% Mizar ND problem: t1_diff_3,diff_3,41,5 
thf(dh_c1_1__diff_3, definition,  ( ( ( (m1_subset_1 @ c1_1__diff_3)  @ k1_numbers)  =>  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ B)  @ c1_1__diff_3) )  @ A) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ B)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ A) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ B)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ A) ) ) ) ) ) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @ k1_numbers)  =>  (! [D: $i] :  ( ( (m1_subset_1 @ D)  @ k1_numbers)  =>  (! [E: $i] :  ( ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ E)  @ C) )  @ D) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ E)  @  ( (k10_real_1 @ C)  @ np__2) ) )  @ D) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ E)  @  (k1_real_1 @  ( (k10_real_1 @ C)  @ np__2) ) ) )  @ D) ) ) ) ) ) ) ) ) ) , introduced(definition, [new_symbol(c1_1__diff_3), file(diff_3, c1_1__diff_3)]), [interesting(np__0.8), axiom, file(diff_3, c1_1__diff_3)]).
thf(dh_c2_1__diff_3, definition,  ( ( ( (m1_subset_1 @ c2_1__diff_3)  @ k1_numbers)  =>  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ A)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) ) ) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ C)  @ c1_1__diff_3) )  @ B) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ C)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ B) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ C)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ B) ) ) ) ) ) ) ) , introduced(definition, [new_symbol(c2_1__diff_3), file(diff_3, c2_1__diff_3)]), [interesting(np__0.8), axiom, file(diff_3, c2_1__diff_3)]).
thf(dh_c3_1__diff_3, definition,  ( ( ( (v1_funct_1 @ c3_1__diff_3)  &  ( ( ( (v1_funct_2 @ c3_1__diff_3)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ c3_1__diff_3)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ c3_1__diff_3)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) )  =>  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ A)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) ) ) ) , introduced(definition, [new_symbol(c3_1__diff_3), file(diff_3, c3_1__diff_3)]), [interesting(np__0.8), axiom, file(diff_3, c3_1__diff_3)]).
thf(cc15_membered, theorem,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_rat_1 @ B) ) ) ) ) , file(membered, cc15_membered), [interesting(np__0.9), axiom, file(membered, cc15_membered)]).
thf(cc19_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k3_numbers) ) ) ) ) , file(valued_0, cc19_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc19_valued_0)]).
thf(cc22_membered, theorem,  (! [A: $i] :  ( (v4_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_membered @ B) ) ) ) ) , file(membered, cc22_membered), [interesting(np__0.9), axiom, file(membered, cc22_membered)]).
thf(cc3_membered, theorem,  (! [A: $i] :  ( (v4_membered @ A)  =>  (v3_membered @ A) ) ) , file(membered, cc3_membered), [interesting(np__0.9), axiom, file(membered, cc3_membered)]).
thf(fc87_valued_1, theorem,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v4_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v4_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc87_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc87_valued_1)]).
thf(fc88_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v4_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k3_numbers) ) ) , file(valued_0, fc88_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc88_valued_0)]).
thf(dt_k3_numbers, plain, $true, file(numbers, k3_numbers), [interesting(np__0.9), axiom, file(numbers, k3_numbers)]).
thf(dt_k4_numbers, plain, $true, file(numbers, k4_numbers), [interesting(np__0.9), axiom, file(numbers, k4_numbers)]).
thf(cc10_membered, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k4_numbers) )  =>  (v5_membered @ A) ) ) , file(membered, cc10_membered), [interesting(np__0.9), axiom, file(membered, cc10_membered)]).
thf(cc12_membered, theorem,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xcmplx_0 @ B) ) ) ) ) , file(membered, cc12_membered), [interesting(np__0.9), axiom, file(membered, cc12_membered)]).
thf(cc13_membered, theorem,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xxreal_0 @ B) ) ) ) ) , file(membered, cc13_membered), [interesting(np__0.9), axiom, file(membered, cc13_membered)]).
thf(cc13_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k3_numbers) ) ) ) ) , file(valued_0, cc13_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc13_valued_0)]).
thf(cc14_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  ( (v5_relat_1 @ B)  @ k4_numbers) ) ) ) ) , file(valued_0, cc14_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc14_valued_0)]).
thf(cc16_membered, theorem,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_int_1 @ B) ) ) ) ) , file(membered, cc16_membered), [interesting(np__0.9), axiom, file(membered, cc16_membered)]).
thf(cc16_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_valued_0 @ C) ) ) ) ) , file(valued_0, cc16_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc16_valued_0)]).
thf(cc17_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v2_valued_0 @ C) ) ) ) ) , file(valued_0, cc17_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc17_valued_0)]).
thf(cc19_membered, theorem,  (! [A: $i] :  ( (v1_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_membered @ B) ) ) ) ) , file(membered, cc19_membered), [interesting(np__0.9), axiom, file(membered, cc19_membered)]).
thf(cc20_membered, theorem,  (! [A: $i] :  ( (v2_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_membered @ B) ) ) ) ) , file(membered, cc20_membered), [interesting(np__0.9), axiom, file(membered, cc20_membered)]).
thf(cc20_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( (v5_relat_1 @ C)  @ k4_numbers) ) ) ) ) , file(valued_0, cc20_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc20_valued_0)]).
thf(cc23_membered, theorem,  (! [A: $i] :  ( (v5_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v5_membered @ B) ) ) ) ) , file(membered, cc23_membered), [interesting(np__0.9), axiom, file(membered, cc23_membered)]).
thf(cc2_membered, theorem,  (! [A: $i] :  ( (v5_membered @ A)  =>  (v4_membered @ A) ) ) , file(membered, cc2_membered), [interesting(np__0.9), axiom, file(membered, cc2_membered)]).
thf(cc2_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc2_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc2_valued_0)]).
thf(cc2_xcmplx_0, theorem,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, cc2_xcmplx_0)]).
thf(cc2_xreal_0, theorem,  (! [A: $i] :  ( (v7_ordinal1 @ A)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc2_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc2_xreal_0)]).
thf(cc3_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc3_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc3_valued_0)]).
thf(cc4_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc4_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc4_valued_0)]).
thf(cc9_membered, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k3_numbers) )  =>  (v4_membered @ A) ) ) , file(membered, cc9_membered), [interesting(np__0.9), axiom, file(membered, cc9_membered)]).
thf(fc3_numbers, theorem,  ~ ( (v1_xboole_0 @ k3_numbers) ) , file(numbers, fc3_numbers), [interesting(np__0.9), axiom, file(numbers, fc3_numbers)]).
thf(fc4_membered, theorem,  (v4_membered @ k3_numbers) , file(membered, fc4_membered), [interesting(np__0.9), axiom, file(membered, fc4_membered)]).
thf(fc4_numbers, theorem,  ~ ( (v1_xboole_0 @ k4_numbers) ) , file(numbers, fc4_numbers), [interesting(np__0.9), axiom, file(numbers, fc4_numbers)]).
thf(fc57_membered, theorem,  (v7_membered @ k3_numbers) , file(membered, fc57_membered), [interesting(np__0.9), axiom, file(membered, fc57_membered)]).
thf(fc58_membered, theorem,  (v7_membered @ k4_numbers) , file(membered, fc58_membered), [interesting(np__0.9), axiom, file(membered, fc58_membered)]).
thf(fc5_membered, theorem,  (v5_membered @ k4_numbers) , file(membered, fc5_membered), [interesting(np__0.9), axiom, file(membered, fc5_membered)]).
thf(fc64_valued_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_rat_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc64_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc64_valued_0)]).
thf(fc65_valued_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  =>  (v1_int_1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc65_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc65_valued_0)]).
thf(fc6_numbers, theorem,  ~ ( (v1_finset_1 @ k4_numbers) ) , file(numbers, fc6_numbers), [interesting(np__0.9), axiom, file(numbers, fc6_numbers)]).
thf(fc7_numbers, theorem,  ~ ( (v1_finset_1 @ k3_numbers) ) , file(numbers, fc7_numbers), [interesting(np__0.9), axiom, file(numbers, fc7_numbers)]).
thf(fc83_valued_1, theorem,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k3_numbers)  &  (v1_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ k3_numbers)  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  @ k3_numbers)  &  (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc83_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc83_valued_1)]).
thf(fc84_valued_1, theorem,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( ( (v5_relat_1 @ A)  @ k4_numbers)  &  (v1_funct_1 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( ( (v5_relat_1 @ B)  @ k4_numbers)  &  (v1_funct_1 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  &  ( ( (v5_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  @ k4_numbers)  &  (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc84_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc84_valued_1)]).
thf(fc85_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v1_membered @ B)  =>  (v1_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc85_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc85_valued_0)]).
thf(fc85_valued_1, theorem,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v1_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v1_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc85_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc85_valued_1)]).
thf(fc86_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v2_membered @ B)  =>  (v2_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc86_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc86_valued_0)]).
thf(fc88_valued_1, theorem,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v5_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v5_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc88_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc88_valued_1)]).
thf(fc89_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v5_membered @ B)  =>  ( (v5_relat_1 @  ( (k2_zfmisc_1 @ A)  @ B) )  @ k4_numbers) ) ) , file(valued_0, fc89_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc89_valued_0)]).
thf(rc5_valued_1, theorem,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( ( (v5_relat_1 @ B)  @ k3_numbers)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  ( (v1_valued_0 @ B)  &  ( (v2_valued_0 @ B)  &  ( (v3_valued_0 @ B)  &  (v4_valued_0 @ B) ) ) ) ) ) ) ) ) ) ) , file(valued_1, rc5_valued_1), [interesting(np__0.9), axiom, file(valued_1, rc5_valued_1)]).
thf(commutativity_k2_xcmplx_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xcmplx_0, k2_xcmplx_0)]).
thf(commutativity_k3_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @ B) )  @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) , file(xcmplx_0, k3_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k3_xcmplx_0)]).
thf(involutiveness_k5_xcmplx_0, theorem,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k5_xcmplx_0 @  (k5_xcmplx_0 @ A) ) )  @ A) ) ) , file(xcmplx_0, k5_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k5_xcmplx_0)]).
thf(reflexivity_r1_tarski, theorem,  (! [A: $i, B: $i] :  ( (r1_tarski @ A)  @ A) ) , file(tarski, r1_tarski), [interesting(np__0.9), axiom, file(tarski, r1_tarski)]).
thf(antisymmetry_r2_hidden, theorem,  (! [A: $i, B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ~ ( ( (r2_hidden @ B)  @ A) ) ) ) , file(hidden, r2_hidden), [interesting(np__0.9), axiom, file(hidden, r2_hidden)]).
thf(dt_k1_xboole_0, plain, $true, file(xboole_0, k1_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, k1_xboole_0)]).
thf(dt_k2_xcmplx_0, plain, $true, file(xcmplx_0, k2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k2_xcmplx_0)]).
thf(dt_k3_xcmplx_0, plain, $true, file(xcmplx_0, k3_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k3_xcmplx_0)]).
thf(dt_k45_valued_1, plain,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  &  (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) , file(valued_1, k45_valued_1), [interesting(np__0.9), axiom, file(valued_1, k45_valued_1)]).
thf(dt_k4_ordinal1, plain, $true, file(ordinal1, k4_ordinal1), [interesting(np__0.9), axiom, file(ordinal1, k4_ordinal1)]).
thf(dt_k5_xcmplx_0, plain,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k5_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k5_xcmplx_0)]).
thf(cc10_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v1_valued_0 @ B) ) ) ) ) , file(valued_0, cc10_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc10_valued_0)]).
thf(cc11_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v2_valued_0 @ B) ) ) ) ) , file(valued_0, cc11_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc11_valued_0)]).
thf(cc14_membered, theorem,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v1_xreal_0 @ B) ) ) ) ) , file(membered, cc14_membered), [interesting(np__0.9), axiom, file(membered, cc14_membered)]).
thf(cc15_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v4_valued_0 @ B) ) ) ) ) , file(valued_0, cc15_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc15_valued_0)]).
thf(cc17_membered, theorem,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ A)  =>  (v7_ordinal1 @ B) ) ) ) ) , file(membered, cc17_membered), [interesting(np__0.9), axiom, file(membered, cc17_membered)]).
thf(cc18_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v3_valued_0 @ C) ) ) ) ) , file(valued_0, cc18_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc18_valued_0)]).
thf(cc1_funct_2, theorem,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_partfun1 @ C)  @ A)  =>  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) , file(funct_2, cc1_funct_2), [interesting(np__0.9), axiom, file(funct_2, cc1_funct_2)]).
thf(cc1_membered, theorem,  (! [A: $i] :  ( (v6_membered @ A)  =>  (v5_membered @ A) ) ) , file(membered, cc1_membered), [interesting(np__0.9), axiom, file(membered, cc1_membered)]).
thf(cc1_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k4_numbers) ) ) ) , file(valued_0, cc1_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc1_valued_0)]).
thf(cc21_membered, theorem,  (! [A: $i] :  ( (v3_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_membered @ B) ) ) ) ) , file(membered, cc21_membered), [interesting(np__0.9), axiom, file(membered, cc21_membered)]).
thf(cc21_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v4_valued_0 @ C) ) ) ) ) , file(valued_0, cc21_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc21_valued_0)]).
thf(cc24_membered, theorem,  (! [A: $i] :  ( (v6_membered @ A)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v6_membered @ B) ) ) ) ) , file(membered, cc24_membered), [interesting(np__0.9), axiom, file(membered, cc24_membered)]).
thf(cc30_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k1_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc30_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc30_valued_0)]).
thf(cc31_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k5_numbers) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc31_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc31_valued_0)]).
thf(cc4_membered, theorem,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v2_membered @ A) ) ) , file(membered, cc4_membered), [interesting(np__0.9), axiom, file(membered, cc4_membered)]).
thf(cc5_membered, theorem,  (! [A: $i] :  ( (v3_membered @ A)  =>  (v1_membered @ A) ) ) , file(membered, cc5_membered), [interesting(np__0.9), axiom, file(membered, cc5_membered)]).
thf(cc7_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  ( (v5_relat_1 @ A)  @ k3_numbers) ) ) ) , file(valued_0, cc7_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc7_valued_0)]).
thf(cc8_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) ) ) ) , file(valued_0, cc8_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc8_valued_0)]).
thf(fc10_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc10_xreal_0)]).
thf(fc11_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc11_xreal_0)]).
thf(fc126_valued_1, theorem,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  (v1_valued_0 @ C) ) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ B)  @ C) )  &  ( ( (v4_relat_1 @  ( (k45_valued_1 @ B)  @ C) )  @ A)  &  (v1_funct_1 @  ( (k45_valued_1 @ B)  @ C) ) ) ) ) ) , file(valued_1, fc126_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc126_valued_1)]).
thf(fc12_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc12_xreal_0)]).
thf(fc130_valued_1, theorem,  (! [A: $i, B: $i, C: $i] :  ( ( ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v1_valued_0 @ B) ) ) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_partfun1 @ C)  @ A)  &  (v1_valued_0 @ C) ) ) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ B)  @ C) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ B)  @ C) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ B)  @ C) )  @ A) ) ) ) ) , file(valued_1, fc130_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc130_valued_1)]).
thf(fc13_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc13_xreal_0)]).
thf(fc14_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc14_xreal_0)]).
thf(fc16_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc16_xreal_0)]).
thf(fc17_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc17_xreal_0)]).
thf(fc18_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc18_xreal_0)]).
thf(fc1_xboole_0, theorem,  (v1_xboole_0 @ k1_xboole_0) , file(xboole_0, fc1_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, fc1_xboole_0)]).
thf(fc21_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc21_xreal_0)]).
thf(fc22_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc22_xreal_0)]).
thf(fc23_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc23_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc23_xreal_0)]).
thf(fc24_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k3_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc24_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc24_xreal_0)]).
thf(fc25_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc25_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc25_xreal_0)]).
thf(fc26_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc26_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc26_xreal_0)]).
thf(fc27_xreal_0, theorem,  (! [A: $i] :  ( ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  (v2_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc27_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc27_xreal_0)]).
thf(fc28_xreal_0, theorem,  (! [A: $i] :  ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  ~ ( (v2_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc28_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc28_xreal_0)]).
thf(fc29_xreal_0, theorem,  (! [A: $i] :  ( ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  (v3_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc29_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc29_xreal_0)]).
thf(fc2_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc2_xcmplx_0)]).
thf(fc30_xreal_0, theorem,  (! [A: $i] :  ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  ~ ( (v3_xxreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) ) , file(xreal_0, fc30_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc30_xreal_0)]).
thf(fc31_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc31_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc31_xreal_0)]).
thf(fc32_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v2_xxreal_0 @  ( (k7_xcmplx_0 @ B)  @ A) ) ) ) ) , file(xreal_0, fc32_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc32_xreal_0)]).
thf(fc33_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v3_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v3_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc33_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc33_xreal_0)]).
thf(fc3_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc3_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc3_xcmplx_0)]).
thf(fc4_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc4_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc4_xcmplx_0)]).
thf(fc4_xreal_0, theorem,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  ( (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) )  &  (v1_xreal_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xreal_0, fc4_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc4_xreal_0)]).
thf(fc59_membered, theorem,  (v7_membered @ k4_ordinal1) , file(membered, fc59_membered), [interesting(np__0.9), axiom, file(membered, fc59_membered)]).
thf(fc5_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  (v1_xcmplx_0 @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) , file(xcmplx_0, fc5_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc5_xcmplx_0)]).
thf(fc5_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc5_xreal_0)]).
thf(fc61_valued_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  =>  (v1_xcmplx_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc61_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc61_valued_0)]).
thf(fc62_valued_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v2_valued_0 @ A) ) )  =>  (v1_xxreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc62_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc62_valued_0)]).
thf(fc66_valued_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) )  =>  (v7_ordinal1 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc66_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc66_valued_0)]).
thf(fc6_membered, theorem,  (v6_membered @ k4_ordinal1) , file(membered, fc6_membered), [interesting(np__0.9), axiom, file(membered, fc6_membered)]).
thf(fc6_xcmplx_0, theorem,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k4_xcmplx_0 @ A) ) )  &  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc6_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc6_xcmplx_0)]).
thf(fc6_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc6_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc6_xreal_0)]).
thf(fc7_xcmplx_0, theorem,  (! [A: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  =>  ( ~ ( (v1_xboole_0 @  (k5_xcmplx_0 @ A) ) )  &  (v1_xcmplx_0 @  (k5_xcmplx_0 @ A) ) ) ) ) , file(xcmplx_0, fc7_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc7_xcmplx_0)]).
thf(fc81_valued_1, theorem,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v1_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) )  &  (v1_valued_0 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc81_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc81_valued_1)]).
thf(fc82_valued_1, theorem,  (! [A: $i, B: $i] :  ( ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  &  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v3_valued_0 @ B) ) ) )  =>  ( (v1_relat_1 @  ( (k45_valued_1 @ A)  @ B) )  &  ( (v1_funct_1 @  ( (k45_valued_1 @ A)  @ B) )  &  (v3_valued_0 @  ( (k45_valued_1 @ A)  @ B) ) ) ) ) ) , file(valued_1, fc82_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc82_valued_1)]).
thf(fc86_valued_1, theorem,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( ( ~ ( (v1_xboole_0 @ B) )  &  (v3_membered @ B) )  &  ( ( ~ ( (v1_xboole_0 @ C) )  &  (v3_membered @ C) )  &  ( ( (v1_funct_1 @ D)  &  ( ( ( (v1_funct_2 @ D)  @ A)  @ B)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (v1_funct_1 @ E)  &  ( ( ( (v1_funct_2 @ E)  @ A)  @ C)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( (k45_valued_1 @ D)  @ E) )  &  ( (v1_partfun1 @  ( (k45_valued_1 @ D)  @ E) )  @ A) ) ) ) , file(valued_1, fc86_valued_1), [interesting(np__0.9), axiom, file(valued_1, fc86_valued_1)]).
thf(fc87_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v3_membered @ B)  =>  (v3_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc87_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc87_valued_0)]).
thf(fc8_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_xcmplx_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xcmplx_0, fc8_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc8_xcmplx_0)]).
thf(fc90_valued_0, theorem,  (! [A: $i, B: $i] :  ( (v6_membered @ B)  =>  (v4_valued_0 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) , file(valued_0, fc90_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc90_valued_0)]).
thf(fc9_xcmplx_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) )  &  ( ~ ( (v1_xboole_0 @ B) )  &  (v1_xcmplx_0 @ B) ) )  =>  ~ ( (v1_xboole_0 @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xcmplx_0, fc9_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, fc9_xcmplx_0)]).
thf(fc9_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc9_xreal_0)]).
thf(rc1_funct_2, theorem,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( ( (v5_relat_1 @ C)  @ B)  &  ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, rc1_funct_2), [interesting(np__0.9), axiom, file(funct_2, rc1_funct_2)]).
thf(rc1_membered, theorem,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc1_membered), [interesting(np__0.9), axiom, file(membered, rc1_membered)]).
thf(rc1_relset_1, theorem,  (! [A: $i, B: $i] :  (? [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  &  ( (v1_xboole_0 @ C)  &  ( (v1_relat_1 @ C)  &  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) ) ) , file(relset_1, rc1_relset_1), [interesting(np__0.9), axiom, file(relset_1, rc1_relset_1)]).
thf(rc1_valued_0, theorem,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, rc1_valued_0), [interesting(np__0.9), axiom, file(valued_0, rc1_valued_0)]).
thf(rc1_xcmplx_0, theorem,  (? [A: $i] :  (v1_xcmplx_0 @ A) ) , file(xcmplx_0, rc1_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, rc1_xcmplx_0)]).
thf(rc2_membered, theorem,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v6_membered @ A) ) ) , file(membered, rc2_membered), [interesting(np__0.9), axiom, file(membered, rc2_membered)]).
thf(rc2_valued_1, theorem,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ~ ( (v1_xboole_0 @ A) ) ) ) ) ) , file(valued_1, rc2_valued_1), [interesting(np__0.9), axiom, file(valued_1, rc2_valued_1)]).
thf(rc2_xcmplx_0, theorem,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, rc2_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, rc2_xcmplx_0)]).
thf(rc2_xreal_0, theorem,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v2_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc2_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc2_xreal_0)]).
thf(rc3_membered, theorem,  (? [A: $i] :  ( ~ ( (v1_xboole_0 @ A) )  &  ( (v6_membered @ A)  &  (v7_membered @ A) ) ) ) , file(membered, rc3_membered), [interesting(np__0.9), axiom, file(membered, rc3_membered)]).
thf(rc3_valued_1, theorem,  (? [A: $i] :  ( (v1_relat_1 @ A)  &  ( ( (v4_relat_1 @ A)  @ k5_numbers)  &  ( (v1_funct_1 @ A)  &  ( ~ ( (v1_xboole_0 @ A) )  &  (v1_finset_1 @ A) ) ) ) ) ) , file(valued_1, rc3_valued_1), [interesting(np__0.9), axiom, file(valued_1, rc3_valued_1)]).
thf(rc3_xreal_0, theorem,  (? [A: $i] :  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  ( (v3_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc3_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc3_xreal_0)]).
thf(rc4_xreal_0, theorem,  (? [A: $i] :  ( (v1_xboole_0 @ A)  &  ( (v1_xcmplx_0 @ A)  &  ( (v1_xxreal_0 @ A)  &  (v1_xreal_0 @ A) ) ) ) ) , file(xreal_0, rc4_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc4_xreal_0)]).
thf(rc6_valued_0, theorem,  (! [A: $i] :  (? [B: $i] :  ( (v1_relat_1 @ B)  &  ( ( (v4_relat_1 @ B)  @ A)  &  ( (v1_funct_1 @ B)  &  ( ( (v1_partfun1 @ B)  @ A)  &  (v4_valued_0 @ B) ) ) ) ) ) ) , file(valued_0, rc6_valued_0), [interesting(np__0.9), axiom, file(valued_0, rc6_valued_0)]).
thf(spc10_arithm, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k3_xcmplx_0 @  (k5_xcmplx_0 @ A) )  @  (k5_xcmplx_0 @ B) ) )  @  (k5_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) ) ) ) ) , file(arithm, spc10_arithm), [interesting(np__0.9), axiom, file(arithm, spc10_arithm)]).
thf(spc11_arithm, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k7_xcmplx_0 @  (k5_xcmplx_0 @ A) )  @  (k5_xcmplx_0 @ B) ) )  @  ( (k7_xcmplx_0 @ B)  @ A) ) ) ) , file(arithm, spc11_arithm), [interesting(np__0.9), axiom, file(arithm, spc11_arithm)]).
thf(spc12_arithm, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xcmplx_0 @ A)  &  (v1_xcmplx_0 @ B) )  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @  (k5_xcmplx_0 @ B) ) )  @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) , file(arithm, spc12_arithm), [interesting(np__0.9), axiom, file(arithm, spc12_arithm)]).
thf(spc1_arithm, theorem,  (! [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), [interesting(np__0.9), axiom, file(arithm, spc1_arithm)]).
thf(spc4_arithm, theorem,  (! [A: $i, B: $i, C: $i] :  ( ( (v1_xcmplx_0 @ A)  &  ( (v1_xcmplx_0 @ B)  &  (v1_xcmplx_0 @ C) ) )  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @  ( (k7_xcmplx_0 @ B)  @ C) ) )  @  ( (k7_xcmplx_0 @  ( (k3_xcmplx_0 @ A)  @ B) )  @ C) ) ) ) , file(arithm, spc4_arithm), [interesting(np__0.9), axiom, file(arithm, spc4_arithm)]).
thf(spc5_arithm, theorem,  (! [A: $i, B: $i, C: $i] :  ( ( (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) ) ) ) ) , file(arithm, spc5_arithm), [interesting(np__0.9), axiom, file(arithm, spc5_arithm)]).
thf(spc6_arithm, theorem,  (! [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), [interesting(np__0.9), axiom, file(arithm, spc6_arithm)]).
thf(spc7_arithm, theorem,  (! [A: $i, B: $i, C: $i] :  ( ( (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) ) ) ) ) , file(arithm, spc6_arithm), [interesting(np__0.9), axiom, file(arithm, spc6_arithm)]).
thf(spc8_arithm, theorem,  (! [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), [interesting(np__0.9), axiom, file(arithm, spc8_arithm)]).
thf(spc9_arithm, theorem,  (! [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), [interesting(np__0.9), axiom, file(arithm, spc9_arithm)]).
thf(t1_numerals, theorem,  ( (m1_subset_1 @ k1_xboole_0)  @ k4_ordinal1) , file(numerals, t1_numerals), [interesting(np__0.9), axiom, file(numerals, t1_numerals)]).
thf(t1_subset, theorem,  (! [A: $i] :  (! [B: $i] :  ( ( (r2_hidden @ A)  @ B)  =>  ( (m1_subset_1 @ A)  @ B) ) ) ) , file(subset, t1_subset), [interesting(np__0.9), axiom, file(subset, t1_subset)]).
thf(t4_subset, theorem,  (! [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), [interesting(np__0.9), axiom, file(subset, t4_subset)]).
thf(t5_subset, theorem,  (! [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), [interesting(np__0.9), axiom, file(subset, t5_subset)]).
thf(involutiveness_k4_xcmplx_0, theorem,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ A) ) )  @ A) ) ) , file(xcmplx_0, k4_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k4_xcmplx_0)]).
thf(existence_m1_subset_1, plain,  (! [A: $i] :  (? [B: $i] :  ( (m1_subset_1 @ B)  @ A) ) ) , file(subset_1, m1_subset_1), [interesting(np__0.9), axiom, file(subset_1, m1_subset_1)]).
thf(existence_m2_subset_1, plain,  (! [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), [interesting(np__0.9), axiom, file(subset_1, m2_subset_1)]).
thf(redefinition_k47_valued_1, definition,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v3_membered @ B)  &  ( (v3_membered @ C)  &  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) )  =>  ( (= @  ( ( ( ( (k47_valued_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  ( (k45_valued_1 @ D)  @ E) ) ) ) , file(valued_1, k47_valued_1), [interesting(np__0.9), axiom, file(valued_1, k47_valued_1)]).
thf(redefinition_k5_numbers, definition,  ( (= @ k5_numbers)  @ k4_ordinal1) , file(numbers, k5_numbers), [interesting(np__0.9), axiom, file(numbers, k5_numbers)]).
thf(redefinition_k6_real_1, definition,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (m1_subset_1 @ B)  @ k1_numbers) )  =>  ( (= @  ( (k6_real_1 @ A)  @ B) )  @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k6_real_1), [interesting(np__0.9), axiom, file(real_1, k6_real_1)]).
thf(redefinition_m2_subset_1, definition,  (! [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), [interesting(np__0.9), axiom, file(subset_1, m2_subset_1)]).
thf(dt_k1_diff_1, plain,  (! [A: $i, B: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  &  (v1_xreal_0 @ B) )  =>  ( (v1_funct_1 @  ( (k1_diff_1 @ A)  @ B) )  &  ( (m1_subset_1 @  ( (k1_diff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) ) , file(diff_1, k1_diff_1), [interesting(np__0.9), axiom, file(diff_1, k1_diff_1)]).
thf(dt_k1_funct_1, plain, $true, file(funct_1, k1_funct_1), [interesting(np__0.9), axiom, file(funct_1, k1_funct_1)]).
thf(dt_k1_numbers, plain, $true, file(numbers, k1_numbers), [interesting(np__0.9), axiom, file(numbers, k1_numbers)]).
thf(dt_k1_zfmisc_1, plain, $true, file(zfmisc_1, k1_zfmisc_1), [interesting(np__0.9), axiom, file(zfmisc_1, k1_zfmisc_1)]).
thf(dt_k2_zfmisc_1, plain, $true, file(zfmisc_1, k2_zfmisc_1), [interesting(np__0.9), axiom, file(zfmisc_1, k2_zfmisc_1)]).
thf(dt_k47_valued_1, plain,  (! [A: $i, B: $i, C: $i, D: $i, E: $i] :  ( ( (v3_membered @ B)  &  ( (v3_membered @ C)  &  ( ( (v1_funct_1 @ D)  &  ( (m1_subset_1 @ D)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) )  &  ( (v1_funct_1 @ E)  &  ( (m1_subset_1 @ E)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ C) ) ) ) ) ) )  =>  ( (v1_funct_1 @  ( ( ( ( (k47_valued_1 @ A)  @ B)  @ C)  @ D)  @ E) )  &  ( (m1_subset_1 @  ( ( ( ( (k47_valued_1 @ A)  @ B)  @ C)  @ D)  @ E) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ k1_numbers) ) ) ) ) ) , file(valued_1, k47_valued_1), [interesting(np__0.9), axiom, file(valued_1, k47_valued_1)]).
thf(dt_k4_xcmplx_0, plain,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (v1_xcmplx_0 @  (k4_xcmplx_0 @ A) ) ) ) , file(xcmplx_0, k4_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k4_xcmplx_0)]).
thf(dt_k5_numbers, plain,  ( (m1_subset_1 @ k5_numbers)  @  (k1_zfmisc_1 @ k1_numbers) ) , file(numbers, k5_numbers), [interesting(np__0.9), axiom, file(numbers, k5_numbers)]).
thf(dt_k6_real_1, plain,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  ( (m1_subset_1 @ B)  @ k1_numbers) )  =>  ( (m1_subset_1 @  ( (k6_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k6_real_1), [interesting(np__0.9), axiom, file(real_1, k6_real_1)]).
thf(dt_k6_xcmplx_0, plain, $true, file(xcmplx_0, k6_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k6_xcmplx_0)]).
thf(dt_k7_xcmplx_0, plain, $true, file(xcmplx_0, k7_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, k7_xcmplx_0)]).
thf(dt_m1_subset_1, plain, $true, file(subset_1, m1_subset_1), [interesting(np__0.9), axiom, file(subset_1, m1_subset_1)]).
thf(dt_m2_subset_1, plain,  (! [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), [interesting(np__0.9), axiom, file(subset_1, m2_subset_1)]).
thf(cc11_membered, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k5_numbers) )  =>  (v6_membered @ A) ) ) , file(membered, cc11_membered), [interesting(np__0.9), axiom, file(membered, cc11_membered)]).
thf(cc12_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @ A) )  =>  (v3_valued_0 @ B) ) ) ) ) , file(valued_0, cc12_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc12_valued_0)]).
thf(cc18_membered, theorem,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v6_membered @ A) ) ) , file(membered, cc18_membered), [interesting(np__0.9), axiom, file(membered, cc18_membered)]).
thf(cc1_relset_1, theorem,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_relat_1 @ C) ) ) ) , file(relset_1, cc1_relset_1), [interesting(np__0.9), axiom, file(relset_1, cc1_relset_1)]).
thf(cc1_xcmplx_0, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xcmplx_0 @ A) ) ) , file(xcmplx_0, cc1_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, cc1_xcmplx_0)]).
thf(cc1_xreal_0, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (v1_xreal_0 @ A) ) ) , file(xreal_0, cc1_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc1_xreal_0)]).
thf(cc25_membered, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k5_numbers)  =>  (v6_membered @ A) ) ) , file(membered, cc25_membered), [interesting(np__0.9), axiom, file(membered, cc25_membered)]).
thf(cc26_membered, theorem,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  (v7_membered @ A) ) ) , file(membered, cc26_membered), [interesting(np__0.9), axiom, file(membered, cc26_membered)]).
thf(cc2_funct_2, theorem,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc2_funct_2), [interesting(np__0.9), axiom, file(funct_2, cc2_funct_2)]).
thf(cc2_relset_1, theorem,  (! [A: $i, B: $i] :  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v4_relat_1 @ C)  @ A)  &  ( (v5_relat_1 @ C)  @ B) ) ) ) ) , file(relset_1, cc2_relset_1), [interesting(np__0.9), axiom, file(relset_1, cc2_relset_1)]).
thf(cc3_funct_2, theorem,  (! [A: $i, B: $i] :  ( ~ ( (v1_xboole_0 @ B) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  =>  ( (v1_partfun1 @ C)  @ A) ) ) ) ) ) , file(funct_2, cc3_funct_2), [interesting(np__0.9), axiom, file(funct_2, cc3_funct_2)]).
thf(cc3_relset_1, theorem,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc3_relset_1), [interesting(np__0.9), axiom, file(relset_1, cc3_relset_1)]).
thf(cc3_xreal_0, theorem,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xcmplx_0 @ A) ) ) , file(xreal_0, cc3_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc3_xreal_0)]).
thf(cc4_funct_2, theorem,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ A) ) )  =>  ( ( ( (v1_funct_2 @ B)  @ A)  @ A)  =>  ( (v1_partfun1 @ B)  @ A) ) ) ) ) , file(funct_2, cc4_funct_2), [interesting(np__0.9), axiom, file(funct_2, cc4_funct_2)]).
thf(cc4_relset_1, theorem,  (! [A: $i, B: $i] :  ( (v1_xboole_0 @ A)  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ B)  @ A) ) )  =>  (v1_xboole_0 @ C) ) ) ) ) , file(relset_1, cc4_relset_1), [interesting(np__0.9), axiom, file(relset_1, cc4_relset_1)]).
thf(cc4_xreal_0, theorem,  (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (v1_xxreal_0 @ A) ) ) , file(xreal_0, cc4_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, cc4_xreal_0)]).
thf(cc5_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v2_valued_0 @ A) ) ) ) , file(valued_0, cc5_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc5_valued_0)]).
thf(cc6_valued_0, theorem,  (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  (v3_valued_0 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v1_valued_0 @ A) ) ) ) , file(valued_0, cc6_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc6_valued_0)]).
thf(cc8_funct_2, theorem,  (! [A: $i, B: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ~ ( (v1_xboole_0 @ B) ) )  =>  (! [C: $i] :  ( ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) )  =>  ( ( (v1_funct_1 @ C)  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) )  =>  ( (v1_funct_1 @ C)  &  ( ~ ( (v1_xboole_0 @ C) )  &  ( ( (v1_funct_2 @ C)  @ A)  @ B) ) ) ) ) ) ) ) , file(funct_2, cc8_funct_2), [interesting(np__0.9), axiom, file(funct_2, cc8_funct_2)]).
thf(cc8_membered, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ k1_numbers) )  =>  (v3_membered @ A) ) ) , file(membered, cc8_membered), [interesting(np__0.9), axiom, file(membered, cc8_membered)]).
thf(cc9_valued_0, theorem,  (! [A: $i] :  ( ( (v1_xboole_0 @ A)  &  (v1_relat_1 @ A) )  =>  ( (v1_relat_1 @ A)  &  (v4_valued_0 @ A) ) ) ) , file(valued_0, cc9_valued_0), [interesting(np__0.9), axiom, file(valued_0, cc9_valued_0)]).
thf(fc15_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc15_xreal_0)]).
thf(fc19_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc19_xreal_0)]).
thf(fc1_numbers, theorem,  ~ ( (v1_xboole_0 @ k1_numbers) ) , file(numbers, fc1_numbers), [interesting(np__0.9), axiom, file(numbers, fc1_numbers)]).
thf(fc20_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc20_xreal_0)]).
thf(fc34_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( ( ~ ( (v2_xxreal_0 @ A) )  &  (v1_xreal_0 @ A) )  &  ( ~ ( (v2_xxreal_0 @ B) )  &  (v1_xreal_0 @ B) ) )  =>  ~ ( (v3_xxreal_0 @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) ) , file(xreal_0, fc34_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc34_xreal_0)]).
thf(fc3_membered, theorem,  (v3_membered @ k1_numbers) , file(membered, fc3_membered), [interesting(np__0.9), axiom, file(membered, fc3_membered)]).
thf(fc3_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc3_xreal_0)]).
thf(fc56_membered, theorem,  (v7_membered @ k1_numbers) , file(membered, fc56_membered), [interesting(np__0.9), axiom, file(membered, fc56_membered)]).
thf(fc63_valued_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  (v1_xreal_0 @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(valued_0, fc63_valued_0), [interesting(np__0.9), axiom, file(valued_0, fc63_valued_0)]).
thf(fc7_xreal_0, theorem,  (! [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), [interesting(np__0.9), axiom, file(xreal_0, fc7_xreal_0)]).
thf(fc8_numbers, theorem,  ~ ( (v1_finset_1 @ k1_numbers) ) , file(numbers, fc8_numbers), [interesting(np__0.9), axiom, file(numbers, fc8_numbers)]).
thf(fc8_xreal_0, theorem,  (! [A: $i, B: $i] :  ( ( (v1_xreal_0 @ A)  &  (v1_xreal_0 @ B) )  =>  (v1_xreal_0 @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) , file(xreal_0, fc8_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, fc8_xreal_0)]).
thf(rc1_xboole_0, theorem,  (? [A: $i] :  (v1_xboole_0 @ A) ) , file(xboole_0, rc1_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, rc1_xboole_0)]).
thf(rc1_xreal_0, theorem,  (? [A: $i] :  (v1_xreal_0 @ A) ) , file(xreal_0, rc1_xreal_0), [interesting(np__0.9), axiom, file(xreal_0, rc1_xreal_0)]).
thf(rc2_xboole_0, theorem,  (? [A: $i] :  ~ ( (v1_xboole_0 @ A) ) ) , file(xboole_0, rc2_xboole_0), [interesting(np__0.9), axiom, file(xboole_0, rc2_xboole_0)]).
thf(rqRealNeg__k4_xcmplx_0__r2_rm2, theorem,  ( (= @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__r2_rm2)]).
thf(rqRealNeg__k4_xcmplx_0__rm2_r2, theorem,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rm2_r2)]).
thf(t2_subset, theorem,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @ B)  =>  ( (v1_xboole_0 @ B)  |  ( (r2_hidden @ A)  @ B) ) ) ) ) , file(subset, t2_subset), [interesting(np__0.9), axiom, file(subset, t2_subset)]).
thf(t3_subset, theorem,  (! [A: $i] :  (! [B: $i] :  ( ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @ B) )  <=>  ( (r1_tarski @ A)  @ B) ) ) ) , file(subset, t3_subset), [interesting(np__0.9), axiom, file(subset, t3_subset)]).
thf(t6_boole, theorem,  (! [A: $i] :  ( (v1_xboole_0 @ A)  =>  ( (= @ A)  @ k1_xboole_0) ) ) , file(boole, t6_boole), [interesting(np__0.9), axiom, file(boole, t6_boole)]).
thf(t7_boole, theorem,  (! [A: $i] :  (! [B: $i] :  ~ ( ( ( (r2_hidden @ A)  @ B)  &  (v1_xboole_0 @ B) ) ) ) ) , file(boole, t7_boole), [interesting(np__0.9), axiom, file(boole, t7_boole)]).
thf(t8_boole, theorem,  (! [A: $i] :  (! [B: $i] :  ~ ( ( (v1_xboole_0 @ A)  &  ( ~ ( ( (= @ A)  @ B) )  &  (v1_xboole_0 @ B) ) ) ) ) ) , file(boole, t8_boole), [interesting(np__0.9), axiom, file(boole, t8_boole)]).
thf(d8_xcmplx_0, definition,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (! [B: $i] :  ( (v1_xcmplx_0 @ B)  =>  ( (= @  ( (k6_xcmplx_0 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ B) ) ) ) ) ) ) , file(xcmplx_0, d8_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, d8_xcmplx_0)]).
thf(d9_xcmplx_0, definition,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  (! [B: $i] :  ( (v1_xcmplx_0 @ B)  =>  ( (= @  ( (k7_xcmplx_0 @ A)  @ B) )  @  ( (k3_xcmplx_0 @ A)  @  (k5_xcmplx_0 @ B) ) ) ) ) ) ) , file(xcmplx_0, d9_xcmplx_0), [interesting(np__0.9), axiom, file(xcmplx_0, d9_xcmplx_0)]).
thf(involutiveness_k1_real_1, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (= @  (k1_real_1 @  (k1_real_1 @ A) ) )  @ A) ) ) , file(real_1, k1_real_1), [interesting(np__0.9), axiom, file(real_1, k1_real_1)]).
thf(redefinition_k10_real_1, definition,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (= @  ( (k10_real_1 @ A)  @ B) )  @  ( (k7_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k10_real_1), [interesting(np__0.9), axiom, file(real_1, k10_real_1)]).
thf(redefinition_k1_real_1, definition,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (= @  (k1_real_1 @ A) )  @  (k4_xcmplx_0 @ A) ) ) ) , file(real_1, k1_real_1), [interesting(np__0.9), axiom, file(real_1, k1_real_1)]).
thf(redefinition_k1_seq_1, definition,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (= @  ( (k1_seq_1 @ A)  @ B) )  @  ( (k1_funct_1 @ A)  @ B) ) ) ) , file(seq_1, k1_seq_1), [interesting(np__0.9), axiom, file(seq_1, k1_seq_1)]).
thf(redefinition_k9_real_1, definition,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (= @  ( (k9_real_1 @ A)  @ B) )  @  ( (k6_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k9_real_1), [interesting(np__0.9), axiom, file(real_1, k9_real_1)]).
thf(dt_k10_real_1, plain,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k10_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k10_real_1), [interesting(np__0.9), axiom, file(real_1, k10_real_1)]).
thf(dt_k1_real_1, plain,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  ( (m1_subset_1 @  (k1_real_1 @ A) )  @ k1_numbers) ) ) , file(real_1, k1_real_1), [interesting(np__0.9), axiom, file(real_1, k1_real_1)]).
thf(dt_k1_seq_1, plain,  (! [A: $i, B: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  (v3_valued_0 @ A) ) )  =>  ( (m1_subset_1 @  ( (k1_seq_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(seq_1, k1_seq_1), [interesting(np__0.9), axiom, file(seq_1, k1_seq_1)]).
thf(dt_k3_diff_1, plain,  (! [A: $i, B: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  &  (v1_xreal_0 @ B) )  =>  ( (v1_funct_1 @  ( (k3_diff_1 @ A)  @ B) )  &  ( (m1_subset_1 @  ( (k3_diff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) ) , file(diff_1, k3_diff_1), [interesting(np__0.9), axiom, file(diff_1, k3_diff_1)]).
thf(dt_k5_diff_1, plain,  (! [A: $i, B: $i] :  ( ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  &  (v1_xreal_0 @ B) )  =>  ( (v1_funct_1 @  ( (k5_diff_1 @ A)  @ B) )  &  ( (m1_subset_1 @  ( (k5_diff_1 @ A)  @ B) )  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) ) , file(diff_1, k5_diff_1), [interesting(np__0.9), axiom, file(diff_1, k5_diff_1)]).
thf(dt_k9_real_1, plain,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k9_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k9_real_1), [interesting(np__0.9), axiom, file(real_1, k9_real_1)]).
thf(dt_c1_1__diff_3, assumption,  ( (m1_subset_1 @ c1_1__diff_3)  @ k1_numbers) , introduced(assumption, [file(diff_3, c1_1__diff_3)]), [interesting(np__0.8), axiom, file(diff_3, c1_1__diff_3)]).
thf(dt_c2_1__diff_3, assumption,  ( (m1_subset_1 @ c2_1__diff_3)  @ k1_numbers) , introduced(assumption, [file(diff_3, c2_1__diff_3)]), [interesting(np__0.8), axiom, file(diff_3, c2_1__diff_3)]).
thf(dt_c3_1__diff_3, assumption,  ( (v1_funct_1 @ c3_1__diff_3)  &  ( ( ( (v1_funct_2 @ c3_1__diff_3)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ c3_1__diff_3)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) ) , introduced(assumption, [file(diff_3, c3_1__diff_3)]), [interesting(np__0.8), axiom, file(diff_3, c3_1__diff_3)]).
thf(d3_diff_1, definition,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( (= @  ( (k3_diff_1 @ A)  @ B) )  @  ( ( ( ( (k47_valued_1 @ k1_numbers)  @ k1_numbers)  @ k1_numbers)  @  ( (k1_diff_1 @ A)  @ B) )  @ A) ) ) ) ) ) , file(diff_1, d3_diff_1), [interesting(np__0.9), axiom, file(diff_1, d3_diff_1)]).
thf(d5_diff_1, definition,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) )  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( (= @  ( (k5_diff_1 @ A)  @ B) )  @  ( ( ( ( (k47_valued_1 @ k1_numbers)  @ k1_numbers)  @ k1_numbers)  @  ( (k1_diff_1 @ A)  @  ( (k6_real_1 @ B)  @ np__2) ) )  @  ( (k1_diff_1 @ A)  @  (k1_real_1 @  ( (k6_real_1 @ B)  @ np__2) ) ) ) ) ) ) ) ) , file(diff_1, d5_diff_1), [interesting(np__0.9), axiom, file(diff_1, d5_diff_1)]).
thf(spc2_numerals, theorem,  ( ( (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), [interesting(np__0.9), axiom, file(numerals, spc2_numerals)]).
thf(spc2_boole, theorem,  ~ ( (v1_xboole_0 @ np__2) ) , file(boole, spc2_boole), [interesting(np__0.9), axiom, file(boole, spc2_boole)]).
thf(commutativity_k7_real_1, theorem,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (= @  ( (k7_real_1 @ A)  @ B) )  @  ( (k7_real_1 @ B)  @ A) ) ) ) , file(real_1, k7_real_1), [interesting(np__0.9), axiom, file(real_1, k7_real_1)]).
thf(redefinition_k3_funct_2, definition,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (= @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @  ( (k1_funct_1 @ C)  @ D) ) ) ) , file(funct_2, k3_funct_2), [interesting(np__0.9), axiom, file(funct_2, k3_funct_2)]).
thf(redefinition_k7_real_1, definition,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (= @  ( (k7_real_1 @ A)  @ B) )  @  ( (k2_xcmplx_0 @ A)  @ B) ) ) ) , file(real_1, k7_real_1), [interesting(np__0.9), axiom, file(real_1, k7_real_1)]).
thf(dt_k3_funct_2, plain,  (! [A: $i, B: $i, C: $i, D: $i] :  ( ( ~ ( (v1_xboole_0 @ A) )  &  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ A)  @ B)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ A)  @ B) ) ) ) )  &  ( (m1_subset_1 @ D)  @ A) ) )  =>  ( (m1_subset_1 @  ( ( ( (k3_funct_2 @ A)  @ B)  @ C)  @ D) )  @ B) ) ) , file(funct_2, k3_funct_2), [interesting(np__0.9), axiom, file(funct_2, k3_funct_2)]).
thf(dt_k7_real_1, plain,  (! [A: $i, B: $i] :  ( ( ( (m1_subset_1 @ A)  @ k1_numbers)  &  (v1_xreal_0 @ B) )  =>  ( (m1_subset_1 @  ( (k7_real_1 @ A)  @ B) )  @ k1_numbers) ) ) , file(real_1, k7_real_1), [interesting(np__0.9), axiom, file(real_1, k7_real_1)]).
thf(rqRealDiff__k6_xcmplx_0__r0_r0_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_r0_r0)]).
thf(rqRealDiff__k6_xcmplx_0__r0_r1_rm1, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_r1_rm1)]).
thf(rqRealDiff__k6_xcmplx_0__r0_r2_rm2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_r2_rm2)]).
thf(rqRealDiff__k6_xcmplx_0__r0_rm1_r1, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm1_r1)]).
thf(rqRealDiff__k6_xcmplx_0__r0_rm2_r2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rm2_r2)]).
thf(rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2)]).
thf(rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__0)  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2)]).
thf(rqRealDiff__k6_xcmplx_0__r1_r0_r1, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_r0_r1)]).
thf(rqRealDiff__k6_xcmplx_0__r1_r1_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__1) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_r1_r0)]).
thf(rqRealDiff__k6_xcmplx_0__r1_r2_rm1, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_r2_rm1)]).
thf(rqRealDiff__k6_xcmplx_0__r1_rm1_r2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_rm1_r2)]).
thf(rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__1)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2)]).
thf(rqRealDiff__k6_xcmplx_0__r2_r0_r2, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r2_r0_r2)]).
thf(rqRealDiff__k6_xcmplx_0__r2_r1_r1, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__1) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r2_r1_r1)]).
thf(rqRealDiff__k6_xcmplx_0__r2_r2_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @ np__2)  @ np__2) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__r2_r2_r0)]).
thf(rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1)]).
thf(rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2)]).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0)]).
thf(rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1)]).
thf(rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2)]).
thf(rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2)]).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, theorem,  ( (= @  ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1)]).
thf(rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0)]).
thf(rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @ np__0) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2)]).
thf(rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @ np__1) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2)]).
thf(rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0)]).
thf(rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @ np__1) , file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1)]).
thf(rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__0) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2)]).
thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2)]).
thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1)]).
thf(rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, theorem,  ( (= @  ( (k6_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @ np__0) , file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0)]).
thf(spc2_arithm, theorem,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ A)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ A) ) ) ) , file(arithm, spc2_arithm), [interesting(np__0.9), axiom, file(arithm, spc2_arithm)]).
thf(spc3_arithm, theorem,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k7_xcmplx_0 @ np__1)  @ A) )  @  (k5_xcmplx_0 @ A) ) ) ) , file(arithm, spc3_arithm), [interesting(np__0.9), axiom, file(arithm, spc3_arithm)]).
thf(t3_arithm, theorem,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ A) )  @ A) ) ) , file(arithm, t3_arithm), [interesting(np__0.9), axiom, file(arithm, t3_arithm)]).
thf(t6_arithm, theorem,  (! [A: $i] :  ( (v1_xcmplx_0 @ A)  =>  ( (= @  ( (k7_xcmplx_0 @ A)  @ np__1) )  @ A) ) ) , file(arithm, t6_arithm), [interesting(np__0.9), axiom, file(arithm, t6_arithm)]).
thf(rqRealAdd__k2_xcmplx_0__r0_r0_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_r0_r0)]).
thf(rqRealAdd__k2_xcmplx_0__r0_r1_r1, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__1) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_r1_r1)]).
thf(rqRealAdd__k2_xcmplx_0__r0_r2_r2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @ np__2) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_r2_r2)]).
thf(rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1)]).
thf(rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2)]).
thf(rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2)]).
thf(rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__0)  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2)]).
thf(rqRealAdd__k2_xcmplx_0__r1_r0_r1, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__0) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_r0_r1)]).
thf(rqRealAdd__k2_xcmplx_0__r1_r1_r2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @ np__1) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_r1_r2)]).
thf(rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1)]).
thf(rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2)]).
thf(rqRealAdd__k2_xcmplx_0__r2_r0_r2, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @ np__0) )  @ np__2) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r2_r0_r2)]).
thf(rqRealAdd__k2_xcmplx_0__r2_rm1_r1, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm1_r1)]).
thf(rqRealAdd__k2_xcmplx_0__r2_rm2_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__2)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r2_rm2_r0)]).
thf(rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, theorem,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__0) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1)]).
thf(rqRealAdd__k2_xcmplx_0__rm1_r1_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r1_r0)]).
thf(rqRealAdd__k2_xcmplx_0__rm1_r2_r1, theorem,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_r2_r1)]).
thf(rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, theorem,  ( (= @  ( (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), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2)]).
thf(rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2)]).
thf(rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, theorem,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1)]).
thf(rqRealAdd__k2_xcmplx_0__rm2_r2_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rm2_r2_r0)]).
thf(rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @ np__0) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2)]).
thf(rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2)]).
thf(rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @ np__1) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1)]).
thf(rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0)]).
thf(rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__1) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2)]).
thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0)]).
thf(rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, theorem,  ( (= @  ( (k2_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1)]).
thf(rqRealDiv__k7_xcmplx_0__r1_r1_r1, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__1)  @ np__1) )  @ np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_r1_r1)]).
thf(rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1)]).
thf(rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2)]).
thf(rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__1)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @ np__2) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2)]).
thf(rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__1)  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2)]).
thf(rqRealDiv__k7_xcmplx_0__r2_r1_r2, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__2)  @ np__1) )  @ np__2) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r2_r1_r2)]).
thf(rqRealDiv__k7_xcmplx_0__r2_r2_r1, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__2)  @ np__2) )  @ np__1) , file(arithm, rqRealDiv__k7_xcmplx_0__r2_r2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r2_r2_r1)]).
thf(rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, theorem,  ( (= @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1)]).
thf(rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, theorem,  ( (= @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2)]).
thf(rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, theorem,  ( (= @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1)]).
thf(rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, theorem,  ( (= @  ( (k7_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1)]).
thf(rqRealMult__k3_xcmplx_0__r0_r0_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_r0_r0)]).
thf(rqRealMult__k3_xcmplx_0__r0_r1_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__1) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_r1_r0)]).
thf(rqRealMult__k3_xcmplx_0__r0_r2_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @ np__2) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_r2_r0)]).
thf(rqRealMult__k3_xcmplx_0__r0_rm2_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @  (k4_xcmplx_0 @ np__2) ) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_rm2_r0)]).
thf(rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__0)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0)]).
thf(rqRealMult__k3_xcmplx_0__r1_r0_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_r0_r0)]).
thf(rqRealMult__k3_xcmplx_0__r1_r2_r2, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__2) )  @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_r2_r2)]).
thf(rqRealMult__k3_xcmplx_0__r1_rm2_rm2, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_rm2_rm2)]).
thf(rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2)]).
thf(rqRealMult__k3_xcmplx_0__r2_r0_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_r0_r0)]).
thf(rqRealMult__k3_xcmplx_0__r2_r1_r2, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @ np__1) )  @ np__2) , file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_r1_r2)]).
thf(rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1)]).
thf(rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__2)  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1)]).
thf(rqRealMult__k3_xcmplx_0__rm2_r0_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_r0_r0)]).
thf(rqRealMult__k3_xcmplx_0__rm2_r1_rm2, theorem,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @ np__1) )  @  (k4_xcmplx_0 @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_r1_rm2)]).
thf(rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, theorem,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1)]).
thf(rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, theorem,  ( (= @  ( (k3_xcmplx_0 @  (k4_xcmplx_0 @ np__2) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1)]).
thf(rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @ np__0) )  @ np__0) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0)]).
thf(rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @ np__2) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1)]).
thf(rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1)]).
thf(rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__1) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2)]).
thf(rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @ np__2) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1)]).
thf(rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) )  @  (k4_xcmplx_0 @ np__2) ) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1)]).
thf(rqRealNeg__k4_xcmplx_0__r0_r0, theorem,  ( (= @  (k4_xcmplx_0 @ np__0) )  @ np__0) , file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__r0_r0)]).
thf(rqRealNeg__k4_xcmplx_0__rm1_r1, theorem,  ( (= @  (k4_xcmplx_0 @  (k4_xcmplx_0 @ np__1) ) )  @ np__1) , file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rm1_r1)]).
thf(rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, theorem,  ( (= @  (k4_xcmplx_0 @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2)]).
thf(spc0_numerals, theorem,  ( ( ( (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), [interesting(np__0.9), axiom, file(numerals, spc0_numerals)]).
thf(spc1_numerals, theorem,  ( ( (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), [interesting(np__0.9), axiom, file(numerals, spc1_numerals)]).
thf(spc0_boole, theorem,  (v1_xboole_0 @ np__0) , file(boole, spc0_boole), [interesting(np__0.9), axiom, file(boole, spc0_boole)]).
thf(spc1_boole, theorem,  ~ ( (v1_xboole_0 @ np__1) ) , file(boole, spc1_boole), [interesting(np__0.9), axiom, file(boole, spc1_boole)]).
thf(t5_diff_1, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @  ( (k5_diff_1 @ C)  @ A) )  @ B) )  @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ C)  @  ( (k7_real_1 @ B)  @  ( (k10_real_1 @ A)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ C)  @  ( (k9_real_1 @ B)  @  ( (k10_real_1 @ A)  @ np__2) ) ) ) ) ) ) ) ) ) ) , file(diff_1, t5_diff_1), [interesting(np__0.9), axiom, file(diff_1, t5_diff_1)]).
thf(rqRealNeg__k4_xcmplx_0__r1_rm1, theorem,  ( (= @  (k4_xcmplx_0 @ np__1) )  @  (k4_xcmplx_0 @ np__1) ) , file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__r1_rm1)]).
thf(rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, theorem,  ( (= @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2)]).
thf(rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, theorem,  ( (= @  ( (k3_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) )  @ np__1) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2)]).
thf(rqRealMult__k3_xcmplx_0__r1_r1_r1, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @ np__1) )  @ np__1) , file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_r1_r1)]).
thf(rqRealAdd__k2_xcmplx_0__r1_rm1_r0, theorem,  ( (= @  ( (k2_xcmplx_0 @ np__1)  @  (k4_xcmplx_0 @ np__1) ) )  @ np__0) , file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0), [interesting(np__0.9), axiom, file(arithm, rqRealAdd__k2_xcmplx_0__r1_rm1_r0)]).
thf(rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, theorem,  ( (= @  (k4_xcmplx_0 @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  ( (k7_xcmplx_0 @  (k4_xcmplx_0 @ np__1) )  @ np__2) ) , file(arithm, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2), [interesting(np__0.9), axiom, file(arithm, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2)]).
thf(rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2, theorem,  ( (= @  ( (k3_xcmplx_0 @ np__1)  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) )  @  ( (k7_xcmplx_0 @ np__1)  @ np__2) ) , file(arithm, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2), [interesting(np__0.9), axiom, file(arithm, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2)]).
thf(e1_1_1__diff_3, plain,  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ c3_1__diff_3)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k7_real_1 @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k7_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k9_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [cc15_membered, cc19_valued_0, cc22_membered, cc3_membered, fc87_valued_1, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc14_valued_0, cc16_membered, cc20_valued_0, cc23_membered, cc2_membered, cc2_valued_0, cc2_xcmplx_0, cc2_xreal_0, cc3_valued_0, cc4_valued_0, cc9_membered, fc3_numbers, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc83_valued_1, fc84_valued_1, fc88_valued_1, fc89_valued_0, rc5_valued_1, antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k45_valued_1, dt_k4_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_membered, cc1_valued_0, cc20_membered, cc21_valued_0, cc24_membered, cc7_valued_0, cc8_valued_0, fc11_xreal_0, fc126_valued_1, fc12_xreal_0, fc130_valued_1, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc6_membered, fc81_valued_1, fc82_valued_1, fc85_valued_0, fc85_valued_1, fc86_valued_0, fc86_valued_1, fc90_valued_0, fc9_xreal_0, rc1_membered, rc1_valued_0, rc2_membered, rc2_xreal_0, rc3_membered, rc3_xreal_0, rc4_xreal_0, rc6_valued_0, t1_numerals, t1_subset, t4_subset, t5_subset, involutiveness_k1_real_1, involutiveness_k5_xcmplx_0, reflexivity_r1_tarski, existence_m2_subset_1, redefinition_k1_real_1, redefinition_k47_valued_1, redefinition_k5_numbers, redefinition_k6_real_1, redefinition_m2_subset_1, dt_k1_diff_1, dt_k1_funct_1, dt_k1_real_1, dt_k47_valued_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_k6_real_1, dt_k6_xcmplx_0, dt_m2_subset_1, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_2, cc21_membered, cc25_membered, cc26_membered, cc2_funct_2, cc30_valued_0, cc31_valued_0, cc3_funct_2, cc3_relset_1, cc3_xreal_0, cc4_membered, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_valued_0, cc8_funct_2, cc9_valued_0, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_xcmplx_0, fc34_xreal_0, fc3_xcmplx_0, fc3_xreal_0, fc4_xcmplx_0, fc4_xreal_0, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_xcmplx_0, rc1_funct_2, rc1_relset_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d8_xcmplx_0, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, existence_m1_subset_1, redefinition_k10_real_1, redefinition_k1_seq_1, redefinition_k3_funct_2, redefinition_k7_real_1, redefinition_k9_real_1, dt_k10_real_1, dt_k1_numbers, dt_k1_seq_1, dt_k1_zfmisc_1, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k5_diff_1, dt_k7_real_1, dt_k7_xcmplx_0, dt_k9_real_1, dt_m1_subset_1, dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc2_relset_1, cc4_funct_2, cc8_membered, fc1_numbers, fc3_membered, fc56_membered, fc8_numbers, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, t3_subset, d5_diff_1, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t5_diff_1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2]), [interesting(np__0.65), file(diff_3, e1_1_1__diff_3), [file(diff_3, e1_1_1__diff_3)]]).
thf(e2_1_1__diff_3, plain,  ( (= @  ( (k9_real_1 @  ( (k7_real_1 @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k7_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k9_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) ) )  @  ( (k9_real_1 @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k7_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) )  @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k9_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc14_valued_0, cc15_membered, cc19_valued_0, cc22_membered, cc2_valued_0, cc3_membered, cc3_valued_0, cc4_valued_0, cc9_membered, fc3_numbers, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc88_valued_0, rc5_valued_1, cc10_valued_0, cc11_valued_0, cc15_valued_0, cc16_membered, cc1_valued_0, cc20_valued_0, cc23_membered, cc2_membered, cc2_xcmplx_0, cc2_xreal_0, cc7_valued_0, cc8_valued_0, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc89_valued_0, rc1_valued_0, rc6_valued_0, reflexivity_r1_tarski, antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k4_ordinal1, cc12_membered, cc12_valued_0, cc13_membered, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc20_membered, cc21_valued_0, cc24_membered, cc30_valued_0, cc31_valued_0, cc5_valued_0, cc6_valued_0, cc9_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc63_valued_0, fc6_membered, fc85_valued_0, fc86_valued_0, fc90_valued_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_relset_1, rc2_membered, rc2_valued_1, rc2_xreal_0, rc3_membered, rc3_valued_1, rc3_xreal_0, rc4_xreal_0, t1_numerals, t1_subset, t4_subset, t5_subset, involutiveness_k5_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_funct_1, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_k6_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc11_membered, cc14_membered, cc18_membered, cc18_valued_0, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc2_funct_2, cc2_relset_1, cc3_funct_2, cc3_relset_1, cc3_xreal_0, cc4_funct_2, cc4_membered, cc4_relset_1, cc4_xreal_0, cc5_membered, cc8_funct_2, cc8_membered, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_xcmplx_0, fc34_xreal_0, fc3_xcmplx_0, fc3_xreal_0, fc4_xcmplx_0, fc4_xreal_0, fc5_xcmplx_0, fc5_xreal_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_xcmplx_0, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_xboole_0, rc2_xcmplx_0, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t3_subset, t6_arithm, t6_boole, t7_boole, t8_boole, d8_xcmplx_0, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, redefinition_k10_real_1, redefinition_k3_funct_2, redefinition_k7_real_1, redefinition_k9_real_1, dt_k10_real_1, dt_k1_numbers, dt_k2_xcmplx_0, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k7_real_1, dt_k7_xcmplx_0, dt_k9_real_1, dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3, fc1_numbers, fc3_membered, fc56_membered, fc8_numbers, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2]), [interesting(np__0.65), file(diff_3, e2_1_1__diff_3), [file(diff_3, e2_1_1__diff_3)]]).
thf(t3_diff_1, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @  ( (k3_diff_1 @ C)  @ A) )  @ B) )  @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ C)  @  ( (k7_real_1 @ B)  @ A) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ C)  @ B) ) ) ) ) ) ) ) ) , file(diff_1, t3_diff_1), [interesting(np__0.9), axiom, file(diff_1, t3_diff_1)]).
thf(e3_1_1__diff_3, plain,  ( (= @  ( (k9_real_1 @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k7_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) )  @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k9_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) ) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k9_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [cc15_membered, cc19_valued_0, cc22_membered, cc3_membered, fc87_valued_1, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc14_valued_0, cc16_membered, cc20_valued_0, cc23_membered, cc2_membered, cc2_valued_0, cc2_xcmplx_0, cc2_xreal_0, cc3_valued_0, cc4_valued_0, cc9_membered, fc3_numbers, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc83_valued_1, fc84_valued_1, fc88_valued_1, fc89_valued_0, rc5_valued_1, antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k45_valued_1, dt_k4_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_membered, cc1_valued_0, cc20_membered, cc21_valued_0, cc24_membered, cc7_valued_0, cc8_valued_0, fc11_xreal_0, fc126_valued_1, fc12_xreal_0, fc130_valued_1, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc6_membered, fc81_valued_1, fc82_valued_1, fc85_valued_0, fc85_valued_1, fc86_valued_0, fc86_valued_1, fc90_valued_0, fc9_xreal_0, rc1_membered, rc1_valued_0, rc2_membered, rc2_xreal_0, rc3_membered, rc3_xreal_0, rc4_xreal_0, rc6_valued_0, t1_numerals, t1_subset, t4_subset, t5_subset, involutiveness_k5_xcmplx_0, reflexivity_r1_tarski, existence_m2_subset_1, redefinition_k47_valued_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_diff_1, dt_k1_funct_1, dt_k47_valued_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_k6_xcmplx_0, dt_m2_subset_1, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_2, cc21_membered, cc25_membered, cc26_membered, cc2_funct_2, cc30_valued_0, cc31_valued_0, cc3_funct_2, cc3_relset_1, cc3_xreal_0, cc4_membered, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_valued_0, cc8_funct_2, cc9_valued_0, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_xcmplx_0, fc34_xreal_0, fc3_xcmplx_0, fc3_xreal_0, fc4_xcmplx_0, fc4_xreal_0, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_xcmplx_0, rc1_funct_2, rc1_relset_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rqRealDiff__k6_xcmplx_0__r0_r0_r0, rqRealDiff__k6_xcmplx_0__r0_r1_rm1, rqRealDiff__k6_xcmplx_0__r0_r2_rm2, rqRealDiff__k6_xcmplx_0__r0_rm1_r1, rqRealDiff__k6_xcmplx_0__r0_rm2_r2, rqRealDiff__k6_xcmplx_0__r0_rn1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__r0_rnm1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r1_r0_r1, rqRealDiff__k6_xcmplx_0__r1_r1_r0, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r0_r2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__r2_r2_r0, rqRealDiff__k6_xcmplx_0__rm1_r0_rm1, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__rm1_rm1_r0, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_r0_rm2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rm2_rm2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_r0_rn1d2, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rn1d2_r0, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_r0_rnm1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealDiff__k6_xcmplx_0__rnm1d2_rnm1d2_r0, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d8_xcmplx_0, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, existence_m1_subset_1, redefinition_k10_real_1, redefinition_k1_seq_1, redefinition_k3_funct_2, redefinition_k7_real_1, redefinition_k9_real_1, dt_k10_real_1, dt_k1_numbers, dt_k1_seq_1, dt_k1_zfmisc_1, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k3_diff_1, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k7_real_1, dt_k7_xcmplx_0, dt_k9_real_1, dt_m1_subset_1, dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc2_relset_1, cc4_funct_2, cc8_membered, fc1_numbers, fc3_membered, fc56_membered, fc8_numbers, rqRealAdd__k2_xcmplx_0__r0_r0_r0, rqRealAdd__k2_xcmplx_0__r0_r1_r1, rqRealAdd__k2_xcmplx_0__r0_r2_r2, rqRealAdd__k2_xcmplx_0__r0_rm1_rm1, rqRealAdd__k2_xcmplx_0__r0_rm2_rm2, rqRealAdd__k2_xcmplx_0__r0_rn1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r0_rnm1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__r1_r0_r1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm1_r0, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_r0_r2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__r2_rm2_r0, rqRealAdd__k2_xcmplx_0__rm1_r0_rm1, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rm2_r2_r0, rqRealAdd__k2_xcmplx_0__rn1d2_r0_rn1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rn1d2_rnm1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rn1d2_r0, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r0_r0_r0, rqRealMult__k3_xcmplx_0__r0_r1_r0, rqRealMult__k3_xcmplx_0__r0_r2_r0, rqRealMult__k3_xcmplx_0__r0_rm2_r0, rqRealMult__k3_xcmplx_0__r0_rn1d2_r0, rqRealMult__k3_xcmplx_0__r1_r0_r0, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r0_r0, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r0_r0, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r0_r0, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r0_r0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, t3_subset, d3_diff_1, d9_xcmplx_0, spc0_numerals, spc1_numerals, spc2_numerals, spc0_boole, spc1_boole, spc2_boole, t3_diff_1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealAdd__k2_xcmplx_0__rm1_r1_r0, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2]), [interesting(np__0.65), file(diff_3, e3_1_1__diff_3), [file(diff_3, e3_1_1__diff_3)]]).
thf(e4_1_1__diff_3, plain,  ( (= @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @  ( (k9_real_1 @ c2_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @  ( ( ( (k3_funct_2 @ k1_numbers)  @ k1_numbers)  @ c3_1__diff_3)  @ c2_1__diff_3) ) ) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [cc15_membered, cc19_valued_0, cc22_membered, cc3_membered, fc87_valued_1, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc14_valued_0, cc16_membered, cc20_valued_0, cc23_membered, cc2_membered, cc2_valued_0, cc2_xcmplx_0, cc2_xreal_0, cc3_valued_0, cc4_valued_0, cc9_membered, fc3_numbers, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc83_valued_1, fc84_valued_1, fc88_valued_1, fc89_valued_0, rc5_valued_1, antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k45_valued_1, dt_k4_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_membered, cc1_valued_0, cc20_membered, cc21_valued_0, cc24_membered, cc7_valued_0, cc8_valued_0, fc11_xreal_0, fc126_valued_1, fc12_xreal_0, fc130_valued_1, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc26_xreal_0, fc29_xreal_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc59_membered, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc6_membered, fc81_valued_1, fc82_valued_1, fc85_valued_0, fc85_valued_1, fc86_valued_0, fc86_valued_1, fc90_valued_0, fc9_xreal_0, rc1_membered, rc1_valued_0, rc2_membered, rc2_xreal_0, rc3_membered, rc3_xreal_0, rc4_xreal_0, rc6_valued_0, t1_numerals, t1_subset, t4_subset, t5_subset, commutativity_k2_xcmplx_0, involutiveness_k5_xcmplx_0, reflexivity_r1_tarski, existence_m2_subset_1, redefinition_k47_valued_1, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_diff_1, dt_k1_funct_1, dt_k2_xcmplx_0, dt_k47_valued_1, dt_k5_numbers, dt_k5_xcmplx_0, dt_k6_xcmplx_0, dt_m2_subset_1, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_funct_2, cc21_membered, cc25_membered, cc26_membered, cc2_funct_2, cc30_valued_0, cc31_valued_0, cc3_funct_2, cc3_relset_1, cc3_xreal_0, cc4_membered, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_valued_0, cc8_funct_2, cc9_valued_0, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc20_xreal_0, fc25_xreal_0, fc27_xreal_0, fc28_xreal_0, fc2_xcmplx_0, fc34_xreal_0, fc3_xcmplx_0, fc3_xreal_0, fc4_xcmplx_0, fc4_xreal_0, fc5_xcmplx_0, fc5_xreal_0, fc63_valued_0, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc7_xreal_0, fc87_valued_0, fc8_xcmplx_0, fc8_xreal_0, fc9_xcmplx_0, rc1_funct_2, rc1_relset_1, rc1_xboole_0, rc1_xcmplx_0, rc1_xreal_0, rc2_valued_1, rc2_xboole_0, rc2_xcmplx_0, rc3_valued_1, rqRealAdd__k2_xcmplx_0__r1_r1_r2, rqRealAdd__k2_xcmplx_0__r1_rm2_rm1, rqRealAdd__k2_xcmplx_0__r1_rnm1d2_rn1d2, rqRealAdd__k2_xcmplx_0__r2_rm1_r1, rqRealAdd__k2_xcmplx_0__rm1_r2_r1, rqRealAdd__k2_xcmplx_0__rm1_rm1_rm2, rqRealAdd__k2_xcmplx_0__rm1_rn1d2_rnm1d2, rqRealAdd__k2_xcmplx_0__rm2_r1_rm1, rqRealAdd__k2_xcmplx_0__rn1d2_rm1_rnm1d2, rqRealAdd__k2_xcmplx_0__rn1d2_rn1d2_r1, rqRealAdd__k2_xcmplx_0__rnm1d2_r1_rn1d2, rqRealAdd__k2_xcmplx_0__rnm1d2_rnm1d2_rm1, rqRealDiff__k6_xcmplx_0__r1_r2_rm1, rqRealDiff__k6_xcmplx_0__r1_rm1_r2, rqRealDiff__k6_xcmplx_0__r1_rn1d2_rn1d2, rqRealDiff__k6_xcmplx_0__r2_r1_r1, rqRealDiff__k6_xcmplx_0__rm1_r1_rm2, rqRealDiff__k6_xcmplx_0__rm1_rm2_r1, rqRealDiff__k6_xcmplx_0__rm1_rnm1d2_rnm1d2, rqRealDiff__k6_xcmplx_0__rm2_rm1_rm1, rqRealDiff__k6_xcmplx_0__rn1d2_r1_rnm1d2, rqRealDiff__k6_xcmplx_0__rn1d2_rnm1d2_r1, rqRealDiff__k6_xcmplx_0__rnm1d2_rm1_rn1d2, rqRealDiff__k6_xcmplx_0__rnm1d2_rn1d2_rm1, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc2_arithm, spc3_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t2_subset, t3_arithm, t6_arithm, t6_boole, t7_boole, t8_boole, d8_xcmplx_0, involutiveness_k1_real_1, commutativity_k3_xcmplx_0, involutiveness_k4_xcmplx_0, commutativity_k7_real_1, existence_m1_subset_1, redefinition_k10_real_1, redefinition_k1_real_1, redefinition_k1_seq_1, redefinition_k3_funct_2, redefinition_k7_real_1, redefinition_k9_real_1, dt_k10_real_1, dt_k1_numbers, dt_k1_real_1, dt_k1_seq_1, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k3_diff_1, dt_k3_funct_2, dt_k3_xcmplx_0, dt_k4_xcmplx_0, dt_k7_real_1, dt_k7_xcmplx_0, dt_k9_real_1, dt_m1_subset_1, dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc2_relset_1, cc4_funct_2, cc8_membered, fc1_numbers, fc3_membered, fc56_membered, fc8_numbers, rqRealDiv__k7_xcmplx_0__r1_r1_r1, rqRealDiv__k7_xcmplx_0__r1_rm1_rm1, rqRealDiv__k7_xcmplx_0__r1_rm2_rnm1d2, rqRealDiv__k7_xcmplx_0__r1_rn1d2_r2, rqRealDiv__k7_xcmplx_0__r1_rnm1d2_rm2, rqRealDiv__k7_xcmplx_0__r2_r1_r2, rqRealDiv__k7_xcmplx_0__r2_r2_r1, rqRealDiv__k7_xcmplx_0__rm1_r1_rm1, rqRealDiv__k7_xcmplx_0__rm1_r2_rnm1d2, rqRealDiv__k7_xcmplx_0__rm2_r2_rm1, rqRealDiv__k7_xcmplx_0__rnm1d2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__r1_r2_r2, rqRealMult__k3_xcmplx_0__r1_rm2_rm2, rqRealMult__k3_xcmplx_0__r1_rnm1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r2_r1_r2, rqRealMult__k3_xcmplx_0__r2_rn1d2_r1, rqRealMult__k3_xcmplx_0__r2_rnm1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_r1_rm2, rqRealMult__k3_xcmplx_0__rm2_rn1d2_rm1, rqRealMult__k3_xcmplx_0__rm2_rnm1d2_r1, rqRealMult__k3_xcmplx_0__rn1d2_r2_r1, rqRealMult__k3_xcmplx_0__rn1d2_rm2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_r1_rnm1d2, rqRealMult__k3_xcmplx_0__rnm1d2_r2_rm1, rqRealMult__k3_xcmplx_0__rnm1d2_rm2_r1, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, rqRealNeg__k4_xcmplx_0__rnm1d2_rn1d2, t3_subset, d3_diff_1, d9_xcmplx_0, spc1_numerals, spc2_numerals, spc1_boole, spc2_boole, t3_diff_1, rqRealNeg__k4_xcmplx_0__r1_rm1, rqRealDiv__k7_xcmplx_0__r1_r2_rn1d2, rqRealMult__k3_xcmplx_0__rn1d2_r1_rn1d2, rqRealMult__k3_xcmplx_0__r1_r1_r1, rqRealNeg__k4_xcmplx_0__rm1_r1, rqRealNeg__k4_xcmplx_0__rn1d2_rnm1d2, rqRealMult__k3_xcmplx_0__r1_rn1d2_rn1d2]), [interesting(np__0.65), file(diff_3, e4_1_1__diff_3), [file(diff_3, e4_1_1__diff_3)]]).
thf(e1_1__diff_3, plain,  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ c3_1__diff_3)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) , inference(iterative_eq, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [cc15_membered, cc19_valued_0, cc22_membered, cc3_membered, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc13_valued_0, cc14_valued_0, cc16_membered, cc20_valued_0, cc23_membered, cc2_membered, cc2_valued_0, cc2_xcmplx_0, cc2_xreal_0, cc3_valued_0, cc4_valued_0, cc9_membered, fc3_numbers, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc89_valued_0, rc5_valued_1, dt_k4_ordinal1, cc10_valued_0, cc11_valued_0, cc12_membered, cc13_membered, cc15_valued_0, cc16_valued_0, cc17_membered, cc17_valued_0, cc19_membered, cc1_funct_2, cc1_membered, cc1_valued_0, cc20_membered, cc21_valued_0, cc24_membered, cc30_valued_0, cc31_valued_0, cc7_valued_0, cc8_valued_0, fc11_xreal_0, fc12_xreal_0, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc21_xreal_0, fc22_xreal_0, fc2_xcmplx_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc4_xcmplx_0, fc59_membered, fc5_xcmplx_0, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_xcmplx_0, fc85_valued_0, fc86_valued_0, fc90_valued_0, fc9_xcmplx_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_relset_1, rc1_valued_0, rc1_xcmplx_0, rc2_membered, rc2_valued_1, rc2_xcmplx_0, rc2_xreal_0, rc3_membered, rc3_valued_1, rc3_xreal_0, rc4_xreal_0, rc6_valued_0, commutativity_k2_xcmplx_0, involutiveness_k4_xcmplx_0, redefinition_k5_numbers, redefinition_m2_subset_1, dt_k1_funct_1, dt_k1_zfmisc_1, dt_k2_xcmplx_0, dt_k2_zfmisc_1, dt_k4_xcmplx_0, dt_k5_numbers, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc11_membered, cc12_valued_0, cc14_membered, cc18_membered, cc18_valued_0, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc21_membered, cc25_membered, cc26_membered, cc2_funct_2, cc2_relset_1, cc3_funct_2, cc3_relset_1, cc3_xreal_0, cc4_funct_2, cc4_membered, cc4_relset_1, cc4_xreal_0, cc5_membered, cc5_valued_0, cc6_valued_0, cc8_funct_2, cc8_membered, cc9_valued_0, fc10_xreal_0, fc15_xreal_0, fc19_xreal_0, fc20_xreal_0, fc34_xreal_0, fc3_xreal_0, fc5_xreal_0, fc63_valued_0, fc7_xreal_0, fc87_valued_0, fc8_xreal_0, rc1_xboole_0, rc1_xreal_0, rc2_xboole_0, involutiveness_k1_real_1, commutativity_k7_real_1, redefinition_k10_real_1, redefinition_k1_real_1, redefinition_k1_seq_1, redefinition_k3_funct_2, redefinition_k7_real_1, redefinition_k9_real_1, dt_k10_real_1, dt_k1_numbers, dt_k1_real_1, dt_k1_seq_1, dt_k3_diff_1, dt_k3_funct_2, dt_k5_diff_1, dt_k7_real_1, dt_k9_real_1, dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3, fc1_numbers, fc3_membered, fc56_membered, fc8_numbers, spc2_numerals, spc2_boole, e1_1_1__diff_3, e2_1_1__diff_3, e3_1_1__diff_3, e4_1_1__diff_3]), [interesting(np__0.8), file(diff_3, e1_1__diff_3), [file(diff_3, e1_1__diff_3)]]).
thf(e2_1__diff_3, plain,  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ c3_1__diff_3)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) , inference(mizar_by, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [cc15_membered, cc19_valued_0, cc22_membered, cc3_membered, fc87_valued_1, fc88_valued_0, dt_k3_numbers, dt_k4_numbers, cc10_membered, cc12_membered, cc13_membered, cc13_valued_0, cc14_valued_0, cc16_membered, cc16_valued_0, cc17_valued_0, cc19_membered, cc20_membered, cc20_valued_0, cc23_membered, cc2_membered, cc2_valued_0, cc2_xcmplx_0, cc2_xreal_0, cc3_valued_0, cc4_valued_0, cc9_membered, fc3_numbers, fc4_membered, fc4_numbers, fc57_membered, fc58_membered, fc5_membered, fc64_valued_0, fc65_valued_0, fc6_numbers, fc7_numbers, fc83_valued_1, fc84_valued_1, fc85_valued_0, fc85_valued_1, fc86_valued_0, fc88_valued_1, fc89_valued_0, rc5_valued_1, commutativity_k2_xcmplx_0, commutativity_k3_xcmplx_0, involutiveness_k5_xcmplx_0, reflexivity_r1_tarski, antisymmetry_r2_hidden, dt_k1_xboole_0, dt_k2_xcmplx_0, dt_k3_xcmplx_0, dt_k45_valued_1, dt_k4_ordinal1, dt_k5_xcmplx_0, cc10_valued_0, cc11_valued_0, cc14_membered, cc15_valued_0, cc17_membered, cc18_valued_0, cc1_funct_2, cc1_membered, cc1_valued_0, cc21_membered, cc21_valued_0, cc24_membered, cc30_valued_0, cc31_valued_0, cc4_membered, cc5_membered, cc7_valued_0, cc8_valued_0, fc10_xreal_0, fc11_xreal_0, fc126_valued_1, fc12_xreal_0, fc130_valued_1, fc13_xreal_0, fc14_xreal_0, fc16_xreal_0, fc17_xreal_0, fc18_xreal_0, fc1_xboole_0, fc21_xreal_0, fc22_xreal_0, fc23_xreal_0, fc24_xreal_0, fc25_xreal_0, fc26_xreal_0, fc27_xreal_0, fc28_xreal_0, fc29_xreal_0, fc2_xcmplx_0, fc30_xreal_0, fc31_xreal_0, fc32_xreal_0, fc33_xreal_0, fc3_xcmplx_0, fc4_xcmplx_0, fc4_xreal_0, fc59_membered, fc5_xcmplx_0, fc5_xreal_0, fc61_valued_0, fc62_valued_0, fc66_valued_0, fc6_membered, fc6_xcmplx_0, fc6_xreal_0, fc7_xcmplx_0, fc81_valued_1, fc82_valued_1, fc86_valued_1, fc87_valued_0, fc8_xcmplx_0, fc90_valued_0, fc9_xcmplx_0, fc9_xreal_0, rc1_funct_2, rc1_membered, rc1_relset_1, rc1_valued_0, rc1_xcmplx_0, rc2_membered, rc2_valued_1, rc2_xcmplx_0, rc2_xreal_0, rc3_membered, rc3_valued_1, rc3_xreal_0, rc4_xreal_0, rc6_valued_0, spc10_arithm, spc11_arithm, spc12_arithm, spc1_arithm, spc4_arithm, spc5_arithm, spc6_arithm, spc7_arithm, spc8_arithm, spc9_arithm, t1_numerals, t1_subset, t4_subset, t5_subset, involutiveness_k4_xcmplx_0, existence_m1_subset_1, existence_m2_subset_1, redefinition_k47_valued_1, redefinition_k5_numbers, redefinition_k6_real_1, redefinition_m2_subset_1, dt_k1_diff_1, dt_k1_funct_1, dt_k1_numbers, dt_k1_zfmisc_1, dt_k2_zfmisc_1, dt_k47_valued_1, dt_k4_xcmplx_0, dt_k5_numbers, dt_k6_real_1, dt_k6_xcmplx_0, dt_k7_xcmplx_0, dt_m1_subset_1, dt_m2_subset_1, cc11_membered, cc12_valued_0, cc18_membered, cc1_relset_1, cc1_xcmplx_0, cc1_xreal_0, cc25_membered, cc26_membered, cc2_funct_2, cc2_relset_1, cc3_funct_2, cc3_relset_1, cc3_xreal_0, cc4_funct_2, cc4_relset_1, cc4_xreal_0, cc5_valued_0, cc6_valued_0, cc8_funct_2, cc8_membered, cc9_valued_0, fc15_xreal_0, fc19_xreal_0, fc1_numbers, fc20_xreal_0, fc34_xreal_0, fc3_membered, fc3_xreal_0, fc56_membered, fc63_valued_0, fc7_xreal_0, fc8_numbers, fc8_xreal_0, rc1_xboole_0, rc1_xreal_0, rc2_xboole_0, rqRealNeg__k4_xcmplx_0__r2_rm2, rqRealNeg__k4_xcmplx_0__rm2_r2, t2_subset, t3_subset, t6_boole, t7_boole, t8_boole, d8_xcmplx_0, d9_xcmplx_0, involutiveness_k1_real_1, redefinition_k10_real_1, redefinition_k1_real_1, redefinition_k1_seq_1, redefinition_k9_real_1, dt_k10_real_1, dt_k1_real_1, dt_k1_seq_1, dt_k3_diff_1, dt_k5_diff_1, dt_k9_real_1, dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3, d3_diff_1, d5_diff_1, spc2_numerals, spc2_boole, e1_1__diff_3]), [interesting(np__0.8), file(diff_3, e2_1__diff_3), [file(diff_3, e2_1__diff_3)]]).
thf(i4_1__diff_3, plain, $true, introduced(tautology, [file(diff_3, i4_1__diff_3)]), [interesting(np__0.8), trivial, file(diff_3, i4_1__diff_3)]).
thf(i3_1__diff_3, plain,  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ c3_1__diff_3)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) , inference(conclusion, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3, dt_c3_1__diff_3])], [e2_1__diff_3, i4_1__diff_3]), [interesting(np__0.8), file(diff_3, i3_1__diff_3), [file(diff_3, i3_1__diff_3)]]).
thf(i3_1_tmp__diff_3, plain,  ( ( (v1_funct_1 @ c3_1__diff_3)  &  ( ( ( (v1_funct_2 @ c3_1__diff_3)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ c3_1__diff_3)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ c3_1__diff_3)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ c3_1__diff_3)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) ) , inference(discharge_asm, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3]), discharge_asm(discharge, [dt_c3_1__diff_3])], [dt_c3_1__diff_3, i3_1__diff_3]), [interesting(np__0.8), i2_1__diff_3]).
thf(i2_1__diff_3, plain,  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ A)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) ) ) , inference(let, [status(thm), assumptions([dt_c1_1__diff_3, dt_c2_1__diff_3])], [i3_1_tmp__diff_3, dh_c3_1__diff_3]), [interesting(np__0.8), file(diff_3, i2_1__diff_3), [file(diff_3, i2_1__diff_3)]]).
thf(i2_1_tmp__diff_3, plain,  ( ( (m1_subset_1 @ c2_1__diff_3)  @ k1_numbers)  =>  (! [A: $i] :  ( ( (v1_funct_1 @ A)  &  ( ( ( (v1_funct_2 @ A)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ A)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ A)  @ c1_1__diff_3) )  @ c2_1__diff_3) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ c2_1__diff_3) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ A)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ c2_1__diff_3) ) ) ) ) ) , inference(discharge_asm, [status(thm), assumptions([dt_c1_1__diff_3]), discharge_asm(discharge, [dt_c2_1__diff_3])], [dt_c2_1__diff_3, i2_1__diff_3]), [interesting(np__0.8), i1_1__diff_3]).
thf(i1_1__diff_3, plain,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ B)  @ c1_1__diff_3) )  @ A) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ B)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ A) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ B)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ A) ) ) ) ) ) ) , inference(let, [status(thm), assumptions([dt_c1_1__diff_3])], [i2_1_tmp__diff_3, dh_c2_1__diff_3]), [interesting(np__0.8), file(diff_3, i1_1__diff_3), [file(diff_3, i1_1__diff_3)]]).
thf(i1_1_tmp__diff_3, plain,  ( ( (m1_subset_1 @ c1_1__diff_3)  @ k1_numbers)  =>  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (v1_funct_1 @ B)  &  ( ( ( (v1_funct_2 @ B)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ B)  @ c1_1__diff_3) )  @ A) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ B)  @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) )  @ A) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ B)  @  (k1_real_1 @  ( (k10_real_1 @ c1_1__diff_3)  @ np__2) ) ) )  @ A) ) ) ) ) ) ) ) , inference(discharge_asm, [status(thm), assumptions([]), discharge_asm(discharge, [dt_c1_1__diff_3])], [dt_c1_1__diff_3, i1_1__diff_3]), [interesting(np__1), t1_diff_3]).
thf(t1_diff_3, theorem,  (! [A: $i] :  ( ( (m1_subset_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m1_subset_1 @ B)  @ k1_numbers)  =>  (! [C: $i] :  ( ( (v1_funct_1 @ C)  &  ( ( ( (v1_funct_2 @ C)  @ k1_numbers)  @ k1_numbers)  &  ( (m1_subset_1 @ C)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k1_numbers)  @ k1_numbers) ) ) ) )  =>  ( (= @  ( (k1_seq_1 @  ( (k5_diff_1 @ C)  @ A) )  @ B) )  @  ( (k9_real_1 @  ( (k1_seq_1 @  ( (k3_diff_1 @ C)  @  ( (k10_real_1 @ A)  @ np__2) ) )  @ B) )  @  ( (k1_seq_1 @  ( (k3_diff_1 @ C)  @  (k1_real_1 @  ( (k10_real_1 @ A)  @ np__2) ) ) )  @ B) ) ) ) ) ) ) ) ) , inference(let, [status(thm), assumptions([])], [i1_1_tmp__diff_3, dh_c1_1__diff_3]), [interesting(np__1), file(diff_3, t1_diff_3), [file(diff_3, t1_diff_3)]]).