% Mizar problem: t105_xxreal_3,xxreal_3,3793,5 
fof(t105_xxreal_3, conjecture,  (! [A] :  (v1_xxreal_0(A) => k1_xxreal_3(k6_xxreal_3(A, 2), k6_xxreal_3(A, 2))=A) ) ).
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_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_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_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(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(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(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_xxreal_3, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v1_xxreal_0(k1_xxreal_3(A, B))) ) ).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_ordinal1, 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_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(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(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_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(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_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(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_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(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_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(fc1_int_1, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v1_int_1(k2_xcmplx_0(A, B))) ) ).
fof(fc1_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
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_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k2_xcmplx_0(A, B))) ) ).
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(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_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(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(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(fc4_nat_1, axiom,  (! [A, B] :  ( (v7_ordinal1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  =>  ~ (v8_ordinal1(k2_xcmplx_0(B, A))) ) ) ).
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_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_xcmplx_0, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_xcmplx_0(k7_xcmplx_0(A, B))) ) ).
fof(fc5_xreal_0, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v1_xreal_0(k2_xcmplx_0(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_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(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_int_1, axiom,  (! [A] :  (v2_int_1(A) => v7_ordinal1(k2_xcmplx_0(A, 1))) ) ).
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(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_int_1, axiom,  (! [A, B] :  ( (v2_int_1(A) &  (v7_ordinal1(B) &  ~ (v8_ordinal1(B)) ) )  => v7_ordinal1(k2_xcmplx_0(A, B))) ) ).
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(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_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(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(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(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_r2_tarski, axiom,  (! [A, B] :  (r2_tarski(A, B) <=> r2_hidden(A, B)) ) ).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, axiom, k2_xcmplx_0(k7_xcmplx_0(1, 2), k7_xcmplx_0(1, 2))=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r1_r1, axiom, k7_xcmplx_0(1, 1)=1).
fof(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, axiom, k7_xcmplx_0(1, 2)=k7_xcmplx_0(1, 2)).
fof(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, axiom, k7_xcmplx_0(1, k7_xcmplx_0(1, 2))=2).
fof(rqRealDiv__k7_xcmplx_0__r2_r1_r2, axiom, k7_xcmplx_0(2, 1)=2).
fof(rqRealDiv__k7_xcmplx_0__r2_r2_r1, axiom, k7_xcmplx_0(2, 2)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r1_r1, axiom, k3_xcmplx_0(1, 1)=1).
fof(rqRealMult__k3_xcmplx_0__r1_r2_r2, axiom, k3_xcmplx_0(1, 2)=2).
fof(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, axiom, k3_xcmplx_0(1, k7_xcmplx_0(1, 2))=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, axiom, k3_xcmplx_0(2, k7_xcmplx_0(1, 2))=1).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 1)=k7_xcmplx_0(1, 2)).
fof(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, axiom, k3_xcmplx_0(k7_xcmplx_0(1, 2), 2)=1).
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(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(1, A)=k5_xcmplx_0(A)) ) ).
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(spc5_arithm, axiom,  (! [A, B, C] :  ( (v1_xcmplx_0(A) &  (v1_xcmplx_0(B) & v1_xcmplx_0(C)) )  => k3_xcmplx_0(k2_xcmplx_0(A, B), C)=k2_xcmplx_0(k3_xcmplx_0(A, C), k3_xcmplx_0(B, C))) ) ).
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(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_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_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t66_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) => k4_xxreal_3(A, k4_xxreal_3(B, C))=k4_xxreal_3(k4_xxreal_3(A, B), C)) ) ) ) ) ) ).
fof(t6_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k7_xcmplx_0(A, 1)=A) ) ).
fof(t81_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k4_xxreal_3(1, A)=A) ) ).
fof(t94_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) => k4_xxreal_3(2, A)=k1_xxreal_3(A, A)) ) ).
fof(t95_xxreal_3, axiom,  (! [A] :  (v1_xxreal_0(A) =>  (! [B] :  (v1_xxreal_0(B) =>  (! [C] :  (v1_xxreal_0(C) =>  (v1_xreal_0(A) => k4_xxreal_3(A, k1_xxreal_3(B, C))=k1_xxreal_3(k4_xxreal_3(A, B), k4_xxreal_3(A, C))) ) ) ) ) ) ) ).
