% Mizar problem: t9_quatern2,quatern2,160,5 
fof(t9_quatern2, conjecture,  (! [A] :  (v1_quaterni(A) =>  (! [B] :  (v1_xreal_0(B) => k20_quaterni(k4_xcmplx_0(B), A)=k23_quaterni(k20_quaterni(B, 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(cc10_ordinal1, axiom,  (! [A] :  (v6_ordinal1(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_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(cc13_ordinal1, axiom,  (! [A] :  ( ~ (v1_zfmisc_1(A))  =>  ~ (v8_ordinal1(A)) ) ) ).
fof(cc14_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) =>  ~ (v10_ordinal1(A)) ) ) ).
fof(cc15_ordinal1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v9_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_ordinal1, axiom,  (! [A] :  (v3_ordinal1(A) =>  (v1_ordinal1(A) & v2_ordinal1(A)) ) ) ).
fof(cc1_quaterni, axiom,  (! [A] :  (m1_subset_1(A, k1_quaterni) => v1_quaterni(A)) ) ).
fof(cc1_relat_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_relat_1(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc20_ordinal1, axiom,  (! [A] :  ( ~ (v1_setfam_1(A))  => v10_ordinal1(A)) ) ).
fof(cc2_ordinal1, axiom,  (! [A] :  ( (v1_ordinal1(A) & v2_ordinal1(A))  => v3_ordinal1(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_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(cc3_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_ordinal1(A)) ) ).
fof(cc3_relat_1, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v3_relat_1(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_ordinal1, axiom,  (! [A] :  (v1_xboole_0(A) => v5_ordinal1(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_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_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_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_k21_quaterni, axiom,  (! [A, B] :  ( (v1_quaterni(A) & v1_quaterni(B))  => k21_quaterni(A, B)=k21_quaterni(B, A)) ) ).
fof(commutativity_k2_tarski, axiom,  (! [A, B] : k2_tarski(A, B)=k2_tarski(B, A)) ).
fof(commutativity_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, B)=k2_xboole_0(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_k6_quaterni, axiom,  (! [A, B] :  ( (v1_quaterni(A) & v1_quaterni(B))  => k6_quaterni(A, B)=k6_quaterni(B, A)) ) ).
fof(d10_quaterni, axiom, k10_quaterni=k5_quaterni(k5_numbers, k5_numbers, 1, k5_numbers)).
fof(d11_quaterni, axiom, k11_quaterni=k5_quaterni(k5_numbers, k5_numbers, k5_numbers, 1)).
fof(d1_quaterni, axiom, k1_quaterni=k2_xboole_0(k6_subset_1(k9_funct_2(4, k1_numbers), a_0_0_quaterni), k2_numbers)).
fof(d1_xcmplx_0, axiom, k1_xcmplx_0=k7_funct_4(k4_ordinal1, k5_numbers, 1, k5_numbers, 1)).
fof(d21_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => k25_quaterni(A)=k21_quaterni(k21_quaterni(k18_quaterni(k12_quaterni(A), k20_quaterni(k4_xcmplx_0(k13_quaterni(A)), k1_xcmplx_0)), k20_quaterni(k4_xcmplx_0(k14_quaterni(A)), k10_quaterni)), k20_quaterni(k4_xcmplx_0(k15_quaterni(A)), k11_quaterni))) ) ).
fof(d3_quaterni, axiom, k3_quaterni=k2_quaterni(k4_ordinal1, k5_numbers, 1, 2, 3, k5_numbers, k5_numbers, 1, k5_numbers)).
fof(d4_quaterni, axiom, k4_quaterni=k2_quaterni(k4_ordinal1, k5_numbers, 1, 2, 3, k5_numbers, k5_numbers, k5_numbers, 1)).
fof(d5_arytm_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) =>  (! [B] :  (m1_subset_1(B, k1_numbers) =>  ( (B=k5_numbers => k5_arytm_0(A, B)=A)  &  ( ~ (B=k5_numbers)  => k5_arytm_0(A, B)=k7_funct_4(k1_numbers, k5_numbers, 1, A, B)) ) ) ) ) ) ).
fof(d7_quaterni, axiom,  (! [A] :  (v1_quaterni(A) =>  (! [B] :  (v1_quaterni(B) =>  (B=k7_quaterni(A) <=> k6_quaterni(A, B)=k5_numbers) ) ) ) ) ).
fof(d8_quaterni, axiom,  (! [A] :  (v1_quaterni(A) =>  (! [B] :  (v1_quaterni(B) => k8_quaterni(A, B)=k6_quaterni(A, k7_quaterni(B))) ) ) ) ).
fof(dt_k10_quaterni, axiom, m1_subset_1(k10_quaterni, k1_quaterni)).
fof(dt_k10_subset_1, axiom,  (! [A, B] : m1_subset_1(k10_subset_1(A, B), B)) ).
fof(dt_k11_quaterni, axiom, m1_subset_1(k11_quaterni, k1_quaterni)).
fof(dt_k12_funct_4, axiom, $true).
fof(dt_k12_quaterni, axiom, $true).
fof(dt_k13_quaterni, axiom, $true).
fof(dt_k14_quaterni, axiom, $true).
fof(dt_k15_quaterni, axiom, $true).
fof(dt_k18_quaterni, axiom, $true).
fof(dt_k1_funct_1, axiom, $true).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_quaterni, axiom, $true).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_xcmplx_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k20_quaterni, axiom, $true).
fof(dt_k21_quaterni, axiom,  (! [A, B] :  ( (v1_quaterni(A) & v1_quaterni(B))  => m1_subset_1(k21_quaterni(A, B), k1_quaterni)) ) ).
fof(dt_k23_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => m1_subset_1(k23_quaterni(A), k1_quaterni)) ) ).
fof(dt_k25_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_quaterni(k25_quaterni(A))) ) ).
fof(dt_k2_enumset1, axiom, $true).
fof(dt_k2_numbers, axiom, $true).
fof(dt_k2_quaterni, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(F, A) &  (m1_subset_1(G, A) &  (m1_subset_1(H, A) & m1_subset_1(I, A)) ) ) )  =>  (v1_funct_1(k2_quaterni(A, B, C, D, E, F, G, H, I)) &  (v1_funct_2(k2_quaterni(A, B, C, D, E, F, G, H, I), k2_enumset1(B, C, D, E), A) & m1_subset_1(k2_quaterni(A, B, C, D, E, F, G, H, I), k1_zfmisc_1(k2_zfmisc_1(k2_enumset1(B, C, D, E), A)))) ) ) ) ).
fof(dt_k2_tarski, axiom, $true).
fof(dt_k2_xboole_0, axiom, $true).
fof(dt_k2_xcmplx_0, axiom, $true).
fof(dt_k2_zfmisc_1, axiom, $true).
fof(dt_k3_quaterni, axiom, $true).
fof(dt_k3_xcmplx_0, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_quaterni, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
fof(dt_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A))) ) ).
fof(dt_k5_arytm_0, axiom,  (! [A, B] :  ( (m1_subset_1(A, k1_numbers) & m1_subset_1(B, k1_numbers))  => m1_subset_1(k5_arytm_0(A, B), k2_numbers)) ) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k4_ordinal1)).
fof(dt_k5_ordinal1, axiom, $true).
fof(dt_k5_quaterni, axiom,  (! [A, B, C, D] :  ( (v1_xreal_0(A) &  (v1_xreal_0(B) &  (v1_xreal_0(C) & v1_xreal_0(D)) ) )  => m1_subset_1(k5_quaterni(A, B, C, D), k1_quaterni)) ) ).
fof(dt_k6_funct_4, axiom, $true).
fof(dt_k6_quaterni, axiom, $true).
fof(dt_k6_subset_1, axiom,  (! [A, B] : m1_subset_1(k6_subset_1(A, B), k1_zfmisc_1(A))) ).
fof(dt_k7_funct_4, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) )  =>  (v1_funct_1(k7_funct_4(A, B, C, D, E)) &  (v1_funct_2(k7_funct_4(A, B, C, D, E), k2_tarski(B, C), A) & m1_subset_1(k7_funct_4(A, B, C, D, E), k1_zfmisc_1(k2_zfmisc_1(k2_tarski(B, C), A)))) ) ) ) ).
fof(dt_k7_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_quaterni(k7_quaterni(A))) ) ).
fof(dt_k8_quaterni, axiom, $true).
fof(dt_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => m1_funct_2(k9_funct_2(A, B), A, B)) ) ).
fof(dt_m1_funct_2, axiom,  (! [A, B] :  (! [C] :  (m1_funct_2(C, A, B) =>  ~ (v1_xboole_0(C)) ) ) ) ).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) =>  (v1_funct_1(D) &  (v1_funct_2(D, A, B) & m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) ) ) ) ) ) ).
fof(existence_m1_funct_2, axiom,  (! [A, B] :  (? [C] : m1_funct_2(C, A, B)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (? [D] : m2_funct_2(D, A, B, C)) ) ) ).
fof(fc10_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k15_quaterni(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_quaterni, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_quaterni(B))  => v1_quaterni(k18_quaterni(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(fc12_quaterni, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_quaterni(B))  => v1_quaterni(k20_quaterni(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_quaterni, axiom,  ~ (v1_xboole_0(k1_quaterni)) ).
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(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(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(fc2_quaterni, axiom, v1_quaterni(k1_xcmplx_0)).
fof(fc2_relat_1, axiom,  (! [A, B] :  (v1_relat_1(A) => v1_relat_1(k4_xboole_0(A, B))) ) ).
fof(fc3_quaterni, axiom, v1_quaterni(k3_quaterni)).
fof(fc3_relat_1, axiom,  (! [A, B] :  ( (v1_relat_1(A) & v1_relat_1(B))  => v1_relat_1(k2_xboole_0(A, B))) ) ).
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(fc4_quaterni, axiom, v1_quaterni(k4_quaterni)).
fof(fc5_quaterni, axiom,  (! [A, B] :  ( (v1_quaterni(A) & v1_quaterni(B))  => v1_quaterni(k6_quaterni(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(fc6_ordinal1, axiom,  ( ~ (v1_xboole_0(k4_ordinal1))  & v3_ordinal1(k4_ordinal1)) ).
fof(fc6_relat_1, axiom,  (! [A, B] : v1_relat_1(k2_zfmisc_1(A, B))) ).
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_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k12_quaterni(A))) ) ).
fof(fc8_ordinal1, axiom, v7_ordinal1(k5_ordinal1)).
fof(fc8_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k13_quaterni(A))) ) ).
fof(fc9_ordinal1, axiom, v8_ordinal1(k5_ordinal1)).
fof(fc9_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k14_quaterni(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(fraenkel_a_0_0_quaterni, axiom,  (! [A] :  (r2_hidden(A, a_0_0_quaterni) <=>  (? [B] :  (m2_funct_2(B, 4, k1_numbers, k9_funct_2(4, k1_numbers)) &  (A=B &  (k1_funct_1(B, 2)=k5_numbers & k1_funct_1(B, 3)=k5_numbers) ) ) ) ) ) ).
fof(idempotence_k2_xboole_0, axiom,  (! [A, B] : k2_xboole_0(A, A)=A) ).
fof(involutiveness_k23_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => k23_quaterni(k23_quaterni(A))=A) ) ).
fof(involutiveness_k4_xcmplx_0, axiom,  (! [A] :  (v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A))=A) ) ).
fof(involutiveness_k7_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => k7_quaterni(k7_quaterni(A))=A) ) ).
fof(l1_quatern2, axiom,  (! [A] :  (v1_quaterni(A) =>  (? [B] :  (m1_subset_1(B, k1_numbers) &  (? [C] :  (m1_subset_1(C, k1_numbers) &  (? [D] :  (m1_subset_1(D, k1_numbers) &  (? [E] :  (m1_subset_1(E, k1_numbers) & A=k5_quaterni(B, C, D, E)) ) ) ) ) ) ) ) ) ) ).
fof(rc10_ordinal1, axiom,  (? [A] :  ~ (v8_ordinal1(A)) ) ).
fof(rc11_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  ~ (v10_ordinal1(A)) ) ) ).
fof(rc12_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) & v9_ordinal1(A)) ) ).
fof(rc13_ordinal1, axiom,  (? [A] :  (v1_relat_1(A) &  ~ (v9_ordinal1(A)) ) ) ).
fof(rc1_ordinal1, axiom,  (? [A] :  (v1_ordinal1(A) & v2_ordinal1(A)) ) ).
fof(rc1_quaterni, axiom,  (? [A] : v1_quaterni(A)) ).
fof(rc1_relat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_relat_1(A)) ) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc2_ordinal1, axiom,  (? [A] : v3_ordinal1(A)) ).
fof(rc2_relat_1, axiom,  (? [A] :  (v1_relat_1(A) & v2_relat_1(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc3_ordinal1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_ordinal1(A) &  (v2_ordinal1(A) & v3_ordinal1(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_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_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(rd1_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => k10_subset_1(A, k1_numbers)=A) ) ).
fof(redefinition_k10_quaterni, axiom, k10_quaterni=k3_quaterni).
fof(redefinition_k11_quaterni, axiom, k11_quaterni=k4_quaterni).
fof(redefinition_k21_quaterni, axiom,  (! [A, B] :  ( (v1_quaterni(A) & v1_quaterni(B))  => k21_quaterni(A, B)=k6_quaterni(A, B)) ) ).
fof(redefinition_k23_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => k23_quaterni(A)=k7_quaterni(A)) ) ).
fof(redefinition_k2_quaterni, axiom,  (! [A, B, C, D, E, F, G, H, I] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(F, A) &  (m1_subset_1(G, A) &  (m1_subset_1(H, A) & m1_subset_1(I, A)) ) ) )  => k2_quaterni(A, B, C, D, E, F, G, H, I)=k12_funct_4(B, C, D, E, F, G, H, I)) ) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k5_ordinal1).
fof(redefinition_k6_subset_1, axiom,  (! [A, B] : k6_subset_1(A, B)=k4_xboole_0(A, B)) ).
fof(redefinition_k7_funct_4, axiom,  (! [A, B, C, D, E] :  ( ( ~ (v1_xboole_0(A))  &  (m1_subset_1(D, A) & m1_subset_1(E, A)) )  => k7_funct_4(A, B, C, D, E)=k6_funct_4(B, C, D, E)) ) ).
fof(redefinition_k9_funct_2, axiom,  (! [A, B] :  ( ~ (v1_xboole_0(B))  => k9_funct_2(A, B)=k1_funct_2(A, B)) ) ).
fof(redefinition_m2_funct_2, axiom,  (! [A, B, C] :  ( ( ~ (v1_xboole_0(B))  & m1_funct_2(C, A, B))  =>  (! [D] :  (m2_funct_2(D, A, B, C) <=> m1_subset_1(D, C)) ) ) ) ).
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(rqRealAdd__k2_xcmplx_0__cr1r0_cr1r0_cr2r0, axiom, k2_xcmplx_0(k1_xcmplx_0, k1_xcmplx_0)=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_cr2r0_cr3r0, axiom, k2_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_cr3r0_cr4r0, axiom, k2_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(3, k1_xcmplx_0))=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_crm1r0_r0, axiom, k2_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=0).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_crm2r0_crm1r0, axiom, k2_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_crm3r0_crm2r0, axiom, k2_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_r0_cr1r0, axiom, k2_xcmplx_0(k1_xcmplx_0, 0)=k1_xcmplx_0).
fof(rqRealAdd__k2_xcmplx_0__cr1r0_r1_cr1r1, axiom, k2_xcmplx_0(k1_xcmplx_0, 1)=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealAdd__k2_xcmplx_0__cr2r0_cr1r0_cr3r0, axiom, k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k1_xcmplx_0)=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr2r0_cr2r0_cr4r0, axiom, k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr2r0_crm1r0_cr1r0, axiom, k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k1_xcmplx_0).
fof(rqRealAdd__k2_xcmplx_0__cr2r0_crm2r0_r0, axiom, k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=0).
fof(rqRealAdd__k2_xcmplx_0__cr2r0_crm4r0_crm2r0, axiom, k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr3r0_cr1r0_cr4r0, axiom, k2_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), k1_xcmplx_0)=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__cr4r0_crm2r0_cr2r0, axiom, k2_xcmplx_0(k3_xcmplx_0(4, k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_cr1r0_r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k1_xcmplx_0)=0).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_cr2r0_cr1r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=k1_xcmplx_0).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_cr3r0_cr2r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(3, k1_xcmplx_0))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_crm1r0_crm2r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_crm2r0_crm3r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_crm3r0_crm4r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_r0_crm1r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 0)=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm1r0_r1_crm1r1, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealAdd__k2_xcmplx_0__crm2r0_cr1r0_crm1r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k1_xcmplx_0)=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm2r0_cr2r0_r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=0).
fof(rqRealAdd__k2_xcmplx_0__crm2r0_cr3r0_cr1r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(3, k1_xcmplx_0))=k1_xcmplx_0).
fof(rqRealAdd__k2_xcmplx_0__crm2r0_cr4r0_cr2r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(4, k1_xcmplx_0))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm2r0_crm1r0_crm3r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm2r0_crm2r0_crm4r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm3r0_cr3r0_r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), k3_xcmplx_0(3, k1_xcmplx_0))=0).
fof(rqRealAdd__k2_xcmplx_0__crm4r0_cr1r0_crm3r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0), k1_xcmplx_0)=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__crm4r0_cr2r0_crm2r0, axiom, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__r0_cr1r0_cr1r0, axiom, k2_xcmplx_0(0, k1_xcmplx_0)=k1_xcmplx_0).
fof(rqRealAdd__k2_xcmplx_0__r0_crm1r0_crm1r0, axiom, k2_xcmplx_0(0, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom, k2_xcmplx_0(0, 0)=0).
fof(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom, k2_xcmplx_0(0, 1)=1).
fof(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom, k2_xcmplx_0(0, 2)=2).
fof(rqRealAdd__k2_xcmplx_0__r0_r3_r3, axiom, k2_xcmplx_0(0, 3)=3).
fof(rqRealAdd__k2_xcmplx_0__r0_r4_r4, axiom, k2_xcmplx_0(0, 4)=4).
fof(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom, k2_xcmplx_0(0, k4_xcmplx_0(1))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom, k2_xcmplx_0(0, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm3_rm3, axiom, k2_xcmplx_0(0, k4_xcmplx_0(3))=k4_xcmplx_0(3)).
fof(rqRealAdd__k2_xcmplx_0__r0_rm4_rm4, axiom, k2_xcmplx_0(0, k4_xcmplx_0(4))=k4_xcmplx_0(4)).
fof(rqRealAdd__k2_xcmplx_0__r1_cr1r0_cr1r1, axiom, k2_xcmplx_0(1, k1_xcmplx_0)=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealAdd__k2_xcmplx_0__r1_crm1r0_crm1r1, axiom, k2_xcmplx_0(1, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom, k2_xcmplx_0(1, 0)=1).
fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom, k2_xcmplx_0(1, 1)=2).
fof(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom, k2_xcmplx_0(1, 2)=3).
fof(rqRealAdd__k2_xcmplx_0__r1_r3_r4, axiom, k2_xcmplx_0(1, 3)=4).
fof(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom, k2_xcmplx_0(1, k4_xcmplx_0(1))=0).
fof(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom, k2_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r1_rm3_rm2, axiom, k2_xcmplx_0(1, k4_xcmplx_0(3))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r1_rm4_rm3, axiom, k2_xcmplx_0(1, k4_xcmplx_0(4))=k4_xcmplx_0(3)).
fof(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom, k2_xcmplx_0(2, 0)=2).
fof(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom, k2_xcmplx_0(2, 1)=3).
fof(rqRealAdd__k2_xcmplx_0__r2_r2_r4, axiom, k2_xcmplx_0(2, 2)=4).
fof(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom, k2_xcmplx_0(2, k4_xcmplx_0(1))=1).
fof(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom, k2_xcmplx_0(2, k4_xcmplx_0(2))=0).
fof(rqRealAdd__k2_xcmplx_0__r2_rm3_rm1, axiom, k2_xcmplx_0(2, k4_xcmplx_0(3))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r2_rm4_rm2, axiom, k2_xcmplx_0(2, k4_xcmplx_0(4))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__r3_r0_r3, axiom, k2_xcmplx_0(3, 0)=3).
fof(rqRealAdd__k2_xcmplx_0__r3_r1_r4, axiom, k2_xcmplx_0(3, 1)=4).
fof(rqRealAdd__k2_xcmplx_0__r3_rm1_r2, axiom, k2_xcmplx_0(3, k4_xcmplx_0(1))=2).
fof(rqRealAdd__k2_xcmplx_0__r3_rm2_r1, axiom, k2_xcmplx_0(3, k4_xcmplx_0(2))=1).
fof(rqRealAdd__k2_xcmplx_0__r3_rm3_r0, axiom, k2_xcmplx_0(3, k4_xcmplx_0(3))=0).
fof(rqRealAdd__k2_xcmplx_0__r3_rm4_rm1, axiom, k2_xcmplx_0(3, k4_xcmplx_0(4))=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__r4_r0_r4, axiom, k2_xcmplx_0(4, 0)=4).
fof(rqRealAdd__k2_xcmplx_0__r4_rm1_r3, axiom, k2_xcmplx_0(4, k4_xcmplx_0(1))=3).
fof(rqRealAdd__k2_xcmplx_0__r4_rm2_r2, axiom, k2_xcmplx_0(4, k4_xcmplx_0(2))=2).
fof(rqRealAdd__k2_xcmplx_0__r4_rm3_r1, axiom, k2_xcmplx_0(4, k4_xcmplx_0(3))=1).
fof(rqRealAdd__k2_xcmplx_0__r4_rm4_r0, axiom, k2_xcmplx_0(4, k4_xcmplx_0(4))=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 0)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 1)=0).
fof(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 2)=1).
fof(rqRealAdd__k2_xcmplx_0__rm1_r3_r2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 3)=2).
fof(rqRealAdd__k2_xcmplx_0__rm1_r4_r3, axiom, k2_xcmplx_0(k4_xcmplx_0(1), 4)=3).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(1))=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(2))=k4_xcmplx_0(3)).
fof(rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4, axiom, k2_xcmplx_0(k4_xcmplx_0(1), k4_xcmplx_0(3))=k4_xcmplx_0(4)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r0_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 0)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 2)=0).
fof(rqRealAdd__k2_xcmplx_0__rm2_r3_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 3)=1).
fof(rqRealAdd__k2_xcmplx_0__rm2_r4_r2, axiom, k2_xcmplx_0(k4_xcmplx_0(2), 4)=2).
fof(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3, axiom, k2_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(1))=k4_xcmplx_0(3)).
fof(rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4, axiom, k2_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(2))=k4_xcmplx_0(4)).
fof(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(3), 1)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(3), 2)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm3_r3_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(3), 3)=0).
fof(rqRealAdd__k2_xcmplx_0__rm3_r4_r1, axiom, k2_xcmplx_0(k4_xcmplx_0(3), 4)=1).
fof(rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4, axiom, k2_xcmplx_0(k4_xcmplx_0(3), k4_xcmplx_0(1))=k4_xcmplx_0(4)).
fof(rqRealAdd__k2_xcmplx_0__rm4_r1_rm3, axiom, k2_xcmplx_0(k4_xcmplx_0(4), 1)=k4_xcmplx_0(3)).
fof(rqRealAdd__k2_xcmplx_0__rm4_r2_rm2, axiom, k2_xcmplx_0(k4_xcmplx_0(4), 2)=k4_xcmplx_0(2)).
fof(rqRealAdd__k2_xcmplx_0__rm4_r3_rm1, axiom, k2_xcmplx_0(k4_xcmplx_0(4), 3)=k4_xcmplx_0(1)).
fof(rqRealAdd__k2_xcmplx_0__rm4_r4_r0, axiom, k2_xcmplx_0(k4_xcmplx_0(4), 4)=0).
fof(rqRealMult__k3_xcmplx_0__cr1r0_cr1r0_rm1, axiom, k3_xcmplx_0(k1_xcmplx_0, k1_xcmplx_0)=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__cr1r0_cr2r0_rm2, axiom, k3_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(2, k1_xcmplx_0))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__cr1r0_cr3r0_rm3, axiom, k3_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(3, k1_xcmplx_0))=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__cr1r0_crm1r0_r1, axiom, k3_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=1).
fof(rqRealMult__k3_xcmplx_0__cr1r0_crm1r1_cr1r1, axiom, k3_xcmplx_0(k1_xcmplx_0, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1))=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealMult__k3_xcmplx_0__cr1r0_crm2r0_r2, axiom, k3_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=2).
fof(rqRealMult__k3_xcmplx_0__cr1r0_crm3r0_r3, axiom, k3_xcmplx_0(k1_xcmplx_0, k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0))=3).
fof(rqRealMult__k3_xcmplx_0__cr1r0_r0_r0, axiom, k3_xcmplx_0(k1_xcmplx_0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__cr1r0_r1_cr1r0, axiom, k3_xcmplx_0(k1_xcmplx_0, 1)=k1_xcmplx_0).
fof(rqRealMult__k3_xcmplx_0__cr1r0_r2_cr2r0, axiom, k3_xcmplx_0(k1_xcmplx_0, 2)=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__cr1r0_r3_cr3r0, axiom, k3_xcmplx_0(k1_xcmplx_0, 3)=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__cr1r0_rm2_crm2r0, axiom, k3_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(2))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__cr1r1_cr1r0_cr1rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 1), k1_xcmplx_0)=k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__cr1r1_crm1r0_crm1r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 1), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__cr1r1_r1_cr1r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 1), 1)=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealMult__k3_xcmplx_0__cr1r2_cr1r0_cr2rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 2), k1_xcmplx_0)=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__cr1r2_crm1r0_crm2r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 2), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__cr1r2_r1_cr1r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 2), 1)=k2_xcmplx_0(k1_xcmplx_0, 2)).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_cr1r0_crm1rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k1_xcmplx_0)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_cr2r0_crm2rm2, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k3_xcmplx_0(2, k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_cr3r0_crm3rm3, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k3_xcmplx_0(3, k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), k4_xcmplx_0(3))).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_crm1r0_cr1r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_crm2r0_cr2r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 2)).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_crm3r0_cr3r3, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), 3)).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_r1_cr1rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), 1)=k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_r2_cr2rm2, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), 2)=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealMult__k3_xcmplx_0__cr1rm1_rm2_crm2r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)), k4_xcmplx_0(2))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 2)).
fof(rqRealMult__k3_xcmplx_0__cr2r0_cr1r0_rm2, axiom, k3_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k1_xcmplx_0)=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__cr2r0_cr2r0_rm4, axiom, k3_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=k4_xcmplx_0(4)).
fof(rqRealMult__k3_xcmplx_0__cr2r0_r1_cr2r0, axiom, k3_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 1)=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__cr2r0_r2_cr4r0, axiom, k3_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 2)=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__cr2rm1_r1_cr2rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(1)), 1)=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__cr2rm2_r1_cr2rm2, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(2)), 1)=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealMult__k3_xcmplx_0__cr3r0_cr1r0_rm3, axiom, k3_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), k1_xcmplx_0)=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__cr3r0_r1_cr3r0, axiom, k3_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), 1)=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__cr3rm3_r1_cr3rm3, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), k4_xcmplx_0(3)), 1)=k2_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), k4_xcmplx_0(3))).
fof(rqRealMult__k3_xcmplx_0__cr4r0_r1_cr4r0, axiom, k3_xcmplx_0(k3_xcmplx_0(4, k1_xcmplx_0), 1)=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_cr1r0_r1, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k1_xcmplx_0)=1).
fof(rqRealMult__k3_xcmplx_0__crm1r0_cr2r0_r2, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=2).
fof(rqRealMult__k3_xcmplx_0__crm1r0_cr3r0_r3, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(3, k1_xcmplx_0))=3).
fof(rqRealMult__k3_xcmplx_0__crm1r0_crm1r0_rm1, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k4_xcmplx_0(1)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_crm2r0_rm2, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_crm3r0_rm3, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0))=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_r1_crm1r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_r2_crm2r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 2)=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_r3_crm3r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 3)=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm1r0_rm2_cr2r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(2))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm1r1_cr1r0_cr1r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1), k1_xcmplx_0)=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealMult__k3_xcmplx_0__crm1r1_cr2r0_cr2r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1), k3_xcmplx_0(2, k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 2)).
fof(rqRealMult__k3_xcmplx_0__crm1r1_crm1r0_crm1rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__crm1r1_r1_crm1r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__crm1r1_r2_crm2r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1), 2)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 2)).
fof(rqRealMult__k3_xcmplx_0__crm1r1_rm2_cr2rm2, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1), k4_xcmplx_0(2))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealMult__k3_xcmplx_0__crm1r2_cr1r0_cr2r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 2), k1_xcmplx_0)=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__crm1r2_crm1r0_crm2rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 2), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__crm1r2_r1_crm1r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 2), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 2)).
fof(rqRealMult__k3_xcmplx_0__crm1rm1_cr1r0_crm1r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1)), k1_xcmplx_0)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__crm1rm1_crm1r0_cr1rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1)), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__crm1rm1_r1_crm1rm1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1)), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealMult__k3_xcmplx_0__crm2r0_cr1r0_r2, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k1_xcmplx_0)=2).
fof(rqRealMult__k3_xcmplx_0__crm2r0_cr2r0_r4, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(2, k1_xcmplx_0))=4).
fof(rqRealMult__k3_xcmplx_0__crm2r0_crm1r0_rm2, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__crm2r0_r1_crm2r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 1)=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm2r1_r1_crm2r1, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 1), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__crm2r2_r1_crm2r2, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 2), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 2)).
fof(rqRealMult__k3_xcmplx_0__crm3r0_r1_crm3r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), 1)=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__crm3r3_r1_crm3r3, axiom, k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), 3), 1)=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), 3)).
fof(rqRealMult__k3_xcmplx_0__crm4r0_r1_crm4r0, axiom, k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0), 1)=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r0_cr1r0_r0, axiom, k3_xcmplx_0(0, k1_xcmplx_0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r0_r0, axiom, k3_xcmplx_0(0, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r1_r0, axiom, k3_xcmplx_0(0, 1)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r2_r0, axiom, k3_xcmplx_0(0, 2)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r3_r0, axiom, k3_xcmplx_0(0, 3)=0).
fof(rqRealMult__k3_xcmplx_0__r0_r4_r0, axiom, k3_xcmplx_0(0, 4)=0).
fof(rqRealMult__k3_xcmplx_0__r0_rm2_r0, axiom, k3_xcmplx_0(0, k4_xcmplx_0(2))=0).
fof(rqRealMult__k3_xcmplx_0__r0_rm3_r0, axiom, k3_xcmplx_0(0, k4_xcmplx_0(3))=0).
fof(rqRealMult__k3_xcmplx_0__r1_cr1r0_cr1r0, axiom, k3_xcmplx_0(1, k1_xcmplx_0)=k1_xcmplx_0).
fof(rqRealMult__k3_xcmplx_0__r1_cr1r1_cr1r1, axiom, k3_xcmplx_0(1, k2_xcmplx_0(k1_xcmplx_0, 1))=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealMult__k3_xcmplx_0__r1_cr2r0_cr2r0, axiom, k3_xcmplx_0(1, k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r1_crm1r0_crm1r0, axiom, k3_xcmplx_0(1, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r1_crm1r1_crm1r1, axiom, k3_xcmplx_0(1, k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealMult__k3_xcmplx_0__r1_crm2r0_crm2r0, axiom, k3_xcmplx_0(1, k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r1_r0_r0, axiom, k3_xcmplx_0(1, 0)=0).
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_r3_r3, axiom, k3_xcmplx_0(1, 3)=3).
fof(rqRealMult__k3_xcmplx_0__r1_r4_r4, axiom, k3_xcmplx_0(1, 4)=4).
fof(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, axiom, k3_xcmplx_0(1, k4_xcmplx_0(2))=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__r1_rm3_rm3, axiom, k3_xcmplx_0(1, k4_xcmplx_0(3))=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__r1_rm4_rm4, axiom, k3_xcmplx_0(1, k4_xcmplx_0(4))=k4_xcmplx_0(4)).
fof(rqRealMult__k3_xcmplx_0__r2_cr1r0_cr2r0, axiom, k3_xcmplx_0(2, k1_xcmplx_0)=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r2_cr2r0_cr4r0, axiom, k3_xcmplx_0(2, k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r2_crm1r0_crm2r0, axiom, k3_xcmplx_0(2, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r2_r0_r0, axiom, k3_xcmplx_0(2, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r2_r1_r2, axiom, k3_xcmplx_0(2, 1)=2).
fof(rqRealMult__k3_xcmplx_0__r2_r2_r4, axiom, k3_xcmplx_0(2, 2)=4).
fof(rqRealMult__k3_xcmplx_0__r2_rm2_rm4, axiom, k3_xcmplx_0(2, k4_xcmplx_0(2))=k4_xcmplx_0(4)).
fof(rqRealMult__k3_xcmplx_0__r3_cr1r0_cr3r0, axiom, k3_xcmplx_0(3, k1_xcmplx_0)=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r3_crm1r0_crm3r0, axiom, k3_xcmplx_0(3, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r3_r0_r0, axiom, k3_xcmplx_0(3, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r3_r1_r3, axiom, k3_xcmplx_0(3, 1)=3).
fof(rqRealMult__k3_xcmplx_0__r4_cr1r0_cr4r0, axiom, k3_xcmplx_0(4, k1_xcmplx_0)=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r4_crm1r0_crm4r0, axiom, k3_xcmplx_0(4, k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__r4_r0_r0, axiom, k3_xcmplx_0(4, 0)=0).
fof(rqRealMult__k3_xcmplx_0__r4_r1_r4, axiom, k3_xcmplx_0(4, 1)=4).
fof(rqRealMult__k3_xcmplx_0__rm2_cr1r0_crm2r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm2_cr2r0_crm4r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm2_crm1r0_cr2r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm2_crm2r0_cr4r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm2_r0_r0, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 1)=k4_xcmplx_0(2)).
fof(rqRealMult__k3_xcmplx_0__rm2_r2_rm4, axiom, k3_xcmplx_0(k4_xcmplx_0(2), 2)=k4_xcmplx_0(4)).
fof(rqRealMult__k3_xcmplx_0__rm2_rm2_r4, axiom, k3_xcmplx_0(k4_xcmplx_0(2), k4_xcmplx_0(2))=4).
fof(rqRealMult__k3_xcmplx_0__rm3_cr1r0_crm3r0, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm3_crm1r0_cr3r0, axiom, k3_xcmplx_0(k4_xcmplx_0(3), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm3_r0_r0, axiom, k3_xcmplx_0(k4_xcmplx_0(3), 0)=0).
fof(rqRealMult__k3_xcmplx_0__rm3_r1_rm3, axiom, k3_xcmplx_0(k4_xcmplx_0(3), 1)=k4_xcmplx_0(3)).
fof(rqRealMult__k3_xcmplx_0__rm4_cr1r0_crm4r0, axiom, k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm4_crm1r0_cr4r0, axiom, k3_xcmplx_0(k4_xcmplx_0(4), k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealMult__k3_xcmplx_0__rm4_r1_rm4, axiom, k3_xcmplx_0(k4_xcmplx_0(4), 1)=k4_xcmplx_0(4)).
fof(rqRealNeg__k4_xcmplx_0__cr1r0_crm1r0, axiom, k4_xcmplx_0(k1_xcmplx_0)=k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__cr1r1_crm1rm1, axiom, k4_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 1))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__cr1r2_crm1rm2, axiom, k4_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, 2))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealNeg__k4_xcmplx_0__cr1rm1_crm1r1, axiom, k4_xcmplx_0(k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1)))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1)).
fof(rqRealNeg__k4_xcmplx_0__cr2r0_crm2r0, axiom, k4_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__cr2r1_crm2rm1, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 1))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__cr2r2_crm2rm2, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 2))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealNeg__k4_xcmplx_0__cr2rm2_crm2r2, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(2)))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 2)).
fof(rqRealNeg__k4_xcmplx_0__cr3r0_crm3r0, axiom, k4_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__cr3r3_crm3rm3, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), 3))=k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), k4_xcmplx_0(3))).
fof(rqRealNeg__k4_xcmplx_0__cr4r0_crm4r0, axiom, k4_xcmplx_0(k3_xcmplx_0(4, k1_xcmplx_0))=k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__crm1r0_cr1r0, axiom, k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0))=k1_xcmplx_0).
fof(rqRealNeg__k4_xcmplx_0__crm1r1_cr1rm1, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 1))=k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__crm1r2_cr1rm2, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), 2))=k2_xcmplx_0(k1_xcmplx_0, k4_xcmplx_0(2))).
fof(rqRealNeg__k4_xcmplx_0__crm1rm1_cr1r1, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(1)))=k2_xcmplx_0(k1_xcmplx_0, 1)).
fof(rqRealNeg__k4_xcmplx_0__crm1rm2_cr1r2, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(1), k1_xcmplx_0), k4_xcmplx_0(2)))=k2_xcmplx_0(k1_xcmplx_0, 2)).
fof(rqRealNeg__k4_xcmplx_0__crm2r0_cr2r0, axiom, k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0))=k3_xcmplx_0(2, k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__crm2r1_cr2rm1, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 1))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(1))).
fof(rqRealNeg__k4_xcmplx_0__crm2r2_cr2rm2, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), 2))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), k4_xcmplx_0(2))).
fof(rqRealNeg__k4_xcmplx_0__crm2rm1_cr2r1, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k4_xcmplx_0(1)))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 1)).
fof(rqRealNeg__k4_xcmplx_0__crm2rm2_cr2r2, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2), k1_xcmplx_0), k4_xcmplx_0(2)))=k2_xcmplx_0(k3_xcmplx_0(2, k1_xcmplx_0), 2)).
fof(rqRealNeg__k4_xcmplx_0__crm3r0_cr3r0, axiom, k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0))=k3_xcmplx_0(3, k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__crm3rm3_cr3r3, axiom, k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(3), k1_xcmplx_0), k4_xcmplx_0(3)))=k2_xcmplx_0(k3_xcmplx_0(3, k1_xcmplx_0), 3)).
fof(rqRealNeg__k4_xcmplx_0__crm4r0_cr4r0, axiom, k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(4), k1_xcmplx_0))=k3_xcmplx_0(4, k1_xcmplx_0)).
fof(rqRealNeg__k4_xcmplx_0__r0_r0, axiom, k4_xcmplx_0(0)=0).
fof(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom, k4_xcmplx_0(1)=k4_xcmplx_0(1)).
fof(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom, k4_xcmplx_0(2)=k4_xcmplx_0(2)).
fof(rqRealNeg__k4_xcmplx_0__r3_rm3, axiom, k4_xcmplx_0(3)=k4_xcmplx_0(3)).
fof(rqRealNeg__k4_xcmplx_0__r4_rm4, axiom, k4_xcmplx_0(4)=k4_xcmplx_0(4)).
fof(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom, k4_xcmplx_0(k4_xcmplx_0(1))=1).
fof(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom, k4_xcmplx_0(k4_xcmplx_0(2))=2).
fof(rqRealNeg__k4_xcmplx_0__rm3_r3, axiom, k4_xcmplx_0(k4_xcmplx_0(3))=3).
fof(rqRealNeg__k4_xcmplx_0__rm4_r4, axiom, k4_xcmplx_0(k4_xcmplx_0(4))=4).
fof(spc0_boole, axiom, v1_xboole_0(0)).
fof(spc0_numerals, axiom, m1_subset_1(0, k4_ordinal1)).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(1)) ).
fof(spc1_numerals, axiom,  (v2_xxreal_0(1) & m1_subset_1(1, k4_ordinal1)) ).
fof(spc2_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(A, k4_xcmplx_0(1))=k4_xcmplx_0(A)) ) ).
fof(spc2_boole, axiom,  ~ (v1_xboole_0(2)) ).
fof(spc2_numerals, axiom,  (v2_xxreal_0(2) & m1_subset_1(2, k4_ordinal1)) ).
fof(spc3_boole, axiom,  ~ (v1_xboole_0(3)) ).
fof(spc3_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_boole, axiom,  ~ (v1_xboole_0(4)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
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(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_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_boole, axiom,  (! [A] : k2_xboole_0(A, k1_xboole_0)=A) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
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_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(t3_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k3_xcmplx_0(1, A)=A) ) ).
fof(t3_boole, axiom,  (! [A] : k4_xboole_0(A, k1_xboole_0)=A) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_boole, axiom,  (! [A] : k4_xboole_0(k1_xboole_0, A)=k1_xboole_0) ).
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)) ) ) ) ) ).
fof(t91_quaterni, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) =>  (! [B] :  (m1_subset_1(B, k1_numbers) => k5_quaterni(A, B, k5_numbers, k5_numbers)=k5_arytm_0(A, B)) ) ) ) ).
