% Mizar problem: t85_xxreal_3,xxreal_3,3345,5 
fof(t85_xxreal_3, conjecture,  (! [A] :  (v1_xxreal_0(A) =>  ~ ( ( ~ (r1_xxreal_0(k5_numbers, A))  &  ( ~ (k2_xxreal_0=A)  &  ~ (k6_xxreal_3(k1_xxreal_0, A)=k2_xxreal_0) ) ) ) ) ) ).
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(cc11_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v7_ordinal1(A)) ) ).
fof(cc12_ordinal1, axiom,  (! [A] :  (v8_ordinal1(A) => v1_zfmisc_1(A)) ) ).
fof(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(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(cc19_ordinal1, axiom,  (! [A] :  (v1_setfam_1(A) =>  ~ (v10_ordinal1(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(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => 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(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(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_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(A)) ) ).
fof(cc2_xcmplx_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xcmplx_0(A)) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_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_int_1, axiom,  (! [A] :  (v1_int_1(A) => v1_xreal_0(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(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(cc4_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc5_int_1, axiom,  (! [A] :  (v2_int_1(A) => v1_int_1(A)) ) ).
fof(cc5_nat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v8_ordinal1(A)) ) ).
fof(cc5_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, A) => v3_ordinal1(B)) ) ) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
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(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc7_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v7_ordinal1(A)) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v8_ordinal1(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc8_ordinal1, axiom,  (! [A] :  (m1_subset_1(A, k4_ordinal1) => v7_ordinal1(A)) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v8_ordinal1(A) & v1_xxreal_0(A)) ) ) ).
fof(cc9_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v6_ordinal1(A)) ) ).
fof(commutativity_k3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, B)=k3_xcmplx_0(B, A)) ) ).
fof(commutativity_k4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => k4_xxreal_3(A, B)=k4_xxreal_3(B, A)) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  =>  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ) ).
fof(d2_xxreal_0, axiom, k1_xxreal_0=k1_numbers).
fof(d3_xxreal_0, axiom, k2_xxreal_0=k4_tarski(k5_numbers, k1_numbers)).
fof(d5_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  ( ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (C=k4_xxreal_3(A, B) <=>  (? [D] :  (v1_xcmplx_0(D) &  (? [E] :  (v1_xcmplx_0(E) &  (A=D &  (B=E & C=k3_xcmplx_0(D, E)) ) ) ) ) ) ) )  &  ( ~ ( ( ~ ( (v1_xreal_0(A) & v1_xreal_0(B)) )  &  ( ( (v2_xxreal_0(A) & v2_xxreal_0(B))  |  (v3_xxreal_0(A) & v3_xxreal_0(B)) )  &  ~ ( (C=k4_xxreal_3(A, B) <=> C=k1_xxreal_0) ) ) ) )  &  ( ~ ( ( ~ ( (v1_xreal_0(A) & v1_xreal_0(B)) )  &  ( ( (v2_xxreal_0(A) & v3_xxreal_0(B))  |  (v3_xxreal_0(A) & v2_xxreal_0(B)) )  &  ~ ( (C=k4_xxreal_3(A, B) <=> C=k2_xxreal_0) ) ) ) )  &  ~ ( ( ~ ( (v1_xreal_0(A) & v1_xreal_0(B)) )  &  ( ~ ( ( ~ ( (v1_xreal_0(A) & v1_xreal_0(B)) )  &  ( (v2_xxreal_0(A) & v2_xxreal_0(B))  |  (v3_xxreal_0(A) & v3_xxreal_0(B)) ) ) )  &  ( ~ ( ( ~ ( (v1_xreal_0(A) & v1_xreal_0(B)) )  &  ( (v2_xxreal_0(A) & v3_xxreal_0(B))  |  (v3_xxreal_0(A) & v2_xxreal_0(B)) ) ) )  &  ~ ( (C=k4_xxreal_3(A, B) <=> C=k5_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d7_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) => k6_xxreal_3(A, B)=k4_xxreal_3(A, k5_xxreal_3(B))) ) ) ) ).
fof(d8_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) =>  (! [B] :  (v1_xcmplx_0(B) => k7_xcmplx_0(A, B)=k3_xcmplx_0(A, k5_xcmplx_0(B))) ) ) ) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_xxreal_0, axiom, $true).
fof(dt_k2_xxreal_0, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_tarski, axiom, $true).
fof(dt_k4_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k4_xxreal_3(A, B))) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A))) ) ).
fof(dt_k5_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => v1_xxreal_0(k5_xxreal_3(A))) ) ).
fof(dt_k6_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k6_xxreal_3(A, B))) ) ).
fof(dt_k7_xcmplx_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_xreal_0, axiom,  ~ (v1_xreal_0(k2_xxreal_0)) ).
fof(fc1_xxreal_0, axiom, v1_xxreal_0(k1_xxreal_0)).
fof(fc23_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc24_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k3_xcmplx_0(B, A))) ) ) ).
fof(fc24_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) & v3_xxreal_0(B)) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v3_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc25_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc25_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v3_xxreal_0(A))  &  (v1_xxreal_0(B) & v3_xxreal_0(B)) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v2_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc26_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k3_xcmplx_0(A, B))) ) ) ).
fof(fc26_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) & v2_xxreal_0(A))  &  (v1_xxreal_0(B) & v2_xxreal_0(B)) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v2_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc27_xreal_0, axiom,  (! [A] :  ( (v2_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v2_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc27_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) &  ~ (v2_xxreal_0(k4_xxreal_3(A, B))) ) ) ) ).
fof(fc28_xreal_0, axiom,  (! [A] :  ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v2_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc28_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k4_xxreal_3(A, B))) ) ) ) ).
fof(fc29_xreal_0, axiom,  (! [A] :  ( (v3_xxreal_0(A) & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v3_xxreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc29_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k4_xxreal_3(A, B))) ) ) ) ).
fof(fc2_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k3_xcmplx_0(A, B))) ) ).
fof(fc2_xreal_0, axiom,  ~ (v1_xreal_0(k1_xxreal_0)) ).
fof(fc2_xxreal_0, axiom, v1_xxreal_0(k2_xxreal_0)).
fof(fc30_xreal_0, axiom,  (! [A] :  ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  =>  (v1_xcmplx_0(k5_xcmplx_0(A)) &  ~ (v3_xxreal_0(k5_xcmplx_0(A))) ) ) ) ).
fof(fc30_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  =>  (v1_xxreal_0(k5_xxreal_3(A)) &  ~ (v2_xxreal_0(k5_xxreal_3(A))) ) ) ) ).
fof(fc31_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc31_xxreal_3, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  =>  (v1_xxreal_0(k5_xxreal_3(A)) &  ~ (v3_xxreal_0(k5_xxreal_3(A))) ) ) ) ).
fof(fc32_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v2_xxreal_0(k7_xcmplx_0(B, A))) ) ) ).
fof(fc32_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k6_xxreal_3(A, B)) &  ~ (v2_xxreal_0(k6_xxreal_3(A, B))) ) ) ) ).
fof(fc33_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v3_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v3_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc33_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k6_xxreal_3(B, A)) &  ~ (v2_xxreal_0(k6_xxreal_3(B, A))) ) ) ) ).
fof(fc34_xreal_0, axiom,  (! [A, B] :  ( ( ( ~ (v2_xxreal_0(A))  & v1_xreal_0(A))  &  ( ~ (v2_xxreal_0(B))  & v1_xreal_0(B)) )  =>  ~ (v3_xxreal_0(k7_xcmplx_0(A, B))) ) ) ).
fof(fc34_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v3_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k6_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k6_xxreal_3(A, B))) ) ) ) ).
fof(fc35_xxreal_3, axiom,  (! [A, B] :  ( ( (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) )  &  (v1_xxreal_0(B) &  ~ (v2_xxreal_0(B)) ) )  =>  (v1_xxreal_0(k6_xxreal_3(A, B)) &  ~ (v3_xxreal_0(k6_xxreal_3(A, B))) ) ) ) ).
fof(fc36_xxreal_3, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xxreal_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xxreal_0(B)) )  =>  ( ~ (v8_ordinal1(k4_xxreal_3(A, B)))  & v1_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc37_xxreal_3, axiom,  (! [A, B] :  ( ( (v8_ordinal1(A) & v1_xxreal_0(A))  & v1_xxreal_0(B))  =>  (v8_ordinal1(k4_xxreal_3(A, B)) & v1_xxreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc38_xxreal_3, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xxreal_0(k5_xxreal_3(A)) & v1_xreal_0(k5_xxreal_3(A))) ) ) ).
fof(fc39_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k4_xxreal_3(A, B)) & v1_xreal_0(k4_xxreal_3(A, B))) ) ) ).
fof(fc3_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(fc3_xxreal_0, axiom, v2_xxreal_0(k1_xxreal_0)).
fof(fc40_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  =>  (v1_xxreal_0(k6_xxreal_3(A, B)) & v1_xreal_0(k6_xxreal_3(A, B))) ) ) ).
fof(fc41_xxreal_3, axiom,  (v8_ordinal1(k5_xxreal_3(k2_xxreal_0)) & v1_xxreal_0(k5_xxreal_3(k2_xxreal_0))) ).
fof(fc42_xxreal_3, axiom,  (v8_ordinal1(k5_xxreal_3(k1_xxreal_0)) & v1_xxreal_0(k5_xxreal_3(k1_xxreal_0))) ).
fof(fc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) =>  (v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A))) ) ) ).
fof(fc4_xxreal_0, axiom, v3_xxreal_0(k2_xxreal_0)).
fof(fc5_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k7_xcmplx_0(A, B))) ) ).
fof(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k3_xcmplx_0(A, B))) ) ).
fof(fc7_xcmplx_0, axiom,  (! [A] :  ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  =>  ( ~ (v8_ordinal1(k5_xcmplx_0(A)))  & v1_xcmplx_0(k5_xcmplx_0(A))) ) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_xcmplx_0, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xcmplx_0(B)) )  =>  ~ (v8_ordinal1(k3_xcmplx_0(A, B))) ) ) ).
fof(fc8_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k7_xcmplx_0(A, B))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_xcmplx_0, axiom,  (! [A, B] :  ( ( ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A))  &  ( ~ (v8_ordinal1(B))  & v1_xcmplx_0(B)) )  =>  ~ (v8_ordinal1(k7_xcmplx_0(A, B))) ) ) ).
fof(ie4_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)  => k4_xxreal_3(A, B)=k3_xcmplx_0(C, D)) ) ) ).
fof(ie5_xxreal_3, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xcmplx_0(B))  =>  (A=B => k5_xxreal_3(A)=k5_xcmplx_0(B)) ) ) ).
fof(ie6_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)  => k6_xxreal_3(A, B)=k7_xcmplx_0(C, D)) ) ) ).
fof(involutiveness_k5_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A))=A) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(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_nat_1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc1_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v2_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) ) ) ).
fof(rc2_int_1, axiom,  (? [A] : v1_int_1(A)) ).
fof(rc2_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) & v8_ordinal1(A)) ) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_xxreal_3, axiom,  (? [A] :  (v1_xxreal_0(A) &  (v3_xxreal_0(A) &  ~ (v1_xreal_0(A)) ) ) ) ).
fof(rc3_int_1, axiom,  (? [A] : v2_int_1(A)) ).
fof(rc3_nat_1, axiom,  (? [A] :  (v7_ordinal1(A) &  ~ (v8_ordinal1(A)) ) ) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(A)) ) ) ) ).
fof(rc3_xcmplx_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xcmplx_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(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc4_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_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(rc4_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc5_ordinal1, axiom,  (? [A] : v7_ordinal1(A)) ).
fof(rc5_xcmplx_0, axiom,  (? [A] :  ( ~ (v8_ordinal1(A))  & v1_xcmplx_0(A)) ) ).
fof(rc5_xreal_0, axiom,  (? [A] :  (v8_ordinal1(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc5_xxreal_0, axiom,  (? [A] :  (v8_ordinal1(A) & v1_xxreal_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(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => r1_xxreal_0(A, A)) ) ).
fof(spc10_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k5_xcmplx_0(k3_xcmplx_0(A, B))) ) ).
fof(spc11_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k7_xcmplx_0(k5_xcmplx_0(A), k5_xcmplx_0(B))=k7_xcmplx_0(B, A)) ) ).
fof(spc12_arithm, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => k3_xcmplx_0(A, k5_xcmplx_0(B))=k7_xcmplx_0(A, B)) ) ).
fof(spc4_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(A, k7_xcmplx_0(B, C))=k7_xcmplx_0(k3_xcmplx_0(A, B), C)) ) ).
fof(spc7_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k3_xcmplx_0(A, B), C)=k3_xcmplx_0(A, k3_xcmplx_0(B, C))) ) ).
fof(t1_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k5_numbers)=k5_numbers) ) ).
fof(t2_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t4_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t5_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers, A)=k5_numbers) ) ).
fof(t5_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ) ) ).
fof(t6_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (r1_xxreal_0(A, B) =>  (v8_ordinal1(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ) ) ).
fof(t82_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  ~ ( (k5_xxreal_3(A)=k5_numbers &  ( ~ (A=k1_xxreal_0)  &  ( ~ (A=k2_xxreal_0)  &  ~ (A=k5_numbers) ) ) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ) ) ).
