% Mizar problem: s12_recdef_2,recdef_2,890,14 
include('Axioms/SET010^0.ax').
thf(n0_type, type, np__0: $i).
thf(n1_type, type, np__1: $i).
thf(n2_type, type, np__2: $i).
thf(n3_type, type, np__3: $i).
thf(n4_type, type, np__4: $i).
thf(f1_s12_recdef_2_type, type, f1_s12_recdef_2: $i).
thf(f2_s12_recdef_2_type, type, f2_s12_recdef_2: $i).
thf(f3_s12_recdef_2_type, type, f3_s12_recdef_2: $i).
thf(f4_s12_recdef_2_type, type, f4_s12_recdef_2: $i).
thf(f5_s12_recdef_2_type, type, f5_s12_recdef_2: $i).
thf(f6_s12_recdef_2_type, type, f6_s12_recdef_2: $i).
thf(f7_s12_recdef_2_type, type, f7_s12_recdef_2: $i > $i > $i > $i > $i > $i).
thf(k1_funct_1_type, type, k1_funct_1: $i > $i > $i).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k1_xboole_0_type, type, k1_xboole_0: $i).
thf(k1_xreal_0_type, type, k1_xreal_0: $i > $i > $i).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_nat_1_type, type, k2_nat_1: $i > $i > $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(k4_ordinal1_type, type, k4_ordinal1: $i).
thf(k4_xcmplx_0_type, type, k4_xcmplx_0: $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(k6_numbers_type, type, k6_numbers: $i).
thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i).
thf(k7_nat_d_type, type, k7_nat_d: $i > $i > $i).
thf(k9_xtuple_0_type, type, k9_xtuple_0: $i > $i).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(m2_subset_1_type, type, m2_subset_1: $i > $i > $i > $o).
thf(r1_tarski_type, type, r1_tarski: $i > $i > $o).
thf(r1_xxreal_0_type, type, r1_xxreal_0: $i > $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v1_int_1_type, type, v1_int_1: $i > $o).
thf(v1_ordinal1_type, type, v1_ordinal1: $i > $o).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_subset_1_type, type, v1_subset_1: $i > $i > $o).
thf(v1_xboole_0_type, type, v1_xboole_0: $i > $o).
thf(v1_xcmplx_0_type, type, v1_xcmplx_0: $i > $o).
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(v1_xxreal_0_type, type, v1_xxreal_0: $i > $o).
thf(v2_ordinal1_type, type, v2_ordinal1: $i > $o).
thf(v2_xxreal_0_type, type, v2_xxreal_0: $i > $o).
thf(v3_ordinal1_type, type, v3_ordinal1: $i > $o).
thf(v3_xxreal_0_type, type, v3_xxreal_0: $i > $o).
thf(v5_ordinal1_type, type, v5_ordinal1: $i > $o).
thf(v6_ordinal1_type, type, v6_ordinal1: $i > $o).
thf(v7_ordinal1_type, type, v7_ordinal1: $i > $o).
thf(antisymmetry_r2_hidden, axiom,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden)).
thf(cc10_ordinal1, axiom,  (! [A: $i] :  ( (v6_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc10_ordinal1)).
thf(cc1_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v3_ordinal1 @ A)  &  (v7_ordinal1 @ A) ) ) ) , file(nat_1, cc1_nat_1)).
thf(cc1_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) ) ) ) , file(ordinal1, cc1_ordinal1)).
thf(cc1_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_xboole_0 @ B) ) ) ) ) , file(subset_1, cc1_subset_1)).
thf(cc1_xreal_0, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0)).
thf(cc2_int_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_int_1 @ A) ) ) , file(int_1, cc2_int_1)).
thf(cc2_nat_1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ~ ( (v3_xxreal_0 @ A) ) ) ) , file(nat_1, cc2_nat_1)).
thf(cc2_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_ordinal1 @ A)  &  (v2_ordinal1 @ A) )  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc2_ordinal1)).
thf(cc2_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( ~ ( ( (v1_subset_1 @ B)  @ A) )  =>  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) ) , file(subset_1, cc2_subset_1)).
thf(cc2_xreal_0, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0)).
thf(cc3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(int_1, cc3_int_1)).
thf(cc3_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ( (v7_ordinal1 @ A)  &  ~ ( (v3_xxreal_0 @ A) ) ) ) ) , file(nat_1, cc3_nat_1)).
thf(cc3_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc3_ordinal1)).
thf(cc3_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v1_xboole_0 @ B)  =>  ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc3_subset_1)).
thf(cc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0)).
thf(cc4_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v5_ordinal1 @ A) ) ) , file(ordinal1, cc4_ordinal1)).
thf(cc4_subset_1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) ) , file(subset_1, cc4_subset_1)).
thf(cc4_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0)).
thf(cc5_ordinal1, axiom,  (! [A: $i] :  ( (v3_ordinal1 @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v3_ordinal1 @ B) ) ) ) ) , file(ordinal1, cc5_ordinal1)).
thf(cc6_ordinal1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v3_ordinal1 @ A) ) ) , file(ordinal1, cc6_ordinal1)).
thf(cc7_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc7_ordinal1)).
thf(cc8_ordinal1, axiom,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k4_ordinal1)  =>  (v7_ordinal1 @ A) ) ) , file(ordinal1, cc8_ordinal1)).
thf(cc9_ordinal1, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_ordinal1 @ A) ) ) , file(ordinal1, cc9_ordinal1)).
thf(commutativity_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_nat_1 @ B)  @ A) ) ) ) , file(nat_1, k2_nat_1)).
thf(commutativity_k2_xcmplx_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k2_xcmplx_0)).
thf(connectedness_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( ( (r1_xxreal_0 @ A)  @ B)  |  ( (r1_xxreal_0 @ B)  @ A) ) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(d2_xboole_0, axiom,  ( (= @ k1_xboole_0)  @  (eps @  (^ [A: $i] :  (v1_xboole_0 @ A) ) ) ) , file(xboole_0, d2_xboole_0)).
thf(dt_f1_s12_recdef_2, axiom, $true, file(recdef_2, f1_s12_recdef_2)).
thf(dt_f2_s12_recdef_2, axiom, $true, file(recdef_2, f2_s12_recdef_2)).
thf(dt_f3_s12_recdef_2, axiom, $true, file(recdef_2, f3_s12_recdef_2)).
thf(dt_f4_s12_recdef_2, axiom, $true, file(recdef_2, f4_s12_recdef_2)).
thf(dt_f5_s12_recdef_2, axiom,  ( (v1_relat_1 @ f5_s12_recdef_2)  &  (v1_funct_1 @ f5_s12_recdef_2) ) , file(recdef_2, f5_s12_recdef_2)).
thf(dt_f6_s12_recdef_2, axiom,  ( (v1_relat_1 @ f6_s12_recdef_2)  &  (v1_funct_1 @ f6_s12_recdef_2) ) , file(recdef_2, f6_s12_recdef_2)).
thf(dt_f7_s12_recdef_2, axiom, $true, file(recdef_2, f7_s12_recdef_2)).
thf(dt_k1_funct_1, axiom, $true, file(funct_1, k1_funct_1)).
thf(dt_k1_numbers, axiom, $true, file(numbers, k1_numbers)).
thf(dt_k1_xboole_0, axiom, $true, file(xboole_0, k1_xboole_0)).
thf(dt_k1_xreal_0, axiom, $true, file(xreal_0, k1_xreal_0)).
thf(dt_k1_zfmisc_1, axiom, $true, file(zfmisc_1, k1_zfmisc_1)).
thf(dt_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( ( (m2_subset_1 @  ( (k2_nat_1 @ A)  @ B) )  @ k1_numbers)  @ k5_numbers) ) ) , file(nat_1, k2_nat_1)).
thf(dt_k2_xcmplx_0, axiom, $true, file(xcmplx_0, k2_xcmplx_0)).
thf(dt_k4_ordinal1, axiom, $true, file(ordinal1, k4_ordinal1)).
thf(dt_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(dt_k5_numbers, axiom,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers)).
thf(dt_k6_numbers, axiom,  ( ( (m2_subset_1 @ k6_numbers)  @ k1_numbers)  @ k5_numbers) , file(numbers, k6_numbers)).
thf(dt_k6_xcmplx_0, axiom, $true, file(xcmplx_0, k6_xcmplx_0)).
thf(dt_k7_nat_d, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  ( (m1_subset_1 @  ( (k7_nat_d @ A)  @ B) )  @ k5_numbers) ) ) , file(nat_d, k7_nat_d)).
thf(dt_k9_xtuple_0, axiom, $true, file(xtuple_0, k9_xtuple_0)).
thf(dt_m1_subset_1, axiom, $true, file(subset_1, m1_subset_1)).
thf(dt_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  =>  ( (m1_subset_1 @ C)  @ A) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(existence_m1_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1)).
thf(existence_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (? [C: $i] :  ( ( (m2_subset_1 @ C)  @ A)  @ B) ) ) ) , file(subset_1, m2_subset_1)).
thf(fc10_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc10_xreal_0)).
thf(fc11_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc11_xreal_0)).
thf(fc12_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc12_xreal_0)).
thf(fc13_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc13_xreal_0)).
thf(fc14_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc14_xreal_0)).
thf(fc15_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v3_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc15_xreal_0)).
thf(fc16_xreal_0, axiom,  (! [A: $i] :  ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  ~ ( (v2_xxreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc16_xreal_0)).
thf(fc17_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc17_xreal_0)).
thf(fc18_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc18_xreal_0)).
thf(fc19_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc19_xreal_0)).
thf(fc1_int_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  (v1_int_1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(int_1, fc1_int_1)).
thf(fc1_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  (v7_ordinal1 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, fc1_nat_1)).
thf(fc1_subset_1, axiom,  (! [A: $i] :  ~ ( (v1_xboole_0 @  (k1_zfmisc_1 @ A) ) ) ) , file(subset_1, fc1_subset_1)).
thf(fc20_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc20_xreal_0)).
thf(fc21_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v3_xxreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc21_xreal_0)).
thf(fc22_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  (v2_xxreal_0 @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(xreal_0, fc22_xreal_0)).
thf(fc37_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k1_xreal_0 @ A)  @ B) ) ) ) , file(xreal_0, fc37_xreal_0)).
thf(fc38_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  ( ~ ( (v3_xxreal_0 @  ( (k1_xreal_0 @ A)  @ B) ) )  &  (v1_xreal_0 @  ( (k1_xreal_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc38_xreal_0)).
thf(fc3_int_1, axiom,  (! [A: $i] :  ( (v1_int_1 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_int_1 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(int_1, fc3_int_1)).
thf(fc3_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v7_ordinal1 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(nat_1, fc3_nat_1)).
thf(fc3_xreal_0, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc3_xreal_0)).
thf(fc4_int_1, axiom,  (! [A: $i, B: $i] :  ( ( (v1_int_1 @ A)  &  (v1_int_1 @ B) )  =>  (v1_int_1 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(int_1, fc4_int_1)).
thf(fc4_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v7_ordinal1 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k2_xcmplx_0 @ B)  @ A) ) ) ) ) , file(nat_1, fc4_nat_1)).
thf(fc4_ordinal1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v5_ordinal1 @ A) ) )  =>  (v3_ordinal1 @  (k9_xtuple_0 @ A) ) ) ) , file(ordinal1, fc4_ordinal1)).
thf(fc4_xtuple_0, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v1_xboole_0 @  (k9_xtuple_0 @ A) ) ) ) , file(xtuple_0, fc4_xtuple_0)).
thf(fc5_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc5_xreal_0)).
thf(fc6_ordinal1, axiom,  ( ~ ( (v1_xboole_0 @ k4_ordinal1) )  &  (v3_ordinal1 @ k4_ordinal1) ) , file(ordinal1, fc6_ordinal1)).
thf(fc7_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc7_xreal_0)).
thf(fc9_xreal_0, axiom,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc9_xreal_0)).
thf(involutiveness_k4_xcmplx_0, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ A) ) )  @ A) ) ) , file(xcmplx_0, k4_xcmplx_0)).
thf(rc1_int_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  ( (v1_xxreal_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xreal_0 @ A)  &  (v1_int_1 @ A) ) ) ) ) ) , file(int_1, rc1_int_1)).
thf(rc1_ordinal1, axiom,  (? [A: $i] :  (v3_ordinal1 @ A) ) , file(ordinal1, rc1_ordinal1)).
thf(rc1_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) ) ) ) ) , file(subset_1, rc1_subset_1)).
thf(rc1_xreal_0, axiom,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0)).
thf(rc2_int_1, axiom,  (? [A: $i] :  (v1_int_1 @ A) ) , file(int_1, rc2_int_1)).
thf(rc2_nat_1, axiom,  (? [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v3_ordinal1 @ A) ) ) ) , file(nat_1, rc2_nat_1)).
thf(rc2_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v1_ordinal1 @ A)  &  ( (v2_ordinal1 @ A)  &  (v3_ordinal1 @ A) ) ) ) ) , file(ordinal1, rc2_ordinal1)).
thf(rc2_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  (v1_xboole_0 @ B) ) ) ) , file(subset_1, rc2_subset_1)).
thf(rc2_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc2_xreal_0)).
thf(rc3_subset_1, axiom,  (! [A: $i] :  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ~ ( ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc3_subset_1)).
thf(rc3_xreal_0, axiom,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0)).
thf(rc4_ordinal1, axiom,  (? [A: $i] :  (v7_ordinal1 @ A) ) , file(ordinal1, rc4_ordinal1)).
thf(rc4_subset_1, axiom,  (! [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  =>  (? [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  &  ( (v1_subset_1 @ B)  @ A) ) ) ) ) , file(subset_1, rc4_subset_1)).
thf(rc4_xreal_0, axiom,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0)).
thf(rc5_ordinal1, axiom,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v7_ordinal1 @ A) ) ) , file(ordinal1, rc5_ordinal1)).
thf(redefinition_k2_nat_1, axiom,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k5_numbers)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k2_nat_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(nat_1, k2_nat_1)).
thf(redefinition_k5_numbers, axiom,  ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers)).
thf(redefinition_k6_numbers, axiom,  ( (= @ k6_numbers)  @ k1_xboole_0) , file(numbers, k6_numbers)).
thf(redefinition_k7_nat_d, axiom,  (! [A: $i, B: $i] :  ( ( (v7_ordinal1 @ A)  &  (v7_ordinal1 @ B) )  =>  ( (= @  ( (k7_nat_d @ A)  @ B) )  @  ( (k1_xreal_0 @ A)  @ B) ) ) ) , file(nat_d, k7_nat_d)).
thf(redefinition_m2_subset_1, axiom,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) ) ) )  =>  (! [C: $i] :  ( ( ( (m2_subset_1 @ C)  @ A)  @ B)  <=>  ( (m1_subset_1 @ C)  @ B) ) ) ) ) , file(subset_1, m2_subset_1)).
thf(reflexivity_r1_tarski, axiom,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski)).
thf(reflexivity_r1_xxreal_0, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xxreal_0 @ A)  &  (v1_xxreal_0 @ B) )  =>  ( (r1_xxreal_0 @ A)  @ A) ) ) , file(xxreal_0, r1_xxreal_0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r2, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r3, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r0_r4, axiom,  ( (r1_xxreal_0 @ np__0)  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r0_rm4, axiom,  ~ ( ( (r1_xxreal_0 @ np__0)  @  (k4_xcmplx_0 @ np__4) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r0_rm4)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r2, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r3, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r1_r4, axiom,  ( (r1_xxreal_0 @ np__1)  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r1_rm4, axiom,  ~ ( ( (r1_xxreal_0 @ np__1)  @  (k4_xcmplx_0 @ np__4) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r1_rm4)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r2, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r3, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_r4, axiom,  ( (r1_xxreal_0 @ np__2)  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r2_rm4, axiom,  ~ ( ( (r1_xxreal_0 @ np__2)  @  (k4_xcmplx_0 @ np__4) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r2_rm4)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r3, axiom,  ( (r1_xxreal_0 @ np__3)  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r3_r4, axiom,  ( (r1_xxreal_0 @ np__3)  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r3_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__3)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r3_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r0, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @ np__0) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_r0)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r1, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_r1)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r2, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_r2)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r3, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @ np__3) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_r3)).
thf(rqLessOrEqual__r1_xxreal_0__r4_r4, axiom,  ( (r1_xxreal_0 @ np__4)  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_r4)).
thf(rqLessOrEqual__r1_xxreal_0__r4_rm1, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @  (k4_xcmplx_0 @ np__1) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__r4_rm2, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__r4_rm3, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__r4_rm4, axiom,  ~ ( ( (r1_xxreal_0 @ np__4)  @  (k4_xcmplx_0 @ np__4) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__r4_rm4)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_r4, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_r4)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm2, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm3, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm1_rm4, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__4) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm1_rm4)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_r4, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_r4)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm2_rm3, axiom,  ~ ( ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm2_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__3) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r3)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_r4, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_r4)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm3_rm3, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm3_rm3)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_r0, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @ np__0) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_r0)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_r1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @ np__1) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_r1)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_r2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @ np__2) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_r2)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_r4, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @ np__4) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_r4)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_rm1, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_rm1)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_rm2, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_rm2)).
thf(rqLessOrEqual__r1_xxreal_0__rm4_rm4, axiom,  ( (r1_xxreal_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqLessOrEqual__r1_xxreal_0__rm4_rm4)).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__1) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__2) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)).
thf(rqRealAdd__k2_xcmplx_0__r0_r3_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__3) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r3_r3)).
thf(rqRealAdd__k2_xcmplx_0__r0_r4_r4, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__4) )  @ np__4) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r4_r4)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r0_rm3_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm3_rm3)).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)).
thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__1) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r1_r2_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__2) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r2_r3)).
thf(rqRealAdd__k2_xcmplx_0__r1_r3_r4, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__3) )  @ np__4) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r3_r4)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm3_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm3_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r1_rm4_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__4) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm4_rm3)).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)).
thf(rqRealAdd__k2_xcmplx_0__r2_r1_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__1) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r1_r3)).
thf(rqRealAdd__k2_xcmplx_0__r2_r2_r4, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__2) )  @ np__4) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r2_r4)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm3_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm3_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r2_rm4_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__4) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm4_rm2)).
thf(rqRealAdd__k2_xcmplx_0__r3_r0_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @ np__0) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_r0_r3)).
thf(rqRealAdd__k2_xcmplx_0__r3_r1_r4, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @ np__1) )  @ np__4) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_r1_r4)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm1_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm1_r2)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm2_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm2_r1)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm3_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm3_r0)).
thf(rqRealAdd__k2_xcmplx_0__r3_rm4_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__4) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r3_rm4_rm1)).
thf(rqRealAdd__k2_xcmplx_0__r4_r0_r4, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__4)  @ np__0) )  @ np__4) , file(arithm, rqRealAdd__k2_xcmplx_0__r4_r0_r4)).
thf(rqRealAdd__k2_xcmplx_0__r4_rm1_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__4)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__r4_rm1_r3)).
thf(rqRealAdd__k2_xcmplx_0__r4_rm2_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__4)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r4_rm2_r2)).
thf(rqRealAdd__k2_xcmplx_0__r4_rm3_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__4)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r4_rm3_r1)).
thf(rqRealAdd__k2_xcmplx_0__r4_rm4_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @ np__4)  @  (k4_xcmplx_0 @ np__4) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r4_rm4_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r3_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r3_r2)).
thf(rqRealAdd__k2_xcmplx_0__rm1_r4_r3, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__4) )  @ np__3) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r4_r3)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm2_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm3_rm4)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r3_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__3) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r3_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm2_r4_r2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__4) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r4_r2)).
thf(rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rm1_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_rm2_rm4)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r1_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r1_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r2_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r2_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r3_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__3) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r3_r0)).
thf(rqRealAdd__k2_xcmplx_0__rm3_r4_r1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__4) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_r4_r1)).
thf(rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm3_rm1_rm4)).
thf(rqRealAdd__k2_xcmplx_0__rm4_r1_rm3, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm4_r1_rm3)).
thf(rqRealAdd__k2_xcmplx_0__rm4_r2_rm2, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm4_r2_rm2)).
thf(rqRealAdd__k2_xcmplx_0__rm4_r3_rm1, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm4_r3_rm1)).
thf(rqRealAdd__k2_xcmplx_0__rm4_r4_r0, axiom,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @ np__4) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm4_r4_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r0_r3_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r3_rm3)).
thf(rqRealDiff__k6_xcmplx_0__r0_r4_rm4, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__4) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r4_rm4)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm3_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm3_r3)).
thf(rqRealDiff__k6_xcmplx_0__r0_rm4_r4, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__4) ) )  @ np__4) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm4_r4)).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__1) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)).
thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r1_r3_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r3_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r1_r4_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__4) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r4_rm3)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm2_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm2_r3)).
thf(rqRealDiff__k6_xcmplx_0__r1_rm3_r4, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__3) ) )  @ np__4) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm3_r4)).
thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)).
thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__1) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)).
thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__2) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0)).
thf(rqRealDiff__k6_xcmplx_0__r2_r3_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r3_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r2_r4_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__4) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r4_rm2)).
thf(rqRealDiff__k6_xcmplx_0__r2_rm1_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rm1_r3)).
thf(rqRealDiff__k6_xcmplx_0__r2_rm2_r4, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__4) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_rm2_r4)).
thf(rqRealDiff__k6_xcmplx_0__r3_r0_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__0) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r0_r3)).
thf(rqRealDiff__k6_xcmplx_0__r3_r1_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__1) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r1_r2)).
thf(rqRealDiff__k6_xcmplx_0__r3_r2_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__2) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r2_r1)).
thf(rqRealDiff__k6_xcmplx_0__r3_r3_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__3) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r3_r0)).
thf(rqRealDiff__k6_xcmplx_0__r3_r4_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @ np__4) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_r4_rm1)).
thf(rqRealDiff__k6_xcmplx_0__r3_rm1_r4, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__3)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__4) , file(arithm, rqRealDiff__k6_xcmplx_0__r3_rm1_r4)).
thf(rqRealDiff__k6_xcmplx_0__r4_r0_r4, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__4)  @ np__0) )  @ np__4) , file(arithm, rqRealDiff__k6_xcmplx_0__r4_r0_r4)).
thf(rqRealDiff__k6_xcmplx_0__r4_r1_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__4)  @ np__1) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__r4_r1_r3)).
thf(rqRealDiff__k6_xcmplx_0__r4_r2_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__4)  @ np__2) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r4_r2_r2)).
thf(rqRealDiff__k6_xcmplx_0__r4_r3_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__4)  @ np__3) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r4_r3_r1)).
thf(rqRealDiff__k6_xcmplx_0__r4_r4_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @ np__4)  @ np__4) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r4_r4_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r2_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r2_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm1_r3_rm4, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__3) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r3_rm4)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm3_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm3_r2)).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm4_r3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__4) ) )  @ np__3) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm4_r3)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r1_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r1_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm2_r2_rm4, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r2_rm4)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm3_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__3) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm3_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm4_r2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__4) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm4_r2)).
thf(rqRealDiff__k6_xcmplx_0__rm3_r0_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__0) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_r0_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm3_r1_rm4, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @ np__1) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_r1_rm4)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm1_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm2_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm3_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm3_r0)).
thf(rqRealDiff__k6_xcmplx_0__rm3_rm4_r1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__4) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm3_rm4_r1)).
thf(rqRealDiff__k6_xcmplx_0__rm4_r0_rm4, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @ np__0) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm4_r0_rm4)).
thf(rqRealDiff__k6_xcmplx_0__rm4_rm1_rm3, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm4_rm1_rm3)).
thf(rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm4_rm2_rm2)).
thf(rqRealDiff__k6_xcmplx_0__rm4_rm3_rm1, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__3) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm4_rm3_rm1)).
thf(rqRealDiff__k6_xcmplx_0__rm4_rm4_r0, axiom,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__4) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm4_rm4_r0)).
thf(rqRealNeg__k4_xcmplx_0__r0_r0, axiom,  ( (= @  (k4_xcmplx_0 @ np__0) )  @ np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1, axiom,  ( (= @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)).
thf(rqRealNeg__k4_xcmplx_0__r2_rm2, axiom,  ( (= @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)).
thf(rqRealNeg__k4_xcmplx_0__r3_rm3, axiom,  ( (= @  (k4_xcmplx_0 @ np__3) )  @  (k4_xcmplx_0 @ np__3) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r3_rm3)).
thf(rqRealNeg__k4_xcmplx_0__r4_rm4, axiom,  ( (= @  (k4_xcmplx_0 @ np__4) )  @  (k4_xcmplx_0 @ np__4) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r4_rm4)).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)).
thf(rqRealNeg__k4_xcmplx_0__rm2_r2, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)).
thf(rqRealNeg__k4_xcmplx_0__rm3_r3, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__3) ) )  @ np__3) , file(arithm, rqRealNeg__k4_xcmplx_0__rm3_r3)).
thf(rqRealNeg__k4_xcmplx_0__rm4_r4, axiom,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__4) ) )  @ np__4) , file(arithm, rqRealNeg__k4_xcmplx_0__rm4_r4)).
thf(spc0_boole, axiom,  (v1_xboole_0 @ np__0) , file(boole, spc0_boole)).
thf(spc0_numerals, axiom,  ( ( ( (m2_subset_1 @ np__0)  @ k1_numbers)  @ k5_numbers)  &  ( ( (m1_subset_1 @ np__0)  @ k5_numbers)  &  ( (m1_subset_1 @ np__0)  @ k1_numbers) ) ) , file(numerals, spc0_numerals)).
thf(spc1_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(arithm, spc1_arithm)).
thf(spc1_boole, axiom,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole)).
thf(spc1_numerals, axiom,  ( ( (v2_xxreal_0 @ np__1)  &  ( ( (m2_subset_1 @ np__1)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__1)  @ k5_numbers)  &  ( (m1_subset_1 @ np__1)  @ k1_numbers) ) ) , file(numerals, spc1_numerals)).
thf(spc2_boole, axiom,  ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole)).
thf(spc2_numerals, axiom,  ( ( (v2_xxreal_0 @ np__2)  &  ( ( (m2_subset_1 @ np__2)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__2)  @ k5_numbers)  &  ( (m1_subset_1 @ np__2)  @ k1_numbers) ) ) , file(numerals, spc2_numerals)).
thf(spc3_boole, axiom,  ~ ( (v1_xboole_0 @ np__3) ) , file(boole, spc3_boole)).
thf(spc3_numerals, axiom,  ( ( (v2_xxreal_0 @ np__3)  &  ( ( (m2_subset_1 @ np__3)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__3)  @ k5_numbers)  &  ( (m1_subset_1 @ np__3)  @ k1_numbers) ) ) , file(numerals, spc3_numerals)).
thf(spc4_boole, axiom,  ~ ( (v1_xboole_0 @ np__4) ) , file(boole, spc4_boole)).
thf(spc4_numerals, axiom,  ( ( (v2_xxreal_0 @ np__4)  &  ( ( (m2_subset_1 @ np__4)  @ k1_numbers)  @ k5_numbers) )  &  ( ( (m1_subset_1 @ np__4)  @ k5_numbers)  &  ( (m1_subset_1 @ np__4)  @ k1_numbers) ) ) , file(numerals, spc4_numerals)).
thf(spc6_arithm, axiom,  (! [A: $i, B: $i, C: $i] :  ( ( (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) ) ) ) ) , file(arithm, spc6_arithm)).
thf(spc8_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (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) ) ) ) ) , file(arithm, spc8_arithm)).
thf(spc9_arithm, axiom,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ A) )  @  (k4_xcmplx_0 @ B) ) )  @  ( (k6_xcmplx_0 @ B)  @ A) ) ) ) , file(arithm, spc9_arithm)).
thf(t1_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k2_xcmplx_0 @ A)  @ k6_numbers) )  @ A) ) ) , file(arithm, t1_arithm)).
thf(t1_numerals, axiom,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals)).
thf(t1_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v2_xxreal_0 @ A) )  =>  (v2_xxreal_0 @ B) ) ) ) ) ) , file(real, t1_real)).
thf(t1_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset)).
thf(t235_xreal_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ B)  @ A)  =>  ( (= @  ( (k2_xcmplx_0 @  ( (k1_xreal_0 @ A)  @ B) )  @ B) )  @ A) ) ) ) ) ) , file(xreal_1, t235_xreal_1)).
thf(t28_nat_1, axiom,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ np__4)  &  ( ~ ( ( (= @ A)  @ k6_numbers) )  &  ( ~ ( ( (= @ A)  @ np__1) )  &  ( ~ ( ( (= @ A)  @ np__2) )  &  ( ~ ( ( (= @ A)  @ np__3) )  &  ~ ( ( (= @ A)  @ np__4) ) ) ) ) ) ) ) ) ) , file(nat_1, t28_nat_1)).
thf(t2_funct_1, axiom,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_funct_1 @ A) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  (v1_funct_1 @ B) )  =>  ( ( ( (= @  (k9_xtuple_0 @ A) )  @  (k9_xtuple_0 @ B) )  &  (! [C: $i] :  ( ( (r2_hidden @ C)  @  (k9_xtuple_0 @ A) )  =>  ( (= @  ( (k1_funct_1 @ A)  @ C) )  @  ( (k1_funct_1 @ B)  @ C) ) ) ) )  =>  ( (= @ A)  @ B) ) ) ) ) ) , file(funct_1, t2_funct_1)).
thf(t2_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( ( (r1_xxreal_0 @ A)  @ B)  &  (v3_xxreal_0 @ B) )  =>  (v3_xxreal_0 @ A) ) ) ) ) ) , file(real, t2_real)).
thf(t2_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset)).
thf(t3_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v3_xxreal_0 @ A) )  &  (v3_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t3_real)).
thf(t3_subset, axiom,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset)).
thf(t4_arithm, axiom,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k6_xcmplx_0 @ A)  @ k6_numbers) )  @ A) ) ) , file(arithm, t4_arithm)).
thf(t4_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ( (r1_xxreal_0 @ A)  @ B)  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v2_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t4_real)).
thf(t4_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ( ( ( (r2_hidden @ A)  @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) ) )  =>  ( (m1_subset_1 @ A)  @ C) ) ) ) ) , file(subset, t4_subset)).
thf(t5_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (v3_xxreal_0 @ A)  |  (v2_xxreal_0 @ B) ) ) ) ) ) ) ) , file(real, t5_real)).
thf(t5_subset, axiom,  (! [A: $i] :  (! [B: $i] :  (! [C: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ C) )  &  (v1_xboole_0 @ C) ) ) ) ) ) ) , file(subset, t5_subset)).
thf(t6_boole, axiom,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (= @ A)  @ k1_xboole_0) ) ) , file(boole, t6_boole)).
thf(t6_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  =>  ( (v1_xboole_0 @ A)  |  ( (v2_xxreal_0 @ B)  |  (v3_xxreal_0 @ A) ) ) ) ) ) ) ) , file(real, t6_real)).
thf(t6_xreal_1, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  (! [C: $i] :  ( (v1_xreal_0 @ C)  =>  ( ( (r1_xxreal_0 @ A)  @ B)  <=>  ( (r1_xxreal_0 @  ( (k2_xcmplx_0 @ A)  @ C) )  @  ( (k2_xcmplx_0 @ B)  @ C) ) ) ) ) ) ) ) ) , file(xreal_1, t6_xreal_1)).
thf(t7_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole)).
thf(t7_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v2_xxreal_0 @ A) )  &  ~ ( (v3_xxreal_0 @ B) ) ) ) ) ) ) ) ) , file(real, t7_real)).
thf(t8_boole, axiom,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole)).
thf(t8_real, axiom,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ~ ( ( ~ ( ( (r1_xxreal_0 @ A)  @ B) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  ~ ( (v2_xxreal_0 @ A) ) ) ) ) ) ) ) ) , file(real, t8_real)).
thf(s5_nat_1, axiom,  (! [A: $i > $o] :  ( (? [B: $i] :  ( (v7_ordinal1 @ B)  &  (A @ B) ) )  =>  (? [B: $i] :  ( (v7_ordinal1 @ B)  &  ( (A @ B)  &  (! [C: $i] :  ( (v7_ordinal1 @ C)  =>  ( (A @ C)  =>  ( (r1_xxreal_0 @ B)  @ C) ) ) ) ) ) ) ) ) , file(nat_1, s5_nat_1)).
thf(s12_recdef_2, conjecture,  ( ( ( (= @  (k9_xtuple_0 @ f5_s12_recdef_2) )  @ k5_numbers)  &  ( ( ( (= @  ( (k1_funct_1 @ f5_s12_recdef_2)  @ k6_numbers) )  @ f1_s12_recdef_2)  &  ( ( (= @  ( (k1_funct_1 @ f5_s12_recdef_2)  @ np__1) )  @ f2_s12_recdef_2)  &  ( ( (= @  ( (k1_funct_1 @ f5_s12_recdef_2)  @ np__2) )  @ f3_s12_recdef_2)  &  ( (= @  ( (k1_funct_1 @ f5_s12_recdef_2)  @ np__3) )  @ f4_s12_recdef_2) ) ) )  &  ( (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ( (= @  ( (k1_funct_1 @ f5_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__4) ) )  @  ( ( ( ( (f7_s12_recdef_2 @ A)  @  ( (k1_funct_1 @ f5_s12_recdef_2)  @ A) )  @  ( (k1_funct_1 @ f5_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__1) ) )  @  ( (k1_funct_1 @ f5_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__2) ) )  @  ( (k1_funct_1 @ f5_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__3) ) ) ) ) )  &  ( ( (= @  (k9_xtuple_0 @ f6_s12_recdef_2) )  @ k5_numbers)  &  ( ( ( (= @  ( (k1_funct_1 @ f6_s12_recdef_2)  @ k6_numbers) )  @ f1_s12_recdef_2)  &  ( ( (= @  ( (k1_funct_1 @ f6_s12_recdef_2)  @ np__1) )  @ f2_s12_recdef_2)  &  ( ( (= @  ( (k1_funct_1 @ f6_s12_recdef_2)  @ np__2) )  @ f3_s12_recdef_2)  &  ( (= @  ( (k1_funct_1 @ f6_s12_recdef_2)  @ np__3) )  @ f4_s12_recdef_2) ) ) )  &  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  ( (= @  ( (k1_funct_1 @ f6_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__4) ) )  @  ( ( ( ( (f7_s12_recdef_2 @ A)  @  ( (k1_funct_1 @ f6_s12_recdef_2)  @ A) )  @  ( (k1_funct_1 @ f6_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__1) ) )  @  ( (k1_funct_1 @ f6_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__2) ) )  @  ( (k1_funct_1 @ f6_s12_recdef_2)  @  ( (k2_nat_1 @ A)  @ np__3) ) ) ) ) ) ) ) ) ) )  =>  ( (= @ f5_s12_recdef_2)  @ f6_s12_recdef_2) ) , file(recdef_2, s12_recdef_2)).
