% Mizar problem: t2_quatern3,quatern3,52,5 
fof(t2_quatern3, conjecture,  (! [A] :  (v1_quaterni(A) =>  (! [B] :  (v1_quaterni(B) =>  (v1_xreal_0(B) => k21_quaterni(B, A)=k21_quaterni(k21_quaterni(k18_quaterni(k2_xcmplx_0(k12_quaterni(B), k12_quaterni(A)), k20_quaterni(k13_quaterni(A), k3_quatern2)), k20_quaterni(k14_quaterni(A), k10_quaterni)), k20_quaterni(k15_quaterni(A), k11_quaterni))) ) ) ) ) ).
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_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_int_1(B)) ) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v7_ordinal1(B)) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc13_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v1_membered(B)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v2_membered(B)) ) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v3_membered(B)) ) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v4_membered(B)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (v5_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v5_membered(B)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v6_membered(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(A)) => v6_membered(B)) ) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_quaterni, axiom,  (! [A] :  (m1_subset_1(A, k1_quaterni) => v1_quaterni(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  (m1_subset_1(A, k1_numbers) => v1_xreal_0(A)) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc6_membered, axiom,  (! [A] :  (v1_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xcmplx_0(B)) ) ) ) ).
fof(cc7_membered, axiom,  (! [A] :  (v2_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xxreal_0(B)) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  (v3_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_xreal_0(B)) ) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  (v4_membered(A) =>  (! [B] :  (m1_subset_1(B, A) => v1_rat_1(B)) ) ) ) ).
fof(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_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(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(dt_k10_quaterni, axiom, m1_subset_1(k10_quaterni, k1_quaterni)).
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_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_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_quatern2, axiom, m1_subset_1(k3_quatern2, k1_quaterni)).
fof(dt_k3_quaterni, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k4_quaterni, axiom, $true).
fof(dt_k4_xboole_0, axiom, $true).
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_complex1, axiom, m1_subset_1(k7_complex1, k2_numbers)).
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_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(fc12_quaterni, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_quaterni(B))  => v1_quaterni(k20_quaterni(A, B))) ) ).
fof(fc13_membered, axiom,  (! [A, B] :  ( (v1_xcmplx_0(A) & v1_xcmplx_0(B))  => v1_membered(k2_tarski(A, B))) ) ).
fof(fc14_membered, axiom,  (! [A, B] :  ( (v1_xxreal_0(A) & v1_xxreal_0(B))  => v2_membered(k2_tarski(A, B))) ) ).
fof(fc15_membered, axiom,  (! [A, B] :  ( (v1_xreal_0(A) & v1_xreal_0(B))  => v3_membered(k2_tarski(A, B))) ) ).
fof(fc16_membered, axiom,  (! [A, B] :  ( (v1_rat_1(A) & v1_rat_1(B))  => v4_membered(k2_tarski(A, B))) ) ).
fof(fc17_membered, axiom,  (! [A, B] :  ( (v1_int_1(A) & v1_int_1(B))  => v5_membered(k2_tarski(A, B))) ) ).
fof(fc18_membered, axiom,  (! [A, B] :  ( (v7_ordinal1(A) & v7_ordinal1(B))  => v6_membered(k2_tarski(A, B))) ) ).
fof(fc1_membered, axiom, v1_membered(k2_numbers)).
fof(fc1_quaterni, axiom,  ~ (v1_xboole_0(k1_quaterni)) ).
fof(fc25_membered, axiom,  (! [A, B] :  ( (v1_membered(A) & v1_membered(B))  => v1_membered(k2_xboole_0(A, B))) ) ).
fof(fc26_membered, axiom,  (! [A, B] :  ( (v2_membered(A) & v2_membered(B))  => v2_membered(k2_xboole_0(A, B))) ) ).
fof(fc27_membered, axiom,  (! [A, B] :  ( (v3_membered(A) & v3_membered(B))  => v3_membered(k2_xboole_0(A, B))) ) ).
fof(fc28_membered, axiom,  (! [A, B] :  ( (v4_membered(A) & v4_membered(B))  => v4_membered(k2_xboole_0(A, B))) ) ).
fof(fc29_membered, axiom,  (! [A, B] :  ( (v5_membered(A) & v5_membered(B))  => v5_membered(k2_xboole_0(A, B))) ) ).
fof(fc2_quaterni, axiom, v1_quaterni(k1_xcmplx_0)).
fof(fc30_membered, axiom,  (! [A, B] :  ( (v6_membered(A) & v6_membered(B))  => v6_membered(k2_xboole_0(A, B))) ) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_quaterni, axiom, v1_quaterni(k3_quaterni)).
fof(fc43_membered, axiom,  (! [A, B] :  (v1_membered(A) => v1_membered(k4_xboole_0(A, B))) ) ).
fof(fc44_membered, axiom,  (! [A, B] :  (v2_membered(A) => v2_membered(k4_xboole_0(A, B))) ) ).
fof(fc45_membered, axiom,  (! [A, B] :  (v3_membered(A) => v3_membered(k4_xboole_0(A, B))) ) ).
fof(fc46_membered, axiom,  (! [A, B] :  (v4_membered(A) => v4_membered(k4_xboole_0(A, B))) ) ).
fof(fc47_membered, axiom,  (! [A, B] :  (v5_membered(A) => v5_membered(k4_xboole_0(A, B))) ) ).
fof(fc48_membered, axiom,  (! [A, B] :  (v6_membered(A) => v6_membered(k4_xboole_0(A, B))) ) ).
fof(fc4_quaterni, axiom, v1_quaterni(k4_quaterni)).
fof(fc55_membered, axiom, v7_membered(k2_numbers)).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
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_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc7_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k12_quaterni(A))) ) ).
fof(fc8_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k13_quaterni(A))) ) ).
fof(fc9_quaterni, axiom,  (! [A] :  (v1_quaterni(A) => v1_xreal_0(k14_quaterni(A))) ) ).
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(l2_quatern3, axiom,  (! [A] :  (v1_quaterni(A) =>  (v1_xreal_0(A) =>  (A=k12_quaterni(A) &  (k13_quaterni(A)=k5_numbers &  (k14_quaterni(A)=k5_numbers & k15_quaterni(A)=k5_numbers) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_quaterni, axiom,  (? [A] : v1_quaterni(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(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_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_k3_quatern2, axiom, k3_quatern2=k1_xcmplx_0).
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_complex1, axiom, k7_complex1=k1_xcmplx_0).
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_r1_cr1r1, axiom, k2_xcmplx_0(k1_xcmplx_0, 1)=k2_xcmplx_0(k1_xcmplx_0, 1)).
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_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__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__r3_r1_r4, axiom, k2_xcmplx_0(3, 1)=4).
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_numerals, axiom,  (v2_xxreal_0(3) & m1_subset_1(3, k4_ordinal1)) ).
fof(spc4_numerals, axiom,  (v2_xxreal_0(4) & m1_subset_1(4, k4_ordinal1)) ).
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(t1_arithm, axiom,  (! [A] :  (v1_xcmplx_0(A) => k2_xcmplx_0(A, k5_numbers)=A) ) ).
fof(t1_quatern2, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) =>  (! [D] :  (v1_xreal_0(D) => k5_quaterni(A, B, C, D)=k21_quaterni(k21_quaterni(k18_quaterni(A, k20_quaterni(B, k7_complex1)), k20_quaterni(C, k10_quaterni)), k20_quaterni(D, k11_quaterni))) ) ) ) ) ) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_tarski(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t23_quaterni, axiom,  (! [A] :  (v1_xreal_0(A) =>  (! [B] :  (v1_xreal_0(B) =>  (! [C] :  (v1_xreal_0(C) =>  (! [D] :  (v1_xreal_0(D) =>  (k12_quaterni(k5_quaterni(A, B, C, D))=A &  (k13_quaterni(k5_quaterni(A, B, C, D))=B &  (k14_quaterni(k5_quaterni(A, B, C, D))=C & k15_quaterni(k5_quaterni(A, B, C, D))=D) ) ) ) ) ) ) ) ) ) ) ).
fof(t25_quaterni, axiom,  (! [A] :  (v1_quaterni(A) =>  (! [B] :  (v1_quaterni(B) =>  ( (k12_quaterni(A)=k12_quaterni(B) &  (k13_quaterni(A)=k13_quaterni(B) &  (k14_quaterni(A)=k14_quaterni(B) & k15_quaterni(A)=k15_quaterni(B)) ) )  => A=B) ) ) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_tarski(A, B)) ) ) ) ).
fof(t2_tarski, axiom,  (! [A] :  (! [B] :  ( (! [C] :  (r2_hidden(C, A) <=> r2_hidden(C, B)) )  => A=B) ) ) ).
fof(t36_quaterni, axiom,  (! [A] :  (v1_quaterni(A) =>  (! [B] :  (v1_quaterni(B) =>  (k12_quaterni(k21_quaterni(A, B))=k2_xcmplx_0(k12_quaterni(A), k12_quaterni(B)) &  (k13_quaterni(k21_quaterni(A, B))=k2_xcmplx_0(k13_quaterni(A), k13_quaterni(B)) &  (k14_quaterni(k21_quaterni(A, B))=k2_xcmplx_0(k14_quaterni(A), k14_quaterni(B)) & k15_quaterni(k21_quaterni(A, B))=k2_xcmplx_0(k15_quaterni(A), k15_quaterni(B))) ) ) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_tarski(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_tarski(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
