% Mizar problem: t181_member_1,member_1,3503,25 
fof(t181_member_1, conjecture,  (! [A] :  (v1_membered(A) =>  (! [B] :  (v1_xcmplx_0(B) => k21_member_1(A, B)=k5_member_1(k19_member_1(A, B))) ) ) ) ).
fof(commutativity_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k1_xxreal_3(A, B)=k1_xxreal_3(B, A)) ) ).
fof(involutiveness_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k2_xxreal_3(k2_xxreal_3(A))=A) ) ).
fof(dt_k1_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k1_xxreal_3(A, B))) ) ).
fof(dt_k2_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => v1_xxreal_0(k2_xxreal_3(A))) ) ).
fof(fc10_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v2_xxreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc11_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(B, A)) & v2_xxreal_0(k1_xxreal_3(B, A))) ) ) ).
fof(fc12_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v3_xxreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc13_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(B, A)) & v3_xxreal_0(k1_xxreal_3(B, A))) ) ) ).
fof(fc14_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  =>  (v1_xxreal_0(k2_xxreal_3(A)) &  ~ (v3_xxreal_0(k2_xxreal_3(A))) ) ) ) ).
fof(fc15_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  =>  (v1_xxreal_0(k2_xxreal_3(A)) &  ~ (v2_xxreal_0(k2_xxreal_3(A))) ) ) ) ).
fof(fc16_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  (v1_xxreal_0(k2_xxreal_3(A)) & v3_xxreal_0(k2_xxreal_3(A))) ) ) ).
fof(fc17_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  (v1_xxreal_0(k2_xxreal_3(A)) & v2_xxreal_0(k2_xxreal_3(A))) ) ) ).
fof(fc1_xxreal_3, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xxreal_0(k2_xxreal_3(A)) & v1_xreal_0(k2_xxreal_3(A))) ) ) ).
fof(fc2_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) & v1_xreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc43_xxreal_3, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  =>  (v7_ordinal1(k1_xxreal_3(A, B)) & v1_xxreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) &  (v1_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) )  =>  ~ (v1_xreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc5_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  (v2_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) )  &  (v1_xxreal_0(B) &  (v2_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v1_xreal_0(k1_xxreal_3(A, B))) ) ) ) ).
fof(fc6_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) )  &  (v1_xxreal_0(B) &  (v3_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v1_xreal_0(k1_xxreal_3(A, B))) ) ) ) ).
fof(fc7_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) )  &  (v1_xxreal_0(B) &  (v2_xxreal_0(B) &  ~ (v1_xreal_0(B)) ) ) )  =>  (v8_ordinal1(k1_xxreal_3(A, B)) & v1_xxreal_0(k1_xxreal_3(A, B))) ) ) ).
fof(fc8_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k1_xxreal_3(A, B))) ) ) ) ).
fof(fc9_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k1_xxreal_3(A, B)) &  ~ (v2_xxreal_0(k1_xxreal_3(A, B))) ) ) ) ).
fof(ie1_xxreal_3, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xcmplx_0(C) & v1_xcmplx_0(D)) ) )  =>  ( (A=C & B=D)  => k1_xxreal_3(A, B)=k2_xcmplx_0(C, D)) ) ) ).
fof(ie2_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xcmplx_0(B))  =>  (A=B => k2_xxreal_3(A)=k4_xcmplx_0(B)) ) ) ).
fof(involutiveness_k1_member_1, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => k1_member_1(k1_member_1(A))=A) ) ).
fof(commutativity_k9_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k9_xxreal_3(A, B)=k9_xxreal_3(B, A)) ) ).
fof(redefinition_k1_member_1, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => k1_member_1(A)=k2_xxreal_3(A)) ) ).
fof(redefinition_k9_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => k9_xxreal_3(A, B)=k1_xxreal_3(A, B)) ) ).
fof(dt_k1_member_1, axiom,  (! [A] :  (m1_subset_1(A, k6_numbers) => m1_subset_1(k1_member_1(A), k6_numbers)) ) ).
fof(dt_k6_numbers, axiom, $true).
fof(dt_k9_xxreal_3, axiom,  (! [A, B] :  ( (m1_subset_1(A, k6_numbers) & m1_subset_1(B, k6_numbers))  => m1_subset_1(k9_xxreal_3(A, B), k6_numbers)) ) ).
fof(fc2_membered, axiom, v2_membered(k6_numbers)).
fof(fraenkel_a_1_0_member_1, axiom,  (! [A, B] :  (v2_membered(B) =>  (r2_hidden(A, a_1_0_member_1(B)) <=>  (? [C] :  (m1_subset_1(C, k6_numbers) &  (A=k1_member_1(C) & r2_tarski(C, B)) ) ) ) ) ) ).
fof(fraenkel_a_2_0_member_1, axiom,  (! [A, B, C] :  ( (v2_membered(B) & v2_membered(C))  =>  (r2_hidden(A, a_2_0_member_1(B, C)) <=>  (? [D, E] :  ( (m1_subset_1(D, k6_numbers) & m1_subset_1(E, k6_numbers))  &  (A=k9_xxreal_3(D, E) &  (r2_tarski(D, B) & r2_tarski(E, C)) ) ) ) ) ) ) ).
fof(involutiveness_k4_member_1, axiom,  (! [A] :  (v2_membered(A) => k4_member_1(k4_member_1(A))=A) ) ).
fof(commutativity_k8_member_1, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => k8_member_1(A, B)=k8_member_1(B, A)) ) ).
fof(dt_k10_member_1, axiom, $true).
fof(dt_k18_member_1, axiom, $true).
fof(dt_k20_member_1, axiom, $true).
fof(dt_k4_member_1, axiom,  (! [A] :  (v2_membered(A) => v2_membered(k4_member_1(A))) ) ).
fof(dt_k8_member_1, axiom, $true).
fof(fc16_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v2_membered(B))  => v1_xboole_0(k8_member_1(A, B))) ) ).
fof(fc17_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v2_membered(B))  => v1_xboole_0(k8_member_1(B, A))) ) ).
fof(fc18_member_1, axiom,  (! [A, B] :  ( ( (v2_membered(A) &  ~ (v1_xboole_0(A)) )  &  (v2_membered(B) &  ~ (v1_xboole_0(B)) ) )  =>  ~ (v1_xboole_0(k8_member_1(A, B))) ) ) ).
fof(fc19_member_1, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => v2_membered(k8_member_1(A, B))) ) ).
fof(fc28_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v2_membered(B))  => v1_xboole_0(k10_member_1(A, B))) ) ).
fof(fc29_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v2_membered(B))  => v1_xboole_0(k10_member_1(B, A))) ) ).
fof(fc30_member_1, axiom,  (! [A, B] :  ( ( (v2_membered(A) &  ~ (v1_xboole_0(A)) )  &  (v2_membered(B) &  ~ (v1_xboole_0(B)) ) )  =>  ~ (v1_xboole_0(k10_member_1(A, B))) ) ) ).
fof(fc31_member_1, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => v2_membered(k10_member_1(A, B))) ) ).
fof(fc3_member_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v2_membered(k4_member_1(A)) & v1_xboole_0(k4_member_1(A))) ) ) ).
fof(fc4_member_1, axiom,  (! [A] :  ( (v2_membered(A) &  ~ (v1_xboole_0(A)) )  =>  (v2_membered(k4_member_1(A)) &  ~ (v1_xboole_0(k4_member_1(A))) ) ) ) ).
fof(fc71_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xxreal_0(B))  => v1_xboole_0(k18_member_1(A, B))) ) ).
fof(fc72_member_1, axiom,  (! [A, B] :  ( ( (v2_membered(A) &  ~ (v1_xboole_0(A)) )  & v1_xxreal_0(B))  =>  ~ (v1_xboole_0(k18_member_1(A, B))) ) ) ).
fof(fc73_member_1, axiom,  (! [A, B] :  ( (v2_membered(A) & v1_xxreal_0(B))  => v2_membered(k18_member_1(A, B))) ) ).
fof(fc80_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xxreal_0(B))  => v1_xboole_0(k20_member_1(A, B))) ) ).
fof(fc81_member_1, axiom,  (! [A, B] :  ( ( (v2_membered(A) &  ~ (v1_xboole_0(A)) )  & v1_xxreal_0(B))  =>  ~ (v1_xboole_0(k20_member_1(A, B))) ) ) ).
fof(fc82_member_1, axiom,  (! [A, B] :  ( (v2_membered(A) & v1_xxreal_0(B))  => v2_membered(k20_member_1(A, B))) ) ).
fof(d7_member_1, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (v2_membered(B) => k10_member_1(A, B)=k8_member_1(A, k4_member_1(B))) ) ) ) ).
fof(d15_member_1, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (v1_xxreal_0(B) => k18_member_1(A, B)=k10_member_1(k1_tarski(B), A)) ) ) ) ).
fof(d17_member_1, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (v1_xxreal_0(B) => k20_member_1(A, B)=k10_member_1(A, k1_tarski(B))) ) ) ) ).
fof(d1_member_1, axiom,  (! [A] :  (v2_membered(A) => k4_member_1(A)=a_1_0_member_1(A)) ) ).
fof(d5_member_1, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (v2_membered(B) => k8_member_1(A, B)=a_2_0_member_1(A, B)) ) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(ie1_member_1, axiom,  (! [A, B] :  ( (v3_membered(A) & v2_membered(B))  =>  (A=B => k5_member_1(A)=k4_member_1(B)) ) ) ).
fof(ie3_member_1, axiom,  (! [A, B, C, D] :  ( (v3_membered(A) &  (v3_membered(B) &  (v2_membered(C) & v2_membered(D)) ) )  =>  ( (A=C & B=D)  => k9_member_1(A, B)=k8_member_1(C, D)) ) ) ).
fof(ie4_member_1, axiom,  (! [A, B, C, D] :  ( (v3_membered(A) &  (v3_membered(B) &  (v2_membered(C) & v2_membered(D)) ) )  =>  ( (A=C & B=D)  => k11_member_1(A, B)=k10_member_1(C, D)) ) ) ).
fof(ie8_member_1, axiom,  (! [A, B, C, D] :  ( (v3_membered(A) &  (v2_membered(B) &  (v1_xreal_0(C) & v1_xxreal_0(D)) ) )  =>  ( (A=B & C=D)  => k19_member_1(A, C)=k18_member_1(B, D)) ) ) ).
fof(ie9_member_1, axiom,  (! [A, B, C, D] :  ( (v3_membered(A) &  (v2_membered(B) &  (v1_xreal_0(C) & v1_xxreal_0(D)) ) )  =>  ( (A=B & C=D)  => k21_member_1(A, C)=k20_member_1(B, D)) ) ) ).
fof(cc1_rat_1, axiom,  (! [A] :  (v1_rat_1(A) => v1_xreal_0(A)) ) ).
fof(cc1_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v3_xxreal_0(A))  &  ~ (v1_xreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc2_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v1_xreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(fc10_membered, axiom,  (! [A] :  (v1_rat_1(A) => v4_membered(k1_tarski(A))) ) ).
fof(fc24_member_1, axiom,  (! [A, B] :  ( (v3_membered(A) & v3_membered(B))  => v3_membered(k9_member_1(A, B))) ) ).
fof(fc25_member_1, axiom,  (! [A, B] :  ( (v4_membered(A) & v4_membered(B))  => v4_membered(k9_member_1(A, B))) ) ).
fof(fc2_rat_1, axiom,  (! [A, B] :  ( (v1_rat_1(A) & v1_rat_1(B))  => v1_rat_1(k2_xcmplx_0(A, B))) ) ).
fof(fc36_member_1, axiom,  (! [A, B] :  ( (v3_membered(A) & v3_membered(B))  => v3_membered(k11_member_1(A, B))) ) ).
fof(fc37_member_1, axiom,  (! [A, B] :  ( (v4_membered(A) & v4_membered(B))  => v4_membered(k11_member_1(A, B))) ) ).
fof(fc5_rat_1, axiom,  (! [A] :  (v1_rat_1(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_rat_1(k4_xcmplx_0(A))) ) ) ).
fof(fc77_member_1, axiom,  (! [A, B] :  ( (v3_membered(A) & v1_xreal_0(B))  => v3_membered(k19_member_1(A, B))) ) ).
fof(fc78_member_1, axiom,  (! [A, B] :  ( (v4_membered(A) & v1_rat_1(B))  => v4_membered(k19_member_1(A, B))) ) ).
fof(fc7_member_1, axiom,  (! [A] :  (v3_membered(A) =>  (v1_membered(k5_member_1(A)) & v3_membered(k5_member_1(A))) ) ) ).
fof(fc86_member_1, axiom,  (! [A, B] :  ( (v3_membered(A) & v1_xreal_0(B))  => v3_membered(k21_member_1(A, B))) ) ).
fof(fc87_member_1, axiom,  (! [A, B] :  ( (v4_membered(A) & v1_rat_1(B))  => v4_membered(k21_member_1(A, B))) ) ).
fof(fc8_member_1, axiom,  (! [A] :  (v4_membered(A) =>  (v1_membered(k5_member_1(A)) & v4_membered(k5_member_1(A))) ) ) ).
fof(fc8_membered, axiom,  (! [A] :  (v1_xxreal_0(A) => v2_membered(k1_tarski(A))) ) ).
fof(rc1_int_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_int_1(A)) ) ) ) ).
fof(rc1_rat_1, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v1_xcmplx_0(A) &  (v1_xreal_0(A) & v1_rat_1(A)) ) ) ) ).
fof(rc1_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v2_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) ) ) ).
fof(rc2_rat_1, axiom,  (? [A] : v1_rat_1(A)) ).
fof(rc2_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(dt_o_0_0_xboole_0, axiom, v1_xboole_0(o_0_0_xboole_0)).
fof(cc10_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_rat_1, axiom,  (! [A] :  (v1_int_1(A) => v1_rat_1(A)) ) ).
fof(cc3_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(fc10_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(fc11_membered, axiom,  (! [A] :  (v1_int_1(A) => v5_membered(k1_tarski(A))) ) ).
fof(fc11_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc12_xreal_0, axiom,  (! [A, B] :  ( ( (v2_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  => v2_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc13_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc14_xreal_0, axiom,  (! [A, B] :  ( ( (v3_xxreal_0(A) & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  => v3_xxreal_0(k2_xcmplx_0(B, A))) ) ).
fof(fc15_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v3_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc16_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k4_xcmplx_0(A)) &  ~ (v2_xxreal_0(k4_xcmplx_0(A))) ) ) ) ).
fof(fc1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k2_xcmplx_0(A, B))) ) ).
fof(fc26_member_1, axiom,  (! [A, B] :  ( (v5_membered(A) & v5_membered(B))  => v5_membered(k9_member_1(A, B))) ) ).
fof(fc38_member_1, axiom,  (! [A, B] :  ( (v5_membered(A) & v5_membered(B))  => v5_membered(k11_member_1(A, B))) ) ).
fof(fc3_int_1, axiom,  (! [A] :  (v1_int_1(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A))) ) ) ).
fof(fc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A))) ) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(A, B))) ) ).
fof(fc79_member_1, axiom,  (! [A, B] :  ( (v5_membered(A) & v1_int_1(B))  => v5_membered(k19_member_1(A, B))) ) ).
fof(fc88_member_1, axiom,  (! [A, B] :  ( (v5_membered(A) & v1_int_1(B))  => v5_membered(k21_member_1(A, B))) ) ).
fof(fc8_int_1, axiom,  (! [A, B] :  ( (v2_int_1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc9_member_1, axiom,  (! [A] :  (v5_membered(A) =>  (v1_membered(k5_member_1(A)) & v5_membered(k5_member_1(A))) ) ) ).
fof(fc9_membered, axiom,  (! [A] :  (v1_xreal_0(A) => v3_membered(k1_tarski(A))) ) ).
fof(fc9_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k2_xcmplx_0(A, B))) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(asymmetry_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) =>  ~ (r2_tarski(B, A)) ) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc16_ordinal1, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) )  =>  (! [B] :  (m1_subset_1(B, A) =>  ~ (v8_ordinal1(B)) ) ) ) ) ).
fof(cc17_ordinal1, axiom,  (! [A] :  ( ~ (v10_ordinal1(A))  => v1_setfam_1(A)) ) ).
fof(cc18_ordinal1, axiom,  (! [A] :  (v10_ordinal1(A) =>  ~ (v1_setfam_1(A)) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc2_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v1_int_1(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc4_int_1, axiom,  (! [A] :  (v7_ordinal1(A) => v2_int_1(A)) ) ).
fof(cc4_nat_1, axiom,  (! [A] :  ( (v7_ordinal1(A) & v8_ordinal1(A))  =>  (v7_ordinal1(A) &  ~ (v2_xxreal_0(A)) ) ) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc6_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  =>  ~ (v1_xboole_0(A)) ) ) ).
fof(cc6_ordinal1, axiom,  (! [A] :  (v7_ordinal1(A) => v3_ordinal1(A)) ) ).
fof(fc11_nat_1, axiom,  (! [A] :  ( ~ (v8_ordinal1(A))  => v1_setfam_1(k1_tarski(A))) ) ).
fof(fc12_membered, axiom,  (! [A] :  (v7_ordinal1(A) => v6_membered(k1_tarski(A))) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc27_member_1, axiom,  (! [A, B] :  ( (v6_membered(A) & v6_membered(B))  => v6_membered(k9_member_1(A, B))) ) ).
fof(fc3_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(A, B))) ) ) ).
fof(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
fof(fc6_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k4_xcmplx_0(A)))  & v1_xcmplx_0(k4_xcmplx_0(A))) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_xcmplx_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xcmplx_0(A)) ) ).
fof(rc4_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc6_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc7_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v7_ordinal1(A)) ) ).
fof(rc8_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(rc9_ordinal1, axiom,  (? [A] : v8_ordinal1(A)) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=o_0_0_xboole_0).
fof(commutativity_k2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(A, B)=k2_xcmplx_0(B, A)) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(fc20_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_membered(B))  => v1_xboole_0(k9_member_1(A, B))) ) ).
fof(fc21_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_membered(B))  => v1_xboole_0(k9_member_1(B, A))) ) ).
fof(fc22_member_1, axiom,  (! [A, B] :  ( ( (v1_membered(A) &  ~ (v1_xboole_0(A)) )  &  (v1_membered(B) &  ~ (v1_xboole_0(B)) ) )  =>  ~ (v1_xboole_0(k9_member_1(A, B))) ) ) ).
fof(fc2_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(fc32_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_membered(B))  => v1_xboole_0(k11_member_1(A, B))) ) ).
fof(fc33_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_membered(B))  => v1_xboole_0(k11_member_1(B, A))) ) ).
fof(fc34_member_1, axiom,  (! [A, B] :  ( ( (v1_membered(A) &  ~ (v1_xboole_0(A)) )  &  (v1_membered(B) &  ~ (v1_xboole_0(B)) ) )  =>  ~ (v1_xboole_0(k11_member_1(A, B))) ) ) ).
fof(fc5_member_1, axiom,  (! [A] :  (v1_xboole_0(A) =>  (v1_membered(k5_member_1(A)) & v1_xboole_0(k5_member_1(A))) ) ) ).
fof(fc6_member_1, axiom,  (! [A] :  ( (v1_membered(A) &  ~ (v1_xboole_0(A)) )  =>  (v1_membered(k5_member_1(A)) &  ~ (v1_xboole_0(k5_member_1(A))) ) ) ) ).
fof(fc74_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xcmplx_0(B))  => v1_xboole_0(k19_member_1(A, B))) ) ).
fof(fc75_member_1, axiom,  (! [A, B] :  ( ( (v1_membered(A) &  ~ (v1_xboole_0(A)) )  & v1_xcmplx_0(B))  =>  ~ (v1_xboole_0(k19_member_1(A, B))) ) ) ).
fof(fc83_member_1, axiom,  (! [A, B] :  ( (v1_xboole_0(A) & v1_xcmplx_0(B))  => v1_xboole_0(k21_member_1(A, B))) ) ).
fof(fc84_member_1, axiom,  (! [A, B] :  ( ( (v1_membered(A) &  ~ (v1_xboole_0(A)) )  & v1_xcmplx_0(B))  =>  ~ (v1_xboole_0(k21_member_1(A, B))) ) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(spc6_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k2_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(A, k2_xcmplx_0(B, C))) ) ).
fof(spc8_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k2_xcmplx_0(k4_xcmplx_0(A), k4_xcmplx_0(B))=k4_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(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)) ) ) ) ) ).
fof(dt_k1_tarski, axiom, $true).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc7_membered, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_membered(k1_tarski(A))) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(fraenkel_a_1_1_member_1, axiom,  (! [A, B] :  (v1_membered(B) =>  (r2_hidden(A, a_1_1_member_1(B)) <=>  (? [C] :  (v1_xcmplx_0(C) &  (A=k4_xcmplx_0(C) & r2_hidden(C, B)) ) ) ) ) ) ).
fof(fraenkel_a_2_1_member_1, axiom,  (! [A, B, C] :  ( (v1_membered(B) & v1_membered(C))  =>  (r2_hidden(A, a_2_1_member_1(B, C)) <=>  (? [D, E] :  ( (v1_xcmplx_0(D) & v1_xcmplx_0(E))  &  (A=k2_xcmplx_0(D, E) &  (r2_hidden(D, B) & r2_hidden(E, C)) ) ) ) ) ) ) ).
fof(involutiveness_k5_member_1, axiom,  (! [A] :  (v1_membered(A) => k5_member_1(k5_member_1(A))=A) ) ).
fof(commutativity_k9_member_1, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => k9_member_1(A, B)=k9_member_1(B, A)) ) ).
fof(dt_k11_member_1, axiom, $true).
fof(dt_k19_member_1, axiom, $true).
fof(dt_k21_member_1, axiom, $true).
fof(dt_k5_member_1, axiom,  (! [A] :  (v1_membered(A) => v1_membered(k5_member_1(A))) ) ).
fof(dt_k9_member_1, axiom, $true).
fof(fc23_member_1, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => v1_membered(k9_member_1(A, B))) ) ).
fof(fc35_member_1, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => v1_membered(k11_member_1(A, B))) ) ).
fof(fc76_member_1, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_xcmplx_0(B))  => v1_membered(k19_member_1(A, B))) ) ).
fof(fc85_member_1, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_xcmplx_0(B))  => v1_membered(k21_member_1(A, B))) ) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(d8_member_1, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (v1_membered(B) => k11_member_1(A, B)=k9_member_1(A, k5_member_1(B))) ) ) ) ).
fof(d16_member_1, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (v1_xcmplx_0(B) => k19_member_1(A, B)=k11_member_1(k1_tarski(B), A)) ) ) ) ).
fof(d18_member_1, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (v1_xcmplx_0(B) => k21_member_1(A, B)=k11_member_1(A, k1_tarski(B))) ) ) ) ).
fof(d2_member_1, axiom,  (! [A] :  (v1_membered(A) => k5_member_1(A)=a_1_1_member_1(A)) ) ).
fof(d6_member_1, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (v1_membered(B) => k9_member_1(A, B)=a_2_1_member_1(A, B)) ) ) ) ).
fof(t71_member_1, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (v1_membered(B) => k5_member_1(k11_member_1(A, B))=k9_member_1(k5_member_1(A), B)) ) ) ) ).
