &  (r2_tarski(k6_mcart_1(A, B, C, D, I), G) & r2_tarski(k7_mcart_1(A, B, C, D, I), H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_xboole_0(B)) ) ) ) ).
fof(cc1_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => v1_xtuple_0(A)) ) ).
fof(cc2_relat_1, axiom,  (! [A] :  (v1_relat_1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_relat_1(B)) ) ) ) ).
fof(cc2_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ( ~ (v1_subset_1(B, A))  =>  ~ (v1_xboole_0(B)) ) ) ) ) ) ).
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(cc3_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  (v1_xboole_0(B) => v1_subset_1(B, A)) ) ) ) ) ).
fof(cc4_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v2_relat_1(A)) ) ) ).
fof(cc4_subset_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) =>  ~ (v1_subset_1(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(d7_xtuple_0, axiom,  (! [A] : k5_xtuple_0(A)=k2_xtuple_0(k1_xtuple_0(A))) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_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_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_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_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_xboole_0(B)) ) ) ) ) ).
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_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xtuple_0, axiom,  (? [A] : v2_xtuple_0(A)) ).
fof(rc3_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) &  ~ (v1_subset_1(B, A)) ) ) ) ).
fof(rc3_xtuple_0, axiom,  (? [A] : v3_xtuple_0(A)) ).
fof(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, A)) ) ) ) ).
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(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
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(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
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)) ) ) ) ) ).
