% Mizar problem: t17_pdiff_7,pdiff_7,780,5 
fof(t17_pdiff_7, conjecture,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r1_xxreal_0(np__1, C) &  (r1_xxreal_0(C, A) &  ( ~ (B=k6_numbers)  & k3_funct_2(k1_numbers, k1_euclid(A), k6_pdiff_1(A, C, k5_euclid(A)), B)=k5_euclid(A)) ) ) ) ) ) ) ).
fof(antisymmetry_r2_hidden, axiom,  (! [A, B] :  (r2_hidden(A, B) =>  ~ (r2_hidden(B, A)) ) ) ).
fof(cc10_finseq_1, axiom,  (! [A] :  (! [B] :  ($true => v1_finseq_1(B)) ) ) ).
fof(cc10_membered, axiom,  (! [A] :  ($true => v5_membered(A)) ) ).
fof(cc10_valued_0, axiom,  (! [A] :  (! [B] :  ($true => v1_valued_0(B)) ) ) ).
fof(cc10_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v2_valued_2(B)) ) ) ).
fof(cc10_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_xxreal_2(A))  =>  (v3_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(cc11_finseq_1, axiom,  (! [A] :  (! [B] :  ($true => v3_finseq_1(B)) ) ) ).
fof(cc11_membered, axiom,  (! [A] :  ($true => v6_membered(A)) ) ).
fof(cc11_valued_0, axiom,  (! [A] :  (! [B] :  ($true => v2_valued_0(B)) ) ) ).
fof(cc11_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v3_valued_2(B)) ) ) ).
fof(cc11_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v2_xxreal_2(A))  =>  (v3_membered(A) & v4_xxreal_2(A)) ) ) ).
fof(cc12_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v3_valued_0(A) &  (v5_valued_0(A) & v1_finseq_1(A)) ) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v3_valued_0(A) & v1_finseq_1(A)) ) ) ) ) ) ).
fof(cc12_membered, axiom,  (! [A] :  (! [B] :  ($true => v1_xcmplx_0(B)) ) ) ).
fof(cc12_valued_0, axiom,  (! [A] :  (! [B] :  ($true => v3_valued_0(B)) ) ) ).
fof(cc12_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v4_valued_2(B)) ) ) ).
fof(cc12_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) & v5_xxreal_2(A))  =>  (v5_membered(A) & v1_finset_1(A)) ) ) ).
fof(cc13_membered, axiom,  (! [A] :  (! [B] :  ($true => v1_xxreal_0(B)) ) ) ).
fof(cc13_valued_0, axiom,  (! [A] :  (! [B] :  ($true => v5_relat_1(B, k3_numbers)) ) ) ).
fof(cc13_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v5_valued_2(B)) ) ) ).
fof(cc13_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) & v4_xxreal_2(A))  =>  (v6_membered(A) &  (v1_finset_1(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc14_membered, axiom,  (! [A] :  (! [B] :  ($true => v1_xreal_0(B)) ) ) ).
fof(cc14_valued_0, axiom,  (! [A] :  (! [B] :  ($true => v5_relat_1(B, k4_numbers)) ) ) ).
fof(cc14_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v6_valued_2(B)) ) ) ).
fof(cc14_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) & v3_membered(A)) ) ) ).
fof(cc15_membered, axiom,  (! [A] :  (! [B] :  ($true => v1_rat_1(B)) ) ) ).
fof(cc15_valued_0, axiom,  (! [A] :  (! [B] :  ($true => v4_valued_0(B)) ) ) ).
fof(cc15_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v1_valued_0(B)) ) ) ).
fof(cc15_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xboole_0(A))  =>  (v2_membered(A) & v6_xxreal_2(A)) ) ) ).
fof(cc16_membered, axiom,  (! [A] :  (! [B] :  ($true => v1_int_1(B)) ) ) ).
fof(cc16_valued_0, axiom,  (! [A, B] :  (! [C] :  ($true => v1_valued_0(C)) ) ) ).
fof(cc16_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v2_valued_0(B)) ) ) ).
fof(cc16_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v1_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc17_membered, axiom,  (! [A] :  (! [B] :  ($true => v7_ordinal1(B)) ) ) ).
fof(cc17_valued_0, axiom,  (! [A, B] :  (! [C] :  ($true => v2_valued_0(C)) ) ) ).
fof(cc17_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v3_valued_0(B)) ) ) ).
fof(cc17_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v2_xxreal_2(A))  =>  (v2_membered(A) &  ~ (v1_xboole_0(A)) ) ) ) ).
fof(cc18_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v6_membered(A)) ) ).
fof(cc18_valued_0, axiom,  (! [A, B] :  (! [C] :  ($true => v3_valued_0(C)) ) ) ).
fof(cc18_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v5_relat_1(B, k3_numbers)) ) ) ).
fof(cc19_membered, axiom,  (! [A] :  (! [B] :  ($true => v1_membered(B)) ) ) ).
fof(cc19_valued_0, axiom,  (! [A, B] :  (! [C] :  ($true => v5_relat_1(C, k3_numbers)) ) ) ).
fof(cc19_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v5_relat_1(B, k4_numbers)) ) ) ).
fof(cc1_euclid, axiom,  (! [A] :  (! [B] :  ($true => v3_card_1(B, A)) ) ) ).
fof(cc1_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc1_finseq_2, axiom,  (! [A, B] :  (! [C] :  ($true => v3_card_1(C, B)) ) ) ).
fof(cc1_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v1_funct_1(A)) ) ).
fof(cc1_funct_2, axiom,  (! [A, B] :  (! [C] :  (v1_partfun1(C, A) => v1_funct_2(C, A, B)) ) ) ).
fof(cc1_membered, axiom,  (! [A] :  (v6_membered(A) => v5_membered(A)) ) ).
fof(cc1_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v3_ordinal1(A) & v7_ordinal1(A)) ) ) ).
fof(cc1_pdiff_6, axiom,  (! [A, B] :  (! [C] :  ( (v1_funct_1(C) &  (v1_funct_2(C, k1_euclid(A), k1_euclid(B)) &  (v1_pdiff_6(C, B, A) & v2_pdiff_6(C, B, A)) ) )  =>  (v1_funct_1(C) &  (v1_funct_2(C, k1_euclid(A), k1_euclid(B)) &  (v1_pdiff_6(C, B, A) &  (v2_pdiff_6(C, B, A) & v3_pdiff_6(C, A, B)) ) ) ) ) ) ) ).
fof(cc1_relset_1, axiom,  (! [A, B] :  (! [C] :  ($true => v1_relat_1(C)) ) ) ).
fof(cc1_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k4_numbers)) ) ) ).
fof(cc1_valued_2, axiom,  (! [A] :  (v6_valued_2(A) => v5_valued_2(A)) ) ).
fof(cc1_xcmplx_0, axiom,  (! [A] :  ($true => v1_xcmplx_0(A)) ) ).
fof(cc1_xreal_0, axiom,  (! [A] :  ($true => v1_xreal_0(A)) ) ).
fof(cc20_membered, axiom,  (! [A] :  (! [B] :  ($true => v2_membered(B)) ) ) ).
fof(cc20_valued_0, axiom,  (! [A, B] :  (! [C] :  ($true => v5_relat_1(C, k4_numbers)) ) ) ).
fof(cc20_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v4_valued_0(B)) ) ) ).
fof(cc21_membered, axiom,  (! [A] :  (! [B] :  ($true => v3_membered(B)) ) ) ).
fof(cc21_valued_0, axiom,  (! [A, B] :  (! [C] :  ($true => v4_valued_0(C)) ) ) ).
fof(cc21_valued_2, axiom,  (! [A] :  (! [B] :  ( (v1_relat_1(B) &  (v5_relat_1(B, A) & v1_funct_1(B)) )  =>  (v1_relat_1(B) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v7_valued_2(B)) ) ) ) ) ) ).
fof(cc22_membered, axiom,  (! [A] :  (! [B] :  ($true => v4_membered(B)) ) ) ).
fof(cc22_valued_0, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) &  (v1_funct_1(A) & v2_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) &  (v5_valued_0(A) & v6_valued_0(A)) ) ) ) ) ) ).
fof(cc22_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v12_valued_2(A))  =>  (v1_relat_1(A) & v11_valued_2(A)) ) ) ).
fof(cc23_membered, axiom,  (! [A] :  (! [B] :  ($true => v5_membered(B)) ) ) ).
fof(cc23_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v5_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v7_valued_0(A)) ) ) ) ) ).
fof(cc23_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v11_valued_2(A))  =>  (v1_relat_1(A) & v10_valued_2(A)) ) ) ).
fof(cc24_membered, axiom,  (! [A] :  (! [B] :  ($true => v6_membered(B)) ) ) ).
fof(cc24_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v6_valued_0(A)) ) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) &  (v2_valued_0(A) & v8_valued_0(A)) ) ) ) ) ).
fof(cc24_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v10_valued_2(A))  =>  (v1_relat_1(A) & v9_valued_2(A)) ) ) ).
fof(cc25_membered, axiom,  (! [A] :  ($true => v6_membered(A)) ) ).
fof(cc25_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_valued_2(A))  =>  (v1_relat_1(A) & v8_valued_2(A)) ) ) ).
fof(cc26_membered, axiom,  (! [A] :  (v1_xboole_0(A) => v7_membered(A)) ) ).
fof(cc26_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v9_valued_2(A))  =>  (v1_relat_1(A) & v7_valued_2(A)) ) ) ).
fof(cc27_valued_2, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v12_valued_2(A)) ) ) ).
fof(cc28_valued_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_1(C) =>  (v1_funct_1(C) & v7_valued_2(C)) ) ) ) ).
fof(cc29_valued_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_1(C) =>  (v1_funct_1(C) & v8_valued_2(C)) ) ) ) ).
fof(cc2_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v1_finset_1(A)) ) ) ) ).
fof(cc2_finseq_2, axiom,  (! [A] :  (! [B] :  ($true => v4_funct_1(B)) ) ) ).
fof(cc2_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ) ).
fof(cc2_funct_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ).
fof(cc2_membered, axiom,  (! [A] :  (v5_membered(A) => v4_membered(A)) ) ).
fof(cc2_nat_1, axiom,  (! [A] :  ($true =>  ~ (v3_xxreal_0(A)) ) ) ).
fof(cc2_relset_1, axiom,  (! [A, B] :  (! [C] :  ($true =>  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ).
fof(cc2_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc2_valued_2, axiom,  (! [A] :  (v5_valued_2(A) => v4_valued_2(A)) ) ).
fof(cc2_xcmplx_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xcmplx_0(A)) ) ).
fof(cc2_xreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xreal_0(A)) ) ).
fof(cc2_xxreal_0, axiom,  (! [A] :  (v7_ordinal1(A) => v1_xxreal_0(A)) ) ).
fof(cc2_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) )  =>  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(A)) ) ) ) ) ).
fof(cc30_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k1_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc30_valued_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_1(C) =>  (v1_funct_1(C) & v9_valued_2(C)) ) ) ) ).
fof(cc31_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k5_numbers))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc31_valued_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_1(C) =>  (v1_funct_1(C) & v10_valued_2(C)) ) ) ) ).
fof(cc32_valued_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_1(C) =>  (v1_funct_1(C) & v11_valued_2(C)) ) ) ) ).
fof(cc33_valued_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_1(C) =>  (v1_funct_1(C) & v12_valued_2(C)) ) ) ) ).
fof(cc3_finseq_1, axiom,  (! [A] :  (! [B] :  ($true => v5_relat_1(B, A)) ) ) ).
fof(cc3_finseq_2, axiom,  (! [A] :  (! [B] :  ($true => v3_finseq_1(B)) ) ) ).
fof(cc3_funct_1, axiom,  (! [A] :  (! [B] :  ($true => v1_funct_1(B)) ) ) ).
fof(cc3_funct_2, axiom,  (! [A, B] :  (! [C] :  (v1_funct_2(C, A, B) => v1_partfun1(C, A)) ) ) ).
fof(cc3_membered, axiom,  (! [A] :  (v4_membered(A) => v3_membered(A)) ) ).
fof(cc3_nat_1, axiom,  (! [A] :  (v7_ordinal1(A) =>  (v7_ordinal1(A) &  ~ (v3_xxreal_0(A)) ) ) ) ).
fof(cc3_relset_1, axiom,  (! [A, B] :  (! [C] :  ($true => v1_xboole_0(C)) ) ) ).
fof(cc3_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k4_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc3_valued_2, axiom,  (! [A] :  (v4_valued_2(A) => v3_valued_2(A)) ) ).
fof(cc3_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xcmplx_0(A)) ) ).
fof(cc3_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v2_xxreal_0(A))  =>  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc3_xxreal_2, axiom,  (! [A] :  ( (v6_membered(A) &  ~ (v1_xboole_0(A)) )  =>  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc4_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) & v1_xboole_0(A))  =>  (v1_relat_1(A) & v1_finseq_1(A)) ) ) ).
fof(cc4_funct_1, axiom,  (! [A] :  ( (v1_xboole_0(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc4_funct_2, axiom,  (! [A] :  (! [B] :  (v1_funct_2(B, A, A) => v1_partfun1(B, A)) ) ) ).
fof(cc4_membered, axiom,  (! [A] :  (v3_membered(A) => v2_membered(A)) ) ).
fof(cc4_relset_1, axiom,  (! [A, B] :  (! [C] :  ($true => v1_xboole_0(C)) ) ) ).
fof(cc4_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v5_relat_1(A, k3_numbers))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc4_valued_2, axiom,  (! [A] :  (v3_valued_2(A) => v1_valued_2(A)) ) ).
fof(cc4_xreal_0, axiom,  (! [A] :  (v1_xreal_0(A) => v1_xxreal_0(A)) ) ).
fof(cc4_xxreal_0, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_xxreal_0(A) &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ) ).
fof(cc4_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) & v5_xxreal_2(A))  =>  (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) ) ) ) ).
fof(cc5_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) & v1_finseq_1(A)) ) ) ) ) ).
fof(cc5_funct_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) )  =>  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) & v1_funct_1(A)) ) ) ) ).
fof(cc5_membered, axiom,  (! [A] :  (v3_membered(A) => v1_membered(A)) ) ).
fof(cc5_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v2_valued_0(A)) ) ) ).
fof(cc5_valued_2, axiom,  (! [A] :  (v3_valued_2(A) => v2_valued_2(A)) ) ).
fof(cc5_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) & v3_xxreal_0(A))  =>  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) ) ) ) ).
fof(cc5_xxreal_2, axiom,  (! [A] :  ( (v2_membered(A) &  (v3_xxreal_2(A) & v4_xxreal_2(A)) )  =>  (v2_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc6_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v1_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ).
fof(cc6_funct_1, axiom,  (! [A] :  ( (v1_zfmisc_1(A) &  (v1_relat_1(A) & v1_funct_1(A)) )  =>  (v1_relat_1(A) &  (v1_funct_1(A) & v3_funct_1(A)) ) ) ) ).
fof(cc6_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v3_valued_0(A))  =>  (v1_relat_1(A) & v1_valued_0(A)) ) ) ).
fof(cc6_valued_2, axiom,  (! [A] :  (v1_xboole_0(A) => v6_valued_2(A)) ) ).
fof(cc6_xxreal_0, axiom,  (! [A] :  ( ( ~ (v1_xboole_0(A))  &  (v1_xxreal_0(A) &  ~ (v2_xxreal_0(A)) ) )  =>  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ) ).
fof(cc6_xxreal_2, axiom,  (! [A] :  ( (v3_membered(A) & v1_finset_1(A))  =>  (v3_membered(A) & v5_xxreal_2(A)) ) ) ).
fof(cc7_finseq_1, axiom,  (! [A] :  ( (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) )  =>  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ) ) ).
fof(cc7_funct_1, axiom,  (! [A] :  (v1_xboole_0(A) => v4_funct_1(A)) ) ).
fof(cc7_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v5_relat_1(A, k3_numbers)) ) ) ).
fof(cc7_valued_2, axiom,  (! [A] :  (v1_valued_2(A) => v4_funct_1(A)) ) ).
fof(cc7_xxreal_0, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_xxreal_0(A))  =>  (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) ) ) ) ).
fof(cc7_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v4_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v2_xxreal_2(A)) ) ) ) ).
fof(cc8_finseq_1, axiom,  (! [A] :  (v1_xboole_0(A) => v3_finseq_1(A)) ) ).
fof(cc8_funct_1, axiom,  (! [A] :  (! [B] :  ($true =>  (v1_relat_1(B) & v1_funct_1(B)) ) ) ) ).
fof(cc8_funct_2, axiom,  (! [A, B] :  (! [C] :  ( (v1_funct_1(C) & v1_funct_2(C, A, B))  =>  (v1_funct_1(C) &  ( ~ (v1_xboole_0(C))  & v1_funct_2(C, A, B)) ) ) ) ) ).
fof(cc8_membered, axiom,  (! [A] :  ($true => v3_membered(A)) ) ).
fof(cc8_valued_0, axiom,  (! [A] :  ( (v1_relat_1(A) & v4_valued_0(A))  =>  (v1_relat_1(A) & v3_valued_0(A)) ) ) ).
fof(cc8_valued_2, axiom,  (! [A] :  (v2_valued_2(A) => v4_funct_1(A)) ) ).
fof(cc8_xxreal_0, axiom,  (! [A] :  ( (v1_xxreal_0(A) &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(A)) ) )  =>  (v1_xboole_0(A) & v1_xxreal_0(A)) ) ) ).
fof(cc8_xxreal_2, axiom,  (! [A] :  ( (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v3_xxreal_2(A)) )  =>  (v5_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_xxreal_2(A)) ) ) ) ).
fof(cc9_finseq_1, axiom,  (! [A] :  (v3_finseq_1(A) => v4_funct_1(A)) ) ).
fof(cc9_funct_1, axiom,  (! [A] :  (! [B] :  ($true => v4_funct_1(B)) ) ) ).
fof(cc9_membered, axiom,  (! [A] :  ($true => v4_membered(A)) ) ).
fof(cc9_valued_0, axiom,  (! [A] :  ( (v1_xboole_0(A) & v1_relat_1(A))  =>  (v1_relat_1(A) & v4_valued_0(A)) ) ) ).
fof(cc9_valued_2, axiom,  (! [A] :  (! [B] :  ($true => v1_valued_2(B)) ) ) ).
fof(cc9_xxreal_2, axiom,  (! [A] :  (v6_membered(A) =>  (v6_membered(A) & v3_xxreal_2(A)) ) ) ).
fof(connectedness_r1_xxreal_0, axiom,  (! [A, B] :  (r1_xxreal_0(A, B) | r1_xxreal_0(B, A)) ) ).
fof(d1_euclid, axiom,  (! [A] : k1_euclid(A)=k4_finseq_2(A, k1_numbers)) ).
fof(d1_finseq_1, axiom,  (! [A] : k1_finseq_1(A)=all([ (! [] : m2_subset_1(k1_numbers, k5_numbers)) ], ![],  (r1_xxreal_0(np__1, ![]) & r1_xxreal_0(![], A)) )) ).
fof(d2_finseq_2, axiom,  (! [A] :  (! [B] : k2_finseq_2(A, B)=k7_funcop_1(k2_finseq_1(A), B)) ) ).
fof(d2_xboole_0, axiom, k1_xboole_0=the(v1_xboole_0)).
fof(d4_euclid, axiom,  (! [A] : k4_euclid(A)=k5_finseq_2(k1_numbers, A, k6_numbers)) ).
fof(d4_finseq_2, axiom,  (! [A] :  (! [B] : k4_finseq_2(A, B)=all([ (! [] : m2_finseq_2(B, k3_finseq_2(B))) ], ![], k3_finseq_1(![])=A)) ) ).
fof(d5_pdiff_1, axiom,  (! [A] :  (! [B] :  (! [C] :  (C=k5_pdiff_1(A, B) <=>  (k9_xtuple_0(C)=k1_numbers &  (! [D] : k1_funct_1(C, D)=k1_finseq_7(k1_numbers, B, A, D)) ) ) ) ) ) ).
fof(dt_k13_finseq_1, axiom,  (! [A] : $true) ).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_euclid, axiom,  (! [A] : m1_finseq_2(k1_euclid(A), k1_numbers)) ).
fof(dt_k1_finseq_1, axiom,  (! [A] : $true) ).
fof(dt_k1_finseq_7, axiom,  (! [A, B, C, D] : m2_finseq_1(k1_finseq_7(A, B, C, D), A)) ).
fof(dt_k1_funct_1, axiom,  (! [A, B] : $true) ).
fof(dt_k1_numbers, axiom, $true).
fof(dt_k1_tarski, axiom,  (! [A] : $true) ).
fof(dt_k1_xboole_0, axiom, $true).
fof(dt_k1_zfmisc_1, axiom,  (! [A] : $true) ).
fof(dt_k2_finseq_1, axiom,  (! [A] : m1_subset_1(k2_finseq_1(A), k1_zfmisc_1(k5_numbers))) ).
fof(dt_k2_finseq_2, axiom,  (! [A, B] :  (v1_relat_1(k2_finseq_2(A, B)) &  (v1_funct_1(k2_finseq_2(A, B)) & v1_finseq_1(k2_finseq_2(A, B))) ) ) ).
fof(dt_k2_funcop_1, axiom,  (! [A, B] : $true) ).
fof(dt_k2_funct_7, axiom,  (! [A, B, C] :  (v1_relat_1(k2_funct_7(A, B, C)) & v1_funct_1(k2_funct_7(A, B, C))) ) ).
fof(dt_k2_zfmisc_1, axiom,  (! [A, B] : $true) ).
fof(dt_k3_finseq_1, axiom,  (! [A] : m2_subset_1(k3_finseq_1(A), k1_numbers, k5_numbers)) ).
fof(dt_k3_finseq_2, axiom,  (! [A] : m1_finseq_2(k3_finseq_2(A), A)) ).
fof(dt_k3_funct_2, axiom,  (! [A, B, C, D] : m1_subset_1(k3_funct_2(A, B, C, D), B)) ).
fof(dt_k3_numbers, axiom, $true).
fof(dt_k4_euclid, axiom,  (! [A] :  (v1_relat_1(k4_euclid(A)) &  (v1_funct_1(k4_euclid(A)) &  (v1_finseq_1(k4_euclid(A)) & v3_valued_0(k4_euclid(A))) ) ) ) ).
fof(dt_k4_finseq_2, axiom,  (! [A, B] : m1_finseq_2(k4_finseq_2(A, B), B)) ).
fof(dt_k4_numbers, axiom, $true).
fof(dt_k4_ordinal1, axiom, $true).
fof(dt_k5_euclid, axiom,  (! [A] : m2_finseq_2(k5_euclid(A), k1_numbers, k1_euclid(A))) ).
fof(dt_k5_finseq_2, axiom,  (! [A, B, C] : m2_finseq_2(k5_finseq_2(A, B, C), A, k4_finseq_2(B, A))) ).
fof(dt_k5_numbers, axiom, m1_subset_1(k5_numbers, k1_zfmisc_1(k1_numbers))).
fof(dt_k5_pdiff_1, axiom,  (! [A, B] :  (v1_relat_1(k5_pdiff_1(A, B)) & v1_funct_1(k5_pdiff_1(A, B))) ) ).
fof(dt_k6_numbers, axiom, m2_subset_1(k6_numbers, k1_numbers, k5_numbers)).
fof(dt_k6_pdiff_1, axiom,  (! [A, B, C] :  (v1_funct_1(k6_pdiff_1(A, B, C)) &  (v1_funct_2(k6_pdiff_1(A, B, C), k1_numbers, k1_euclid(A)) & m1_subset_1(k6_pdiff_1(A, B, C), k1_zfmisc_1(k2_zfmisc_1(k1_numbers, k1_euclid(A))))) ) ) ).
fof(dt_k7_funcop_1, axiom,  (! [A, B] :  (v1_funct_1(k7_funcop_1(A, B)) &  (v1_funct_2(k7_funcop_1(A, B), A, k1_tarski(B)) & m1_subset_1(k7_funcop_1(A, B), k1_zfmisc_1(k2_zfmisc_1(A, k1_tarski(B))))) ) ) ).
fof(dt_k9_xtuple_0, axiom,  (! [A] : $true) ).
fof(dt_m1_finseq_1, axiom,  (! [A] :  (! [B] :  (m1_finseq_1(B, A) =>  (v1_relat_1(B) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ).
fof(dt_m1_finseq_2, axiom,  (! [A] :  (! [B] :  (m1_finseq_2(B, A) => $true) ) ) ).
fof(dt_m1_subset_1, axiom,  (! [A] :  (! [B] :  (m1_subset_1(B, A) => $true) ) ) ).
fof(dt_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) =>  (v1_funct_1(B) &  (v1_finseq_1(B) & m1_subset_1(B, k1_zfmisc_1(k2_zfmisc_1(k5_numbers, A)))) ) ) ) ) ).
fof(dt_m2_finseq_2, axiom,  (! [A, B] :  (! [C] :  (m2_finseq_2(C, A, B) => m2_finseq_1(C, A)) ) ) ).
fof(dt_m2_subset_1, axiom,  (! [A, B] :  (! [C] :  (m2_subset_1(C, A, B) => m1_subset_1(C, A)) ) ) ).
fof(existence_m1_finseq_1, axiom,  (! [A] :  (? [B] : m1_finseq_1(B, A)) ) ).
fof(existence_m1_finseq_2, axiom,  (! [A] :  (? [B] : m1_finseq_2(B, A)) ) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(existence_m2_finseq_1, axiom,  (! [A] :  (? [B] : m2_finseq_1(B, A)) ) ).
fof(existence_m2_finseq_2, axiom,  (! [A, B] :  (? [C] : m2_finseq_2(C, A, B)) ) ).
fof(existence_m2_subset_1, axiom,  (! [A, B] :  (? [C] : m2_subset_1(C, A, B)) ) ).
fof(fc108_valued_1, axiom,  (! [A] : v6_membered(k9_xtuple_0(A))) ).
fof(fc10_euclid, axiom,  (! [A] : v3_valued_2(k1_euclid(A))) ).
fof(fc10_membered, axiom,  (! [A] : v4_membered(k1_tarski(A))) ).
fof(fc10_nat_1, axiom,  (! [A, B] : v5_ordinal1(k2_funcop_1(A, B))) ).
fof(fc11_membered, axiom,  (! [A] : v5_membered(k1_tarski(A))) ).
fof(fc11_xxreal_2, axiom,  ( ~ (v3_xxreal_2(k1_numbers))  &  ~ (v4_xxreal_2(k1_numbers)) ) ).
fof(fc12_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k13_finseq_1(A))) ) ).
fof(fc12_membered, axiom,  (! [A] : v6_membered(k1_tarski(A))) ).
fof(fc14_funct_1, axiom,  (! [A] : v4_funct_1(k1_tarski(A))) ).
fof(fc14_valued_2, axiom,  (! [A, B, C, D] :  (v1_relat_1(k1_funct_1(D, B)) & v1_funct_1(k1_funct_1(D, B))) ) ).
fof(fc15_valued_2, axiom,  (! [A, B, C, D] :  (v1_relat_1(k1_funct_1(D, B)) & v1_funct_1(k1_funct_1(D, B))) ) ).
fof(fc16_valued_2, axiom,  (! [A, B, C, D] : v1_valued_0(k1_funct_1(D, B))) ).
fof(fc17_funct_1, axiom,  (! [A, B, C] :  (v1_relat_1(k1_funct_1(C, B)) & v1_funct_1(k1_funct_1(C, B))) ) ).
fof(fc17_valued_2, axiom,  (! [A, B, C, D] : v2_valued_0(k1_funct_1(D, B))) ).
fof(fc17_xxreal_2, axiom, v6_xxreal_2(k1_numbers)).
fof(fc18_funct_1, axiom,  (! [A] :  ~ (v1_zfmisc_1(k9_xtuple_0(A))) ) ).
fof(fc18_valued_2, axiom,  (! [A, B, C, D] : v3_valued_0(k1_funct_1(D, B))) ).
fof(fc19_funct_1, axiom,  (! [A, B] : v1_xboole_0(k1_funct_1(A, B))) ).
fof(fc19_valued_2, axiom,  (! [A, B, C, D] : v5_relat_1(k1_funct_1(D, B), k3_numbers)) ).
fof(fc1_euclid, axiom,  (! [A] :  ~ (v1_xboole_0(k1_euclid(A))) ) ).
fof(fc1_finseq_1, axiom,  (! [A] : v1_xboole_0(k1_finseq_1(A))) ).
fof(fc1_numbers, axiom,  ~ (v1_xboole_0(k1_numbers)) ).
fof(fc1_pdiff_6, axiom,  (! [A, B] :  (v1_funct_1(k2_funcop_1(k1_euclid(B), k5_euclid(A))) &  (v1_funct_2(k2_funcop_1(k1_euclid(B), k5_euclid(A)), k1_euclid(B), k1_euclid(A)) &  (v1_pdiff_6(k2_funcop_1(k1_euclid(B), k5_euclid(A)), A, B) & v2_pdiff_6(k2_funcop_1(k1_euclid(B), k5_euclid(A)), A, B)) ) ) ) ).
fof(fc1_valued_2, axiom,  (! [A] : v1_valued_2(k1_tarski(A))) ).
fof(fc1_xboole_0, axiom, v1_xboole_0(k1_xboole_0)).
fof(fc20_valued_2, axiom,  (! [A, B, C, D] : v5_relat_1(k1_funct_1(D, B), k4_numbers)) ).
fof(fc21_valued_2, axiom,  (! [A, B, C, D] : v4_valued_0(k1_funct_1(D, B))) ).
fof(fc22_finseq_1, axiom,  (! [A] : v4_funct_1(k13_finseq_1(A))) ).
fof(fc23_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc27_finseq_1, axiom,  (! [A] : v3_finseq_1(k13_finseq_1(A))) ).
fof(fc29_finseq_1, axiom,  (! [A, B, C] : v1_finseq_1(k1_funct_1(B, C))) ).
fof(fc2_finseq_1, axiom,  (! [A] :  ~ (v1_xboole_0(k1_finseq_1(A))) ) ).
fof(fc2_xboole_0, axiom,  (! [A] :  ~ (v1_xboole_0(k1_tarski(A))) ) ).
fof(fc3_finseq_1, axiom,  (! [A] : v1_finset_1(k1_finseq_1(A))) ).
fof(fc3_finseq_2, axiom,  (! [A, B] : v1_finseq_1(k2_funcop_1(k2_finseq_1(A), B))) ).
fof(fc3_membered, axiom, v3_membered(k1_numbers)).
fof(fc3_numbers, axiom,  ~ (v1_xboole_0(k3_numbers)) ).
fof(fc40_valued_2, axiom,  (! [A, B] :  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ).
fof(fc41_valued_2, axiom,  (! [A, B] :  (v1_relat_1(k1_funct_1(A, B)) & v1_funct_1(k1_funct_1(A, B))) ) ).
fof(fc42_valued_2, axiom,  (! [A, B] : v1_valued_0(k1_funct_1(A, B))) ).
fof(fc43_valued_2, axiom,  (! [A, B] : v2_valued_0(k1_funct_1(A, B))) ).
fof(fc44_valued_2, axiom,  (! [A, B] : v3_valued_0(k1_funct_1(A, B))) ).
fof(fc45_valued_2, axiom,  (! [A, B] : v5_relat_1(k1_funct_1(A, B), k3_numbers)) ).
fof(fc46_valued_2, axiom,  (! [A, B] : v5_relat_1(k1_funct_1(A, B), k4_numbers)) ).
fof(fc47_valued_2, axiom,  (! [A, B] : v4_valued_0(k1_funct_1(A, B))) ).
fof(fc4_finseq_1, axiom,  (! [A] : v3_card_1(k1_finseq_1(A), A)) ).
fof(fc4_finseq_2, axiom,  (! [A, B] :  (v1_relat_1(k2_finseq_2(A, B)) &  (v1_funct_1(k2_finseq_2(A, B)) &  (v3_card_1(k2_finseq_2(A, B), A) & v1_finseq_1(k2_finseq_2(A, B))) ) ) ) ).
fof(fc4_membered, axiom, v4_membered(k3_numbers)).
fof(fc4_numbers, axiom,  ~ (v1_xboole_0(k4_numbers)) ).
fof(fc4_xtuple_0, axiom,  (! [A] : v1_xboole_0(k9_xtuple_0(A))) ).
fof(fc56_membered, axiom, v7_membered(k1_numbers)).
fof(fc57_membered, axiom, v7_membered(k3_numbers)).
fof(fc58_membered, axiom, v7_membered(k4_numbers)).
fof(fc59_membered, axiom, v7_membered(k4_ordinal1)).
fof(fc5_finseq_2, axiom,  (! [A, B] :  ~ (v1_xboole_0(k4_finseq_2(A, B))) ) ).
fof(fc5_membered, axiom, v5_membered(k4_numbers)).
fof(fc61_valued_0, axiom,  (! [A, B] : v1_xcmplx_0(k1_funct_1(A, B))) ).
fof(fc62_valued_0, axiom,  (! [A, B] : v1_xxreal_0(k1_funct_1(A, B))) ).
fof(fc63_valued_0, axiom,  (! [A, B] : v1_xreal_0(k1_funct_1(A, B))) ).
fof(fc64_valued_0, axiom,  (! [A, B] : v1_rat_1(k1_funct_1(A, B))) ).
fof(fc65_valued_0, axiom,  (! [A, B] : v1_int_1(k1_funct_1(A, B))) ).
fof(fc66_valued_0, axiom,  (! [A, B] : v7_ordinal1(k1_funct_1(A, B))) ).
fof(fc67_valued_0, axiom,  (! [A, B] : v1_valued_0(k2_funcop_1(A, B))) ).
fof(fc68_valued_0, axiom,  (! [A, B] : v2_valued_0(k2_funcop_1(A, B))) ).
fof(fc69_valued_0, axiom,  (! [A, B] : v3_valued_0(k2_funcop_1(A, B))) ).
fof(fc6_membered, axiom, v6_membered(k4_ordinal1)).
fof(fc6_numbers, axiom,  ~ (v1_finset_1(k4_numbers)) ).
fof(fc70_valued_0, axiom,  (! [A, B] : v5_relat_1(k2_funcop_1(A, B), k3_numbers)) ).
fof(fc71_valued_0, axiom,  (! [A, B] : v5_relat_1(k2_funcop_1(A, B), k4_numbers)) ).
fof(fc72_valued_0, axiom,  (! [A, B] : v4_valued_0(k2_funcop_1(A, B))) ).
fof(fc7_finseq_2, axiom,  (! [A] :  (v1_relat_1(k2_finseq_2(A, k6_numbers)) &  (v3_relat_1(k2_finseq_2(A, k6_numbers)) &  (v1_funct_1(k2_finseq_2(A, k6_numbers)) & v1_finseq_1(k2_finseq_2(A, k6_numbers))) ) ) ) ).
fof(fc7_membered, axiom,  (! [A] : v1_membered(k1_tarski(A))) ).
fof(fc7_numbers, axiom,  ~ (v1_finset_1(k3_numbers)) ).
fof(fc85_valued_0, axiom,  (! [A, B] : v1_valued_0(k2_zfmisc_1(A, B))) ).
fof(fc86_valued_0, axiom,  (! [A, B] : v2_valued_0(k2_zfmisc_1(A, B))) ).
fof(fc87_valued_0, axiom,  (! [A, B] : v3_valued_0(k2_zfmisc_1(A, B))) ).
fof(fc88_valued_0, axiom,  (! [A, B] : v5_relat_1(k2_zfmisc_1(A, B), k3_numbers)) ).
fof(fc89_valued_0, axiom,  (! [A, B] : v5_relat_1(k2_zfmisc_1(A, B), k4_numbers)) ).
fof(fc8_euclid, axiom,  (! [A, B] : v3_finseq_1(k4_finseq_2(A, B))) ).
fof(fc8_membered, axiom,  (! [A] : v2_membered(k1_tarski(A))) ).
fof(fc8_numbers, axiom,  ~ (v1_finset_1(k1_numbers)) ).
fof(fc8_relset_1, axiom,  (! [A, B, C, D] : v1_relat_1(k9_xtuple_0(D))) ).
fof(fc90_valued_0, axiom,  (! [A, B] : v4_valued_0(k2_zfmisc_1(A, B))) ).
fof(fc9_euclid, axiom,  (! [A] : v3_finseq_1(k1_euclid(A))) ).
fof(fc9_membered, axiom,  (! [A] : v3_membered(k1_tarski(A))) ).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(projectivity_k3_finseq_1, axiom,  (! [A] : k3_finseq_1(k3_finseq_1(A))=k3_finseq_1(A)) ).
fof(rc1_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v5_relat_1(B, A) &  (v1_funct_1(B) & v1_finseq_1(B)) ) ) ) ) ) ).
fof(rc1_finseq_2, axiom,  (! [A] :  (? [B] :  ~ (v1_xboole_0(B)) ) ) ).
fof(rc1_finseq_5, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  (v2_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc1_funct_2, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) &  (v1_funct_1(C) & v1_funct_2(C, A, B)) ) ) ) ) ) ).
fof(rc1_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc1_pdiff_6, axiom,  (! [A, B] :  (? [C] :  ( ~ (v1_xboole_0(C))  &  (v1_relat_1(C) &  (v4_relat_1(C, k1_euclid(B)) &  (v5_relat_1(C, k1_euclid(A)) &  (v1_funct_1(C) &  (v1_partfun1(C, k1_euclid(B)) &  (v1_funct_2(C, k1_euclid(B), k1_euclid(A)) &  (v7_valued_2(C) &  (v8_valued_2(C) &  (v9_valued_2(C) &  (v1_pdiff_6(C, A, B) & v2_pdiff_6(C, A, B)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc1_relset_1, axiom,  (! [A, B] :  (? [C] :  (v1_xboole_0(C) &  (v1_relat_1(C) &  (v4_relat_1(C, A) & v5_relat_1(C, B)) ) ) ) ) ).
fof(rc1_valued_0, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v4_valued_0(A)) ) ) ).
fof(rc1_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  (v1_valued_0(A) & v1_finseq_1(A)) ) ) ) ).
fof(rc1_valued_2, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_valued_2(A)) ) ).
fof(rc1_xboole_0, axiom,  (? [A] : v1_xboole_0(A)) ).
fof(rc1_xcmplx_0, axiom,  (? [A] : v1_xcmplx_0(A)) ).
fof(rc1_xreal_0, axiom,  (? [A] : v1_xreal_0(A)) ).
fof(rc1_xxreal_0, axiom,  (? [A] : v1_xxreal_0(A)) ).
fof(rc1_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v2_xxreal_2(A)) ) ) ) ) ) ) ) ) ).
fof(rc2_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_xboole_0(B) &  (v1_finset_1(B) & v1_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc2_finseq_5, axiom,  (! [A] :  (? [B] :  ( ~ (v1_xboole_0(B))  &  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v2_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(rc2_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v6_membered(A)) ) ).
fof(rc2_nat_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_ordinal1(A)) ) ).
fof(rc2_valued_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v5_relat_1(A, k3_numbers) &  (v5_relat_1(A, k4_numbers) &  (v1_funct_1(A) &  (v3_funct_1(A) & v4_valued_0(A)) ) ) ) ) ) ) ).
fof(rc2_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  ~ (v1_xboole_0(A)) ) ) ) ) ).
fof(rc2_valued_2, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v12_valued_2(A)) ) ) ).
fof(rc2_xboole_0, axiom,  (? [A] :  ~ (v1_xboole_0(A)) ) ).
fof(rc2_xcmplx_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v1_xcmplx_0(A)) ) ).
fof(rc2_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v2_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc2_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v2_xxreal_0(A)) ) ).
fof(rc2_xxreal_2, axiom,  (? [A] :  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ) ).
fof(rc3_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_finseq_1(A)) ) ) ).
fof(rc3_finseq_5, axiom,  (? [A] :  ( ~ (v1_zfmisc_1(A))  &  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc3_membered, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v6_membered(A) & v7_membered(A)) ) ) ).
fof(rc3_valued_0, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  &  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v5_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  (v1_partfun1(A, k5_numbers) &  (v1_funct_2(A, k5_numbers, k5_numbers) &  (v1_valued_0(A) &  (v2_valued_0(A) &  (v3_valued_0(A) &  (v4_valued_0(A) & v5_valued_0(A)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(rc3_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  & v1_finset_1(A)) ) ) ) ) ).
fof(rc3_xreal_0, axiom,  (? [A] :  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) &  (v3_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc3_xxreal_0, axiom,  (? [A] :  (v1_xxreal_0(A) & v3_xxreal_0(A)) ) ).
fof(rc3_xxreal_2, axiom,  (? [A] :  (v1_membered(A) &  (v2_membered(A) &  (v3_membered(A) &  (v4_membered(A) &  (v5_membered(A) &  (v6_membered(A) &  ( ~ (v1_xboole_0(A))  &  (v1_xxreal_2(A) & v5_xxreal_2(A)) ) ) ) ) ) ) ) ) ).
fof(rc4_finseq_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  ( ~ (v1_xboole_0(A))  &  (v1_finset_1(A) &  (v1_finseq_1(A) & v2_finseq_1(A)) ) ) ) ) ) ) ).
fof(rc4_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v3_funct_1(B) & v1_funct_2(B, k5_numbers, A)) ) ) ) ) ) ) ).
fof(rc4_valued_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v4_relat_1(A, k5_numbers) &  (v1_funct_1(A) &  (v1_finset_1(A) & v3_card_1(A, np__1)) ) ) ) ) ).
fof(rc4_xreal_0, axiom,  (? [A] :  (v1_xboole_0(A) &  (v1_xcmplx_0(A) &  (v1_xxreal_0(A) & v1_xreal_0(A)) ) ) ) ).
fof(rc4_xxreal_0, axiom,  (? [A] :  (v1_xboole_0(A) & v1_xxreal_0(A)) ) ).
fof(rc4_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  & v6_xxreal_2(A)) ) ) ).
fof(rc5_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) &  ~ (v3_funct_1(A)) ) ) ) ).
fof(rc5_valued_1, axiom,  (! [A] :  (? [B] :  (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)) ) ) ) ) ) ) ) ) ) ).
fof(rc5_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc6_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  ( ~ (v1_xboole_0(B))  &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(rc6_funct_1, axiom,  (! [A, B] :  (? [C] :  (v1_relat_1(C) &  (v4_relat_1(C, A) &  (v5_relat_1(C, B) & v1_funct_1(C)) ) ) ) ) ).
fof(rc6_valued_0, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, A) &  (v1_funct_1(B) &  (v1_partfun1(B, A) & v4_valued_0(B)) ) ) ) ) ) ).
fof(rc6_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xxreal_2(A))  &  (v2_xxreal_2(A) & v6_xxreal_2(A)) ) ) ) ).
fof(rc7_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v3_card_1(B, A) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(rc7_funct_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v4_funct_1(A)) ) ).
fof(rc7_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  (v1_xxreal_2(A) &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ).
fof(rc8_finseq_1, axiom,  (? [A] :  ( ~ (v1_xboole_0(A))  & v3_finseq_1(A)) ) ).
fof(rc8_xxreal_2, axiom,  (? [A] :  (v2_membered(A) &  ( ~ (v1_xboole_0(A))  &  ( ~ (v1_xxreal_2(A))  &  ( ~ (v2_xxreal_2(A))  & v6_xxreal_2(A)) ) ) ) ) ).
fof(rc9_finseq_1, axiom,  (! [A] :  (? [B] :  (v1_relat_1(B) &  (v4_relat_1(B, k5_numbers) &  (v5_relat_1(B, A) &  (v1_funct_1(B) &  (v1_finset_1(B) &  (v1_finseq_1(B) & v2_finseq_1(B)) ) ) ) ) ) ) ) ).
fof(redefinition_k1_finseq_7, axiom,  (! [A, B, C, D] : k1_finseq_7(A, B, C, D)=k2_funct_7(B, C, D)) ).
fof(redefinition_k2_finseq_1, axiom,  (! [A] : k2_finseq_1(A)=k1_finseq_1(A)) ).
fof(redefinition_k3_finseq_1, axiom,  (! [A] : k3_finseq_1(A)=k1_card_1(A)) ).
fof(redefinition_k3_finseq_2, axiom,  (! [A] : k3_finseq_2(A)=k13_finseq_1(A)) ).
fof(redefinition_k3_funct_2, axiom,  (! [A, B, C, D] : k3_funct_2(A, B, C, D)=k1_funct_1(C, D)) ).
fof(redefinition_k5_euclid, axiom,  (! [A] : k5_euclid(A)=k4_euclid(A)) ).
fof(redefinition_k5_finseq_2, axiom,  (! [A, B, C] : k5_finseq_2(A, B, C)=k2_finseq_2(B, C)) ).
fof(redefinition_k5_numbers, axiom, k5_numbers=k4_ordinal1).
fof(redefinition_k6_numbers, axiom, k6_numbers=k1_xboole_0).
fof(redefinition_k6_pdiff_1, axiom,  (! [A, B, C] : k6_pdiff_1(A, B, C)=k5_pdiff_1(B, C)) ).
fof(redefinition_k7_funcop_1, axiom,  (! [A, B] : k7_funcop_1(A, B)=k2_funcop_1(A, B)) ).
fof(redefinition_m2_finseq_1, axiom,  (! [A] :  (! [B] :  (m2_finseq_1(B, A) <=> m1_finseq_1(B, A)) ) ) ).
fof(redefinition_m2_finseq_2, axiom,  (! [A, B] :  (! [C] :  (m2_finseq_2(C, A, B) <=> m1_subset_1(C, B)) ) ) ).
fof(redefinition_m2_subset_1, axiom,  (! [A, B] :  (! [C] :  (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(reflexivity_r1_xxreal_0, axiom,  (! [A, B] : r1_xxreal_0(A, A)) ).
fof(rqLessOrEqual__r1_xxreal_0__r0_r0, axiom, r1_xxreal_0(np__0, np__0)).
fof(rqLessOrEqual__r1_xxreal_0__r0_r1, axiom, r1_xxreal_0(np__0, np__1)).
fof(rqLessOrEqual__r1_xxreal_0__r1_r0, axiom,  ~ (r1_xxreal_0(np__1, np__0)) ).
fof(rqLessOrEqual__r1_xxreal_0__r1_r1, axiom, r1_xxreal_0(np__1, np__1)).
fof(spc0_boole, axiom, v1_xboole_0(np__0)).
fof(spc0_numerals, axiom,  (m2_subset_1(np__0, k1_numbers, k5_numbers) &  (m1_subset_1(np__0, k5_numbers) & m1_subset_1(np__0, k1_numbers)) ) ).
fof(spc1_boole, axiom,  ~ (v1_xboole_0(np__1)) ).
fof(spc1_numerals, axiom,  ( (v2_xxreal_0(np__1) & m2_subset_1(np__1, k1_numbers, k5_numbers))  &  (m1_subset_1(np__1, k5_numbers) & m1_subset_1(np__1, k1_numbers)) ) ).
fof(t11_pdiff_7, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r1_xxreal_0(np__1, C) &  (r1_xxreal_0(C, A) &  ( ~ (B=k6_numbers)  & k1_finseq_7(k1_numbers, k5_euclid(A), C, B)=k5_euclid(A)) ) ) ) ) ) ) ).
fof(t1_numerals, axiom, m1_subset_1(k1_xboole_0, k4_ordinal1)).
fof(t1_real, axiom,  (! [A] :  (! [B] :  ( (r1_xxreal_0(A, B) & v2_xxreal_0(A))  => v2_xxreal_0(B)) ) ) ).
fof(t1_subset, axiom,  (! [A] :  (! [B] :  (r2_hidden(A, B) => m1_subset_1(A, B)) ) ) ).
fof(t2_real, axiom,  (! [A] :  (! [B] :  ( (r1_xxreal_0(A, B) & v3_xxreal_0(B))  => v3_xxreal_0(A)) ) ) ).
fof(t2_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, B) =>  (v1_xboole_0(B) | r2_hidden(A, B)) ) ) ) ).
fof(t3_real, axiom,  (! [A] :  (! [B] :  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v3_xxreal_0(A))  & v3_xxreal_0(B)) ) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
fof(t4_real, axiom,  (! [A] :  (! [B] :  ~ ( (r1_xxreal_0(A, B) &  ( ~ (v2_xxreal_0(B))  & v2_xxreal_0(A)) ) ) ) ) ).
fof(t4_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ( (r2_hidden(A, B) & m1_subset_1(B, k1_zfmisc_1(C)))  => m1_subset_1(A, C)) ) ) ) ).
fof(t5_real, axiom,  (! [A] :  (! [B] :  (r1_xxreal_0(A, B) =>  (v1_xboole_0(B) |  (v3_xxreal_0(A) | v2_xxreal_0(B)) ) ) ) ) ).
fof(t5_subset, axiom,  (! [A] :  (! [B] :  (! [C] :  ~ ( (r2_hidden(A, B) &  (m1_subset_1(B, k1_zfmisc_1(C)) & v1_xboole_0(C)) ) ) ) ) ) ).
fof(t6_boole, axiom,  (! [A] :  (v1_xboole_0(A) => A=k1_xboole_0) ) ).
fof(t6_real, axiom,  (! [A] :  (! [B] :  (r1_xxreal_0(A, B) =>  (v1_xboole_0(A) |  (v2_xxreal_0(B) | v3_xxreal_0(A)) ) ) ) ) ).
fof(t7_boole, axiom,  (! [A] :  (! [B] :  ~ ( (r2_hidden(A, B) & v1_xboole_0(B)) ) ) ) ).
fof(t7_real, axiom,  (! [A] :  (! [B] :  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v2_xxreal_0(A))  &  ~ (v3_xxreal_0(B)) ) ) ) ) ) ).
fof(t8_boole, axiom,  (! [A] :  (! [B] :  ~ ( (v1_xboole_0(A) &  ( ~ (A=B)  & v1_xboole_0(B)) ) ) ) ) ).
fof(t8_real, axiom,  (! [A] :  (! [B] :  ~ ( ( ~ (r1_xxreal_0(A, B))  &  ( ~ (v3_xxreal_0(B))  &  ~ (v2_xxreal_0(A)) ) ) ) ) ) ).