% Mizar problem: t24_domain_1,domain_1,463,5 
fof(t24_domain_1, conjecture,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  (m1_subset_1(D, k1_zfmisc_1(A)) =>  (! [E] :  (m1_subset_1(E, k1_zfmisc_1(B)) =>  (! [F] :  (m1_subset_1(F, k1_zfmisc_1(C)) => k9_mcart_1(A, B, C, D, E, F)=a_6_0_domain_1(A, 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_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_mcart_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  (! [D] :  (m1_subset_1(D, k3_zfmisc_1(A, B, C)) => v2_xtuple_0(D)) ) ) ) ).
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(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(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(d10_xboole_0, axiom,  (! [A] :  (! [B] :  (A=B <=>  (r1_tarski(A, B) & r1_tarski(B, A)) ) ) ) ).
fof(d3_tarski, axiom,  (! [A] :  (! [B] :  (r1_tarski(A, B) <=>  (! [C] :  (r2_hidden(C, A) => r2_hidden(C, B)) ) ) ) ) ).
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(d6_xtuple_0, axiom,  (! [A] : k4_xtuple_0(A)=k1_xtuple_0(k1_xtuple_0(A))) ).
fof(d7_xtuple_0, axiom,  (! [A] : k5_xtuple_0(A)=k2_xtuple_0(k1_xtuple_0(A))) ).
fof(dt_k1_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k1_mcart_1(A, B, C, D), A)) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xtuple_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k2_mcart_1(A, B, C, D), B)) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xtuple_0, axiom, $true).
fof(dt_k3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => m1_subset_1(k3_mcart_1(A, B, C, D), C)) ) ).
fof(dt_k3_xtuple_0, axiom, $true).
fof(dt_k3_zfmisc_1, axiom, $true).
fof(dt_k4_domain_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (m1_subset_1(D, A) &  (m1_subset_1(E, B) & m1_subset_1(F, C)) ) ) ) )  => m1_subset_1(k4_domain_1(A, B, C, D, E, F), k3_zfmisc_1(A, B, C))) ) ).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xtuple_0, axiom, $true).
fof(dt_k5_xtuple_0, axiom, $true).
fof(dt_k9_mcart_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(D, k1_zfmisc_1(A)) &  (m1_subset_1(E, k1_zfmisc_1(B)) & m1_subset_1(F, k1_zfmisc_1(C))) )  => m1_subset_1(k9_mcart_1(A, B, C, D, E, F), k1_zfmisc_1(k3_zfmisc_1(A, B, C)))) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc11_subset_1, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ~ (v1_xboole_0(C)) ) )  =>  ~ (v1_xboole_0(k3_zfmisc_1(A, B, C))) ) ) ).
fof(fc1_subset_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_zfmisc_1(A))) ) ).
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(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(fraenkel_a_6_0_domain_1, axiom,  (! [A, B, C, D, E, F, G] :  ( ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  ( ~ (v1_xboole_0(D))  &  (m1_subset_1(E, k1_zfmisc_1(B)) &  (m1_subset_1(F, k1_zfmisc_1(C)) & m1_subset_1(G, k1_zfmisc_1(D))) ) ) ) )  =>  (r2_hidden(A, a_6_0_domain_1(B, C, D, E, F, G)) <=>  (? [H, I, J] :  ( (m1_subset_1(H, B) &  (m1_subset_1(I, C) & m1_subset_1(J, D)) )  &  (A=k4_domain_1(B, C, D, H, I, J) &  (r2_tarski(H, E) &  (r2_tarski(I, F) & r2_tarski(J, G)) ) ) ) ) ) ) ) ).
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_xboole_0, axiom,  (? [A] : v1_xboole_0(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_subset_1, axiom,  (! [A] :  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_xboole_0(B)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
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(rc4_subset_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (? [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) & v1_subset_1(B, 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(rd4_xtuple_0, axiom,  (! [A, B, C] : k4_xtuple_0(k3_xtuple_0(A, B, C))=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(rd7_xtuple_0, axiom,  (! [A] :  (v2_xtuple_0(A) => k3_xtuple_0(k4_xtuple_0(A), k5_xtuple_0(A), k2_xtuple_0(A))=A) ) ).
fof(redefinition_k1_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k1_mcart_1(A, B, C, D)=k4_xtuple_0(D)) ) ).
fof(redefinition_k2_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k2_mcart_1(A, B, C, D)=k5_xtuple_0(D)) ) ).
fof(redefinition_k3_mcart_1, axiom,  (! [A, B, C, D] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  & m1_subset_1(D, k3_zfmisc_1(A, B, C))) ) )  => k3_mcart_1(A, B, C, D)=k2_xtuple_0(D)) ) ).
fof(redefinition_k4_domain_1, axiom,  (! [A, B, C, D, E, F] :  ( ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xboole_0(B))  &  ( ~ (v1_xboole_0(C))  &  (m1_subset_1(D, A) &  (m1_subset_1(E, B) & m1_subset_1(F, C)) ) ) ) )  => k4_domain_1(A, B, C, D, E, F)=k3_xtuple_0(D, E, F)) ) ).
fof(redefinition_k9_mcart_1, axiom,  (! [A, B, C, D, E, F] :  ( (m1_subset_1(D, k1_zfmisc_1(A)) &  (m1_subset_1(E, k1_zfmisc_1(B)) & m1_subset_1(F, k1_zfmisc_1(C))) )  => k9_mcart_1(A, B, C, D, E, F)=k3_zfmisc_1(D, E, F)) ) ).
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(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t31_mcart_1, axiom,  (! [A] :  (! [B] :  (! [C] :  ( ( ~ (A=k1_xboole_0)  &  ( ~ (B=k1_xboole_0)  &  ~ (C=k1_xboole_0) ) )  <=>  ~ (k3_zfmisc_1(A, B, C)=k1_xboole_0) ) ) ) ) ).
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(t69_mcart_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  (! [E] :  (! [F] :  (r2_hidden(k3_xtuple_0(A, B, C), k3_zfmisc_1(D, E, F)) <=>  (r2_hidden(A, D) &  (r2_hidden(B, E) & r2_hidden(C, F)) ) ) ) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t72_mcart_1, axiom,  (! [A] :  ( ~ (v1_xboole_0(A))  =>  (! [B] :  ( ~ (v1_xboole_0(B))  =>  (! [C] :  ( ~ (v1_xboole_0(C))  =>  (! [D] :  ( ( ~ (v1_xboole_0(D))  & m1_subset_1(D, k1_zfmisc_1(A)))  =>  (! [E] :  ( ( ~ (v1_xboole_0(E))  & m1_subset_1(E, k1_zfmisc_1(B)))  =>  (! [F] :  ( ( ~ (v1_xboole_0(F))  & m1_subset_1(F, k1_zfmisc_1(C)))  =>  (! [G] :  (m1_subset_1(G, k3_zfmisc_1(A, B, C)) =>  (r2_tarski(G, k3_zfmisc_1(D, E, F)) =>  (r2_tarski(k1_mcart_1(A, B, C, G), D) &  (r2_tarski(k2_mcart_1(A, B, C, G), E) & r2_tarski(k3_mcart_1(A, B, C, G), F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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)) ) ) ) ) ).
