% Mizar problem: t42_bagorder,bagorder,3606,55 fof(t42_bagorder,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( v1_wellfnd1(A) => v1_wellfnd1(k14_bagorder(A)) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc1_card_1,cc1_card_5,cc1_finseq_1,cc1_finset_1,cc1_finsub_1,cc1_funct_1,cc1_funct_2,cc1_nat_1,cc1_ordinal1,cc1_relat_1,cc1_relset_1,cc1_xreal_0,cc2_card_1,cc2_card_5,cc2_finset_1,cc2_finsub_1,cc2_funct_1,cc2_funct_2,cc2_nat_1,cc2_ordinal1,cc2_xreal_0,cc3_card_1,cc3_finsub_1,cc3_funct_2,cc3_nat_1,cc3_ordinal1,cc3_polynom1,cc3_xreal_0,cc4_funct_2,cc4_polynom1,cc4_xreal_0,cc5_funct_2,cc5_polynom1,cc5_xreal_0,cc6_funct_2,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d11_dickson,d15_bagorder,d17_bagorder,d18_bagorder,d19_bagorder,d1_funct_2,d1_mcart_1,d1_tarski,d20_bagorder,d24_waybel_4,d26_waybel_4,d29_waybel_0,d2_mcart_1,d2_zfmisc_1,d4_xboole_0,d5_finsub_1,d5_funct_1,d5_tarski,d7_wellfnd1,d9_orders_2,dt_g1_orders_2,dt_k11_bagorder,dt_k12_bagorder,dt_k13_bagorder,dt_k14_bagorder,dt_k15_bagorder,dt_k16_bagorder,dt_k1_domain_1,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_domain_1,dt_k2_finsub_1,dt_k2_mcart_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_domain_1,dt_k3_tarski,dt_k4_relset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k5_finsub_1,dt_k5_numbers,dt_k5_ordinal2,dt_k6_domain_1,dt_k7_dickson,dt_k8_funct_2,dt_l1_orders_2,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_bagorder,fc10_xreal_0,fc11_bagorder,fc11_finseq_1,fc11_xreal_0,fc12_finset_1,fc12_relat_1,fc12_xreal_0,fc14_finset_1,fc14_polynom1,fc17_finseq_1,fc1_finset_1,fc1_finsub_1,fc1_nat_1,fc1_numbers,fc1_orders_2,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc20_polynom1,fc2_finseq_1,fc2_finset_1,fc2_finsub_1,fc2_orders_2,fc2_ordinal1,fc2_subset_1,fc3_nat_1,fc3_orders_2,fc3_polynom1,fc3_relat_1,fc3_subset_1,fc3_xreal_0,fc4_nat_1,fc4_ordinal1,fc4_relat_1,fc4_subset_1,fc5_polynom1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc7_xreal_0,fc8_relat_1,fc8_xreal_0,fc9_xreal_0,fraenkel_a_1_4_bagorder,free_g1_orders_2,rc11_polynom1,rc12_polynom1,rc12_waybel_0,rc1_card_1,rc1_card_5,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_funct_2,rc1_nat_1,rc1_orders_2,rc1_ordinal1,rc1_relat_1,rc1_subset_1,rc1_xreal_0,rc2_card_1,rc2_card_5,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_funct_2,rc2_nat_1,rc2_orders_2,rc2_ordinal1,rc2_polynom1,rc2_relat_1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_nat_1,rc3_ordinal1,rc3_relat_1,rc3_struct_0,rc3_xreal_0,rc4_finset_1,rc4_funct_1,rc4_xreal_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc7_polynom1,rc8_finseq_1,redefinition_k1_domain_1,redefinition_k1_nat_1,redefinition_k2_domain_1,redefinition_k2_finsub_1,redefinition_k3_domain_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k6_domain_1,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_orders_2,s1_nat_1__e16_73_1__bagorder,s1_nat_1__e29_73__bagorder,s1_nat_1__e32_73__bagorder,s1_nat_1__e35_73__bagorder,s2_funct_2__e24_73__bagorder,s2_recdef_1__e20_73__bagorder,s3_funct_2__e20_73_1__bagorder,s3_funct_2__e7_73_1__bagorder,spc0_boole,spc1_boole,spc1_numerals,t12_relset_1,t15_wellfnd1,t1_arithm,t1_bagorder,t1_numerals,t1_real,t1_subset,t28_nat_1,t29_nat_1,t2_real,t2_subset,t2_tarski,t37_bagorder,t3_boole,t3_real,t3_subset,t40_bagorder,t41_bagorder,t4_boole,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real]), [file(bagorder,t42_bagorder)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(card_1,cc1_card_1), []). fof(cc1_card_5,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_xboole_0(A) ) ), file(card_5,cc1_card_5), []). fof(cc1_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) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_finsub_1,axiom,( ! [A] : ( v4_finsub_1(A) => ( v1_finsub_1(A) & v3_finsub_1(A) ) ) ), file(finsub_1,cc1_finsub_1), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) ), file(ordinal1,cc1_ordinal1), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc2_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc2_card_1), []). fof(cc2_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(card_5,cc2_card_5), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_finsub_1,axiom,( ! [A] : ( ( v1_finsub_1(A) & v3_finsub_1(A) ) => v4_finsub_1(A) ) ), file(finsub_1,cc2_finsub_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). fof(cc2_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_ordinal1,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) ), file(ordinal1,cc2_ordinal1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_card_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_finset_1(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_card_1(A) ) ) ), file(card_1,cc3_card_1), []). fof(cc3_finsub_1,axiom,( ! [A,B] : ( m1_subset_1(B,k5_finsub_1(A)) => v1_finset_1(B) ) ), file(finsub_1,cc3_finsub_1), []). fof(cc3_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_2), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ) ), file(ordinal1,cc3_ordinal1), []). fof(cc3_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_seqm_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ) ), file(polynom1,cc3_polynom1), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_funct_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( ( v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) ) => ( v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ) ) ), file(funct_2,cc4_funct_2), []). fof(cc4_polynom1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k5_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) ) => ( v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v7_seqm_3(B) ) ) ) ), file(polynom1,cc4_polynom1), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_polynom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_polynom1(A) ) ) ), file(polynom1,cc5_polynom1), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d11_dickson,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( k1_relat_1(A) = k5_numbers & r2_hidden(B,k2_relat_1(A)) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( C = k7_dickson(A,B) <=> ( k1_funct_1(A,C) = B & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( k1_funct_1(A,D) = B => r1_xreal_0(C,D) ) ) ) ) ) ) ) ), file(dickson,d11_dickson), []). fof(d15_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k11_bagorder(A,B) <=> ( r2_hidden(C,B) & r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) ), file(bagorder,d15_bagorder), []). fof(d17_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => k13_bagorder(A) = k3_tarski(k2_relat_1(k12_bagorder(A))) ) ), file(bagorder,d17_bagorder), []). fof(d18_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => k14_bagorder(A) = g1_orders_2(k5_finsub_1(u1_struct_0(A)),k13_bagorder(A)) ) ), file(bagorder,d18_bagorder), []). fof(d19_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( ( v1_wellfnd1(A) & r1_tarski(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k15_bagorder(A,B) <=> ( r2_hidden(C,B) & r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) ) ), file(bagorder,d19_bagorder), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_mcart_1,axiom,( ! [A] : ( ? [B,C] : A = k4_tarski(B,C) => ! [B] : ( B = k1_mcart_1(A) <=> ! [C,D] : ( A = k4_tarski(C,D) => B = C ) ) ) ), file(mcart_1,d1_mcart_1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d20_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) ) => ( D = k16_bagorder(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,u1_struct_0(A),D,E) = k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(E,C)) ) ) ) ) ) ) ), file(bagorder,d20_bagorder), []). fof(d24_waybel_4,axiom,( ! [A,B,C] : ( v1_relat_1(C) => ( r2_waybel_4(A,B,C) <=> ( r2_hidden(B,A) & ! [D] : ~ ( r2_hidden(D,A) & D != B & r2_hidden(k4_tarski(B,D),C) ) ) ) ) ), file(waybel_4,d24_waybel_4), []). fof(d26_waybel_4,axiom,( ! [A,B,C] : ( v1_relat_1(C) => ( r4_waybel_4(A,B,C) <=> ( r2_hidden(B,A) & ! [D] : ~ ( r2_hidden(D,A) & D != B & r2_hidden(k4_tarski(D,B),C) ) ) ) ) ), file(waybel_4,d26_waybel_4), []). fof(d29_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v16_waybel_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) | r1_orders_2(A,C,B) ) ) ) ) ) ), file(waybel_0,d29_waybel_0), []). fof(d2_mcart_1,axiom,( ! [A] : ( ? [B,C] : A = k4_tarski(B,C) => ! [B] : ( B = k2_mcart_1(A) <=> ! [C,D] : ( A = k4_tarski(C,D) => B = D ) ) ) ), file(mcart_1,d2_mcart_1), []). fof(d2_zfmisc_1,axiom,( ! [A,B,C] : ( C = k2_zfmisc_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E,F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k4_tarski(E,F) ) ) ) ), file(zfmisc_1,d2_zfmisc_1), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(d5_finsub_1,axiom,( ! [A,B] : ( v4_finsub_1(B) => ( B = k5_finsub_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r1_tarski(C,A) & v1_finset_1(C) ) ) ) ) ), file(finsub_1,d5_finsub_1), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d7_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( v3_wellfnd1(B,A) <=> ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)) != k8_funct_2(k5_numbers,u1_struct_0(A),B,C) & r2_hidden(k4_tarski(k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) ) ), file(wellfnd1,d7_wellfnd1), []). fof(d9_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ), file(orders_2,d9_orders_2), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_k11_bagorder,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) ) => m1_subset_1(k11_bagorder(A,B),u1_struct_0(A)) ) ), file(bagorder,k11_bagorder), []). fof(dt_k12_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( v1_funct_1(k12_bagorder(A)) & v1_funct_2(k12_bagorder(A),k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))) & m2_relset_1(k12_bagorder(A),k5_numbers,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))) ) ) ), file(bagorder,k12_bagorder), []). fof(dt_k13_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( v1_partfun1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) & v1_relat_2(k13_bagorder(A)) & v4_relat_2(k13_bagorder(A)) & v8_relat_2(k13_bagorder(A)) & m2_relset_1(k13_bagorder(A),k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))) ) ) ), file(bagorder,k13_bagorder), []). fof(dt_k14_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( v2_orders_2(k14_bagorder(A)) & v3_orders_2(k14_bagorder(A)) & v4_orders_2(k14_bagorder(A)) & l1_orders_2(k14_bagorder(A)) ) ) ), file(bagorder,k14_bagorder), []). fof(dt_k15_bagorder,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) ) => m1_subset_1(k15_bagorder(A,B),u1_struct_0(A)) ) ), file(bagorder,k15_bagorder), []). fof(dt_k16_bagorder,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m1_relset_1(B,k5_numbers,u1_struct_0(A)) & m1_subset_1(C,k5_numbers) ) => ( v1_funct_1(k16_bagorder(A,B,C)) & v1_funct_2(k16_bagorder(A,B,C),k5_numbers,u1_struct_0(A)) & m2_relset_1(k16_bagorder(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ), file(bagorder,k16_bagorder), []). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_1), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_domain_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) ) => m1_subset_1(k2_domain_1(A,B,C),A) ) ), file(domain_1,k2_domain_1), []). fof(dt_k2_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m1_subset_1(k2_finsub_1(A,B,C),A) ) ), file(finsub_1,k2_finsub_1), []). fof(dt_k2_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_domain_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) ) => m1_subset_1(k3_domain_1(A,B,C),B) ) ), file(domain_1,k3_domain_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), []). fof(dt_k7_dickson,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m2_subset_1(k7_dickson(A,B),k1_numbers,k5_numbers) ) ), file(dickson,k7_dickson), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k14_bagorder(A)) & v2_orders_2(k14_bagorder(A)) & v3_orders_2(k14_bagorder(A)) & v4_orders_2(k14_bagorder(A)) ) ) ), file(bagorder,fc10_bagorder), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k14_bagorder(A)) & v2_orders_2(k14_bagorder(A)) & v3_orders_2(k14_bagorder(A)) & v4_orders_2(k14_bagorder(A)) & v16_waybel_0(k14_bagorder(A)) ) ) ), file(bagorder,fc11_bagorder), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_polynom1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) ), file(polynom1,fc14_polynom1), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_zfmisc_1(A)) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)) ) ), file(finsub_1,fc1_finsub_1), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). fof(fc1_orders_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,A) ) => ( ~ v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc1_orders_2), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc20_polynom1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_seq_1(k1_xboole_0) & v1_matrlin(k1_xboole_0) & v7_seqm_3(k1_xboole_0) & v1_polynom1(k1_xboole_0) ), file(polynom1,fc20_polynom1), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finsub_1(A)) & v1_finsub_1(k5_finsub_1(A)) & v3_finsub_1(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) ) ), file(finsub_1,fc2_finsub_1), []). fof(fc2_orders_2,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(u1_orders_2(A)) & v1_relat_2(u1_orders_2(A)) & v4_relat_2(u1_orders_2(A)) & v8_relat_2(u1_orders_2(A)) & v1_partfun1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(orders_2,fc2_orders_2), []). fof(fc2_ordinal1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) & v3_ordinal1(k1_xboole_0) ), file(ordinal1,fc2_ordinal1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_orders_2,axiom,( ! [A,B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => ( v1_orders_2(g1_orders_2(A,B)) & v2_orders_2(g1_orders_2(A,B)) & v3_orders_2(g1_orders_2(A,B)) & v4_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc3_orders_2), []). fof(fc3_polynom1,axiom, ( v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_xboole_0(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) & v1_funcop_1(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) & v1_matrlin(k1_xboole_0) ), file(polynom1,fc3_polynom1), []). fof(fc3_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k4_xboole_0(A,B)) ) ), file(relat_1,fc3_relat_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(k3_tarski(A)) & v2_ordinal1(k3_tarski(A)) & v3_ordinal1(k3_tarski(A)) ) ) ), file(ordinal1,fc4_ordinal1), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_polynom1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrlin(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) & v1_finset_1(k1_funct_1(A,B)) & v1_finseq_1(k1_funct_1(A,B)) ) ) ), file(polynom1,fc5_polynom1), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_1_4_bagorder,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v16_waybel_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_4_bagorder(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(k14_bagorder(B))) & m2_relset_1(C,k5_numbers,u1_struct_0(k14_bagorder(B))) & A = C & v3_wellfnd1(C,k14_bagorder(B)) ) ) ) ), file(bagorder,a_1_4_bagorder), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(rc11_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_seq_1(A) & v7_seqm_3(A) & v1_polynom1(A) ) ), file(polynom1,rc11_polynom1), []). fof(rc12_polynom1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k5_numbers) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k5_numbers) & v1_seq_1(B) & v7_seqm_3(B) & v1_polynom1(B) ) ), file(polynom1,rc12_polynom1), []). fof(rc12_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) ) ), file(waybel_0,rc12_waybel_0), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). fof(rc1_card_5,axiom,( ? [A] : ~ v1_finset_1(A) ), file(card_5,rc1_card_5), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) ) ), file(orders_2,rc1_orders_2), []). fof(rc1_ordinal1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc1_ordinal1), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) ), file(card_1,rc2_card_1), []). fof(rc2_card_5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) ) ), file(card_5,rc2_card_5), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) ) ), file(orders_2,rc2_orders_2), []). fof(rc2_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc2_ordinal1), []). fof(rc2_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_funcop_1(A) & v1_matrlin(A) ) ), file(polynom1,rc2_polynom1), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc3_ordinal1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_polynom1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v7_seqm_3(A) ) ), file(polynom1,rc7_polynom1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(redefinition_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k2_domain_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) ) => k2_domain_1(A,B,C) = k1_mcart_1(C) ) ), file(domain_1,k2_domain_1), []). fof(redefinition_k2_finsub_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k2_finsub_1(A,B,C) = k4_xboole_0(B,C) ) ), file(finsub_1,k2_finsub_1), []). fof(redefinition_k3_domain_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(A,B)) ) => k3_domain_1(A,B,C) = k2_mcart_1(C) ) ), file(domain_1,k3_domain_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r3_orders_2(A,B,C) <=> r1_orders_2(A,B,C) ) ) ), file(orders_2,r3_orders_2), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(reflexivity_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r3_orders_2(A,B,B) ) ), file(orders_2,r3_orders_2), []). fof(s1_nat_1__e16_73_1__bagorder,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(k7_dickson(B,k15_bagorder(A,k2_relat_1(B))),0)) = k15_bagorder(A,k2_relat_1(B)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(k7_dickson(B,k15_bagorder(A,k2_relat_1(B))),C)) = k15_bagorder(A,k2_relat_1(B)) => k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(k7_dickson(B,k15_bagorder(A,k2_relat_1(B))),k1_nat_1(C,1))) = k15_bagorder(A,k2_relat_1(B)) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(k7_dickson(B,k15_bagorder(A,k2_relat_1(B))),C)) = k15_bagorder(A,k2_relat_1(B)) ) ) ) ), file(bagorder,s1_nat_1__e16_73_1__bagorder), []). fof(s1_nat_1__e29_73__bagorder,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) & m2_relset_1(C,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) ) => ( ( ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(E,k5_numbers,u1_struct_0(k14_bagorder(A))) & E = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,0)) & ! [F] : ( r2_hidden(F,k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),E,D)) => ( F != k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,0)) & r2_hidden(k4_tarski(F,k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,0))),u1_orders_2(A)) ) ) ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ? [I] : ( v1_funct_1(I) & v1_funct_2(I,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(I,k5_numbers,u1_struct_0(k14_bagorder(A))) & I = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G)) & ! [J] : ( r2_hidden(J,k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),I,H)) => ( J != k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G)) & r2_hidden(k4_tarski(J,k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G))),u1_orders_2(A)) ) ) ) ) => ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ? [L] : ( v1_funct_1(L) & v1_funct_2(L,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(L,k5_numbers,u1_struct_0(k14_bagorder(A))) & L = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,k1_nat_1(G,1))) & ! [M] : ( r2_hidden(M,k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),L,K)) => ( M != k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,k1_nat_1(G,1))) & r2_hidden(k4_tarski(M,k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,k1_nat_1(G,1)))),u1_orders_2(A)) ) ) ) ) ) ) ) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [N] : ( m2_subset_1(N,k1_numbers,k5_numbers) => ? [O] : ( v1_funct_1(O) & v1_funct_2(O,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(O,k5_numbers,u1_struct_0(k14_bagorder(A))) & O = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G)) & ! [P] : ( r2_hidden(P,k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),O,N)) => ( P != k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G)) & r2_hidden(k4_tarski(P,k2_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G))),u1_orders_2(A)) ) ) ) ) ) ) ) ), file(bagorder,s1_nat_1__e29_73__bagorder), []). fof(s1_nat_1__e32_73__bagorder,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) & m2_relset_1(C,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) & v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) ) => ( ( ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(E,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) & E = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,0)) & r2_hidden(k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(0,1)),k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),E,F)) ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ? [H] : ( v1_funct_1(H) & v1_funct_2(H,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(H,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [I] : ( m2_subset_1(I,k1_numbers,k5_numbers) & H = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G)) & r2_hidden(k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(G,1)),k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),H,I)) ) ) => ? [J] : ( v1_funct_1(J) & v1_funct_2(J,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(J,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) & J = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,k1_nat_1(G,1))) & r2_hidden(k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(k1_nat_1(G,1),1)),k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),J,K)) ) ) ) ) ) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ? [L] : ( v1_funct_1(L) & v1_funct_2(L,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(L,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) & L = k3_domain_1(u1_struct_0(A),B,k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),C,G)) & r2_hidden(k8_funct_2(k5_numbers,u1_struct_0(A),D,k1_nat_1(G,1)),k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),L,M)) ) ) ) ) ) ), file(bagorder,s1_nat_1__e32_73__bagorder), []). fof(s1_nat_1__e35_73__bagorder,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ( ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(0,1)) != k8_funct_2(k5_numbers,u1_struct_0(A),B,0) & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(0,1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,0)),u1_orders_2(A)) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)) != k8_funct_2(k5_numbers,u1_struct_0(A),B,C) & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) => ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(k1_nat_1(C,1),1)) != k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)) & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(k1_nat_1(C,1),1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1))),u1_orders_2(A)) ) ) ) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)) != k8_funct_2(k5_numbers,u1_struct_0(A),B,C) & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k8_funct_2(k5_numbers,u1_struct_0(A),B,k1_nat_1(C,1)),k8_funct_2(k5_numbers,u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) ), file(bagorder,s1_nat_1__e35_73__bagorder), []). fof(s2_funct_2__e24_73__bagorder,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) & m2_relset_1(C,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) ) => ( ! [D] : ( r2_hidden(D,k5_numbers) => r2_hidden(k1_mcart_1(k1_funct_1(C,D)),u1_struct_0(A)) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,u1_struct_0(A)) & m2_relset_1(D,k5_numbers,u1_struct_0(A)) & ! [E] : ( r2_hidden(E,k5_numbers) => k1_funct_1(D,E) = k1_mcart_1(k1_funct_1(C,E)) ) ) ) ) ), file(bagorder,s2_funct_2__e24_73__bagorder), []). fof(s2_recdef_1__e20_73__bagorder,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),B)) ) => ( ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),B)) => ? [F] : ( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),B)) & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(G,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [H] : ( v1_funct_1(H) & v1_funct_2(H,k5_numbers,u1_struct_0(A)) & m2_relset_1(H,k5_numbers,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) & ? [K] : ( v1_funct_1(K) & v1_funct_2(K,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(K,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [L] : ( v1_funct_1(L) & v1_funct_2(L,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(L,k5_numbers,u1_struct_0(k14_bagorder(A))) & G = k2_mcart_1(E) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ? [N] : ( m1_subset_1(N,k5_finsub_1(u1_struct_0(A))) & N = k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),G,M) & N != k1_xboole_0 & k8_funct_2(k5_numbers,u1_struct_0(A),H,M) = k11_bagorder(A,N) ) ) & I = k15_bagorder(A,k2_relat_1(H)) & J = k7_dickson(H,I) & K = k16_bagorder(k14_bagorder(A),G,J) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),L,M) = k4_xboole_0(k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),K,M),k6_domain_1(u1_struct_0(A),I)) ) & ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ( r1_xreal_0(J,M) => k8_funct_2(k5_numbers,u1_struct_0(A),H,M) = I ) ) & F = k1_domain_1(u1_struct_0(A),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(k14_bagorder(A)))),I,L) ) ) ) ) ) ) ) ) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) & m2_relset_1(D,k5_numbers,k2_zfmisc_1(u1_struct_0(A),B)) & k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),D,0) = C & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ? [O] : ( v1_funct_1(O) & v1_funct_2(O,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(O,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [P] : ( v1_funct_1(P) & v1_funct_2(P,k5_numbers,u1_struct_0(A)) & m2_relset_1(P,k5_numbers,u1_struct_0(A)) & ? [Q] : ( m1_subset_1(Q,u1_struct_0(A)) & ? [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) & ? [S] : ( v1_funct_1(S) & v1_funct_2(S,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(S,k5_numbers,u1_struct_0(k14_bagorder(A))) & ? [T] : ( v1_funct_1(T) & v1_funct_2(T,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(T,k5_numbers,u1_struct_0(k14_bagorder(A))) & O = k2_mcart_1(k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),D,E)) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ? [V] : ( m1_subset_1(V,k5_finsub_1(u1_struct_0(A))) & V = k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),O,U) & V != k1_xboole_0 & k8_funct_2(k5_numbers,u1_struct_0(A),P,U) = k11_bagorder(A,V) ) ) & Q = k15_bagorder(A,k2_relat_1(P)) & R = k7_dickson(P,Q) & S = k16_bagorder(k14_bagorder(A),O,R) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),T,U) = k4_xboole_0(k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),S,U),k6_domain_1(u1_struct_0(A),Q)) ) & ! [U] : ( m2_subset_1(U,k1_numbers,k5_numbers) => ( r1_xreal_0(R,U) => k8_funct_2(k5_numbers,u1_struct_0(A),P,U) = Q ) ) & k8_funct_2(k5_numbers,k2_zfmisc_1(u1_struct_0(A),B),D,k1_nat_1(E,1)) = k1_domain_1(u1_struct_0(A),k1_zfmisc_1(k2_zfmisc_1(k5_numbers,u1_struct_0(k14_bagorder(A)))),Q,T) ) ) ) ) ) ) ) ) ) ) ), file(bagorder,s2_recdef_1__e20_73__bagorder), []). fof(s3_funct_2__e20_73_1__bagorder,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(B,k5_numbers,u1_struct_0(k14_bagorder(A))) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) ) => ( ! [D] : ( m1_subset_1(D,k5_numbers) => ? [E] : ( m1_subset_1(E,k5_finsub_1(u1_struct_0(A))) & ? [F] : ( m1_subset_1(F,k5_finsub_1(u1_struct_0(A))) & F = k4_xboole_0(k1_funct_1(k16_bagorder(k14_bagorder(A),B,k7_dickson(C,k15_bagorder(A,k2_relat_1(C)))),D),k6_domain_1(u1_struct_0(A),k15_bagorder(A,k2_relat_1(C)))) & E = F ) ) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k5_finsub_1(u1_struct_0(A))) & m2_relset_1(D,k5_numbers,k5_finsub_1(u1_struct_0(A))) & ! [E] : ( m1_subset_1(E,k5_numbers) => ? [G] : ( m1_subset_1(G,k5_finsub_1(u1_struct_0(A))) & G = k4_xboole_0(k1_funct_1(k16_bagorder(k14_bagorder(A),B,k7_dickson(C,k15_bagorder(A,k2_relat_1(C)))),E),k6_domain_1(u1_struct_0(A),k15_bagorder(A,k2_relat_1(C)))) & k8_funct_2(k5_numbers,k5_finsub_1(u1_struct_0(A)),D,E) = G ) ) ) ) ) ), file(bagorder,s3_funct_2__e20_73_1__bagorder), []). fof(s3_funct_2__e7_73_1__bagorder,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(k14_bagorder(A))) & m2_relset_1(B,k5_numbers,u1_struct_0(k14_bagorder(A))) ) => ( ! [C] : ( m1_subset_1(C,k5_numbers) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,k5_finsub_1(u1_struct_0(A))) & E = k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),B,C) & E != k1_xboole_0 & D = k11_bagorder(A,E) ) ) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k5_numbers,u1_struct_0(A)) & m2_relset_1(C,k5_numbers,u1_struct_0(A)) & ! [D] : ( m1_subset_1(D,k5_numbers) => ? [F] : ( m1_subset_1(F,k5_finsub_1(u1_struct_0(A))) & F = k8_funct_2(k5_numbers,u1_struct_0(k14_bagorder(A)),B,D) & F != k1_xboole_0 & k8_funct_2(k5_numbers,u1_struct_0(A),C,D) = k11_bagorder(A,F) ) ) ) ) ) ), file(bagorder,s3_funct_2__e7_73_1__bagorder), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t15_wellfnd1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v1_wellfnd1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ~ v3_wellfnd1(B,A) ) ) ) ), file(wellfnd1,t15_wellfnd1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_bagorder,axiom,( ! [A,B,C] : ( ( r2_hidden(C,A) & r2_hidden(C,B) ) => ( k4_xboole_0(A,k1_tarski(C)) = k4_xboole_0(B,k1_tarski(C)) <=> A = B ) ) ), file(bagorder,t1_bagorder), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t28_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( r1_xreal_0(A,B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => B != k2_xcmplx_0(A,C) ) ) ) ) ), file(nat_1,t28_nat_1), []). fof(t29_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ), file(nat_1,t29_nat_1), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t37_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & r2_hidden(k4_tarski(B,k1_xboole_0),k3_tarski(k2_relat_1(k12_bagorder(A)))) ) ) ) ), file(bagorder,t37_bagorder), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t40_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_bagorder(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_bagorder(A))) => ( r2_hidden(k1_domain_1(u1_struct_0(k14_bagorder(A)),u1_struct_0(k14_bagorder(A)),B,C),u1_orders_2(k14_bagorder(A))) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k5_finsub_1(u1_struct_0(A))) & B = D & C = E & ~ ( D != k1_xboole_0 & ~ ( D != k1_xboole_0 & E != k1_xboole_0 & k11_bagorder(A,D) != k11_bagorder(A,E) & r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),k11_bagorder(A,D),k11_bagorder(A,E)),u1_orders_2(A)) ) & ~ ( D != k1_xboole_0 & E != k1_xboole_0 & k11_bagorder(A,D) = k11_bagorder(A,E) & r2_hidden(k4_tarski(k4_xboole_0(D,k6_domain_1(u1_struct_0(A),k11_bagorder(A,D))),k4_xboole_0(E,k6_domain_1(u1_struct_0(A),k11_bagorder(A,E)))),k13_bagorder(A)) ) ) ) ) ) ) ) ) ), file(bagorder,t40_bagorder), []). fof(t41_bagorder,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k5_numbers,u1_struct_0(A)) & m2_relset_1(B,k5_numbers,u1_struct_0(A)) ) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ( v3_wellfnd1(B,A) => v3_wellfnd1(k16_bagorder(A,B,C),A) ) ) ) ) ), file(bagorder,t41_bagorder), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).