% Mizar problem: t46_lattice5,lattice5,4754,41 fof(t46_lattice5,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m2_lattice5(B,u1_struct_0(A),A,k17_lattice5(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(C,C),u1_struct_0(A)) & v1_lattice5(D,C,A) & v2_lattice5(D,C,A) & v3_lattice5(D,C,A) & m2_relset_1(D,k2_zfmisc_1(C,C),u1_struct_0(A)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_lattice5(C))) & v19_waybel_0(E,A,k1_lattice5(C)) & v20_waybel_0(E,A,k1_lattice5(C)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_lattice5(C))) ) => ! [F] : ( m1_subset_1(F,C) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( ( v1_partfun1(H,C,C) & v3_relat_2(H) & v8_relat_2(H) & m2_relset_1(H,C,C) ) => ! [I] : ( ( v1_partfun1(I,C,C) & v3_relat_2(I) & v8_relat_2(I) & m2_relset_1(I,C,C) ) => ! [J,K] : ~ ( E = k5_lattice5(C,A,D) & C = k3_tarski(a_2_5_lattice5(A,B)) & D = k3_tarski(a_2_6_lattice5(A,B)) & r2_hidden(H,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E))) & r2_hidden(I,u1_struct_0(k2_lattice5(A,k1_lattice5(C),E))) & r2_hidden(k4_tarski(J,K),k5_eqrel_1(C,H,I)) & ! [L] : ( ( ~ v1_xboole_0(L) & m2_finseq_1(L,C) ) => ~ ( k3_finseq_1(L) = k1_nat_1(3,2) & r1_lattice5(C,L,J,K,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v3_lattices,antisymmetry_r2_hidden,cc11_yellow_0,cc12_yellow_0,cc1_abian,cc1_arytm_3,cc1_card_1,cc1_finseq_1,cc1_lattice3,cc1_lattices,cc1_ordinal1,cc1_partfun1,cc1_relset_1,cc1_yellow_0,cc2_arytm_3,cc2_card_1,cc2_int_1,cc2_lattice3,cc2_lattices,cc2_ordinal1,cc2_yellow_0,cc3_arytm_3,cc3_card_1,cc3_int_1,cc3_ordinal1,cc3_yellow_0,cc4_int_1,cc4_yellow_0,cc5_yellow_0,cc6_yellow_0,cc7_yellow_0,cc8_yellow_0,commutativity_k13_lattice3,commutativity_k1_nat_1,commutativity_k2_nat_1,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,commutativity_k5_eqrel_1,connectedness_r1_xreal_0,d15_yellow_0,d1_binop_1,d1_finseq_1,d1_lattice5,d2_lattice3,d2_yellow_2,d3_finseq_1,d3_lattice5,d3_tarski,d4_finseq_1,d5_funct_1,d5_tarski,d9_lattice5,dt_g1_orders_2,dt_g3_lattices,dt_k10_lattice3,dt_k13_lattice3,dt_k17_lattice5,dt_k1_binop_1,dt_k1_card_1,dt_k1_domain_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_lattice5,dt_k1_mcart_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_yellow_2,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_lattice3,dt_k2_lattice5,dt_k2_mcart_1,dt_k2_msualg_5,dt_k2_nat_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k2_yellow_2,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_lattice3,dt_k3_relat_1,dt_k3_tarski,dt_k3_xcmplx_0,dt_k4_finseq_1,dt_k4_lattice5,dt_k4_relset_1,dt_k4_tarski,dt_k5_eqrel_1,dt_k5_finsop_1,dt_k5_finsub_1,dt_k5_lattice5,dt_k5_numbers,dt_k5_ordinal2,dt_k5_yellow_0,dt_k7_yellow_2,dt_k8_yellow_2,dt_k9_filter_1,dt_l1_lattices,dt_l1_orders_2,dt_l1_struct_0,dt_l2_lattices,dt_l3_lattices,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m2_finseq_1,dt_m2_lattice5,dt_m2_relset_1,dt_m2_subset_1,dt_u1_lattices,dt_u1_orders_2,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_orders_2,existence_l1_struct_0,existence_l2_lattices,existence_l3_lattices,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m2_finseq_1,existence_m2_lattice5,existence_m2_relset_1,existence_m2_subset_1,fc10_abian,fc11_abian,fc11_finseq_1,fc12_abian,fc17_abian,fc17_finseq_1,fc1_abian,fc1_finseq_1,fc1_int_1,fc1_lattice5,fc1_numbers,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_yellow_0,fc1_yellow_1,fc2_abian,fc2_card_1,fc2_finseq_1,fc2_int_1,fc2_lattice5,fc2_ordinal1,fc2_subset_1,fc3_abian,fc3_lattices,fc3_subset_1,fc4_lattice3,fc4_ordinal1,fc4_subset_1,fc6_abian,fc6_int_1,fc7_abian,fc7_int_1,fc8_abian,fc9_abian,fraenkel_a_0_0_lattice5,fraenkel_a_1_0_finseq_1,fraenkel_a_2_5_lattice5,fraenkel_a_2_6_lattice5,free_g1_orders_2,free_g3_lattices,idempotence_k5_eqrel_1,l67_lattice5,l68_lattice5,rc1_abian,rc1_arytm_3,rc1_card_1,rc1_finseq_1,rc1_int_1,rc1_lattice3,rc1_lattice5,rc1_ordinal1,rc1_partfun1,rc1_pralg_1,rc1_subset_1,rc1_yellow_0,rc2_abian,rc2_card_1,rc2_finseq_1,rc2_int_1,rc2_lattice3,rc2_lattice5,rc2_ordinal1,rc2_partfun1,rc2_subset_1,rc2_yellow_0,rc3_abian,rc3_finseq_1,rc3_lattice5,rc3_lattices,rc3_ordinal1,rc3_partfun1,rc3_struct_0,rc3_yellow_0,rc4_abian,rc4_finseq_1,rc4_yellow_0,rc5_struct_0,rc6_finseq_1,rc6_lattices,rc7_finseq_1,rc8_finseq_1,rc9_lattices,redefinition_k13_lattice3,redefinition_k1_domain_1,redefinition_k1_nat_1,redefinition_k1_yellow_2,redefinition_k2_finseq_1,redefinition_k2_lattice3,redefinition_k2_lattice5,redefinition_k2_nat_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k4_lattice5,redefinition_k4_relset_1,redefinition_k5_finsop_1,redefinition_k5_numbers,redefinition_k7_yellow_2,redefinition_k8_yellow_2,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_orders_2,s1_finseq_1__e35_82__lattice5,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,spc5_boole,spc5_numerals,t10_lattice5,t1_arithm,t1_numerals,t1_real,t1_subset,t25_finseq_1,t2_arithm,t2_real,t2_subset,t2_tarski,t2_waybel_6,t30_relat_1,t3_arithm,t3_real,t3_subset,t45_lattice5,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t8_boole,t8_real,t97_orders_1]), [file(lattice5,t46_lattice5)]). 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(abstractness_v3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( v3_lattices(A) => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ), file(lattices,v3_lattices), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc11_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc11_yellow_0), []). fof(cc12_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc12_yellow_0), []). fof(cc1_abian,axiom,( ! [A] : ( v2_setfam_1(A) => v1_realset1(A) ) ), file(abian,cc1_abian), []). fof(cc1_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). 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_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_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). fof(cc1_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v3_struct_0(A) & v10_lattices(A) ) => ( ~ v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) ) ) ) ), file(lattices,cc1_lattices), []). fof(cc1_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) ), file(ordinal1,cc1_ordinal1), []). fof(cc1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) ), file(partfun1,cc1_partfun1), []). 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_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(yellow_0,cc1_yellow_0), []). fof(cc2_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). 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_int_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_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc2_lattice3), []). fof(cc2_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v3_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) ) => ( ~ v3_struct_0(A) & v10_lattices(A) ) ) ) ), file(lattices,cc2_lattices), []). fof(cc2_ordinal1,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) ), file(ordinal1,cc2_ordinal1), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). 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_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_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_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow_0,cc3_yellow_0), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(cc5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) ), file(yellow_0,cc5_yellow_0), []). fof(cc6_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v2_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc6_yellow_0), []). fof(cc7_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v3_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc7_yellow_0), []). fof(cc8_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc8_yellow_0), []). fof(commutativity_k13_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k13_lattice3(A,B,C) = k13_lattice3(A,C,B) ) ), file(lattice3,k13_lattice3), []). 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_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) ), file(nat_1,k2_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(commutativity_k3_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), []). fof(commutativity_k5_eqrel_1,axiom,( ! [A,B,C] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) ) => k5_eqrel_1(A,B,C) = k5_eqrel_1(A,C,B) ) ), file(eqrel_1,k5_eqrel_1), []). 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(d15_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_orders_2(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ( C = k5_yellow_0(A,B) <=> u1_struct_0(C) = B ) ) ) ) ), file(yellow_0,d15_yellow_0), []). fof(d1_binop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ), file(binop_1,d1_binop_1), []). fof(d1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k1_finseq_1(A) = a_1_0_finseq_1(A) ) ), file(finseq_1,d1_finseq_1), []). fof(d1_lattice5,axiom,( ! [A] : k1_lattice5(A) = k3_lattice3(k2_msualg_5(A)) ), file(lattice5,d1_lattice5), []). fof(d2_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)) ) ), file(lattice3,d2_lattice3), []). fof(d2_yellow_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => k2_yellow_2(A,B,C) = k5_yellow_0(B,k1_yellow_2(A,B,C)) ) ) ) ), file(yellow_2,d2_yellow_2), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C,D,E] : ( v1_relat_1(E) => ! [F] : ( v1_relat_1(F) => ( r1_lattice5(A,B,C,D,E,F) <=> ( k1_funct_1(B,1) = C & k1_funct_1(B,k3_finseq_1(B)) = D & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r1_xreal_0(1,G) => ( r1_xreal_0(k3_finseq_1(B),G) | ( ( ~ v1_abian(G) => r2_hidden(k4_tarski(k1_funct_1(B,G),k1_funct_1(B,k1_nat_1(G,1))),E) ) & ( v1_abian(G) => r2_hidden(k4_tarski(k1_funct_1(B,G),k1_funct_1(B,k1_nat_1(G,1))),F) ) ) ) ) ) ) ) ) ) ) ) ), file(lattice5,d3_lattice5), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_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(d9_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & v1_lattice5(C,A,B) & v2_lattice5(C,A,B) & v3_lattice5(C,A,B) & m2_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(k1_lattice5(A))) & m2_relset_1(D,u1_struct_0(B),u1_struct_0(k1_lattice5(A))) ) => ( D = k5_lattice5(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( v1_partfun1(F,A,A) & v3_relat_2(F) & v8_relat_2(F) & m2_relset_1(F,A,A) & F = k7_yellow_2(u1_struct_0(B),k1_lattice5(A),D,E) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ( r2_hidden(k1_domain_1(A,A,G,H),F) <=> r3_orders_2(B,k4_lattice5(A,B,C,G,H),E) ) ) ) ) ) ) ) ) ) ) ), file(lattice5,d9_lattice5), []). 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_g3_lattices,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) ) => ( v3_lattices(g3_lattices(A,B,C)) & l3_lattices(g3_lattices(A,B,C)) ) ) ), file(lattices,g3_lattices), []). fof(dt_k10_lattice3,axiom,( ! [A,B,C] : ( ( l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k10_lattice3(A,B,C),u1_struct_0(A)) ) ), file(lattice3,k10_lattice3), []). fof(dt_k13_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k13_lattice3(A,B,C),u1_struct_0(A)) ) ), file(lattice3,k13_lattice3), []). fof(dt_k17_lattice5,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( v1_funct_1(k17_lattice5(A)) & v1_funct_2(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & v1_lattice5(k17_lattice5(A),u1_struct_0(A),A) & v2_lattice5(k17_lattice5(A),u1_struct_0(A),A) & v3_lattice5(k17_lattice5(A),u1_struct_0(A),A) & m2_relset_1(k17_lattice5(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(lattice5,k17_lattice5), []). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). 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_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_lattice5,axiom,( ! [A] : ( v2_orders_2(k1_lattice5(A)) & v3_orders_2(k1_lattice5(A)) & v4_orders_2(k1_lattice5(A)) & l1_orders_2(k1_lattice5(A)) ) ), file(lattice5,k1_lattice5), []). 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_yellow_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ), file(yellow_2,k1_yellow_2), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_relat_2(k2_lattice3(A)) & v4_relat_2(k2_lattice3(A)) & v8_relat_2(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(lattice3,k2_lattice3), []). fof(dt_k2_lattice5,axiom,( ! [A,B,C] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v20_waybel_0(C,A,B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_orders_2(k2_lattice5(A,B,C)) & v4_yellow_0(k2_lattice5(A,B,C),B) & v5_yellow_0(k2_lattice5(A,B,C),B) & v6_yellow_0(k2_lattice5(A,B,C),B) & m1_yellow_0(k2_lattice5(A,B,C),B) ) ) ), file(lattice5,k2_lattice5), []). fof(dt_k2_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), []). fof(dt_k2_msualg_5,axiom,( ! [A] : ( ~ v3_struct_0(k2_msualg_5(A)) & v3_lattices(k2_msualg_5(A)) & v10_lattices(k2_msualg_5(A)) & l3_lattices(k2_msualg_5(A)) ) ), file(msualg_5,k2_msualg_5), []). fof(dt_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k2_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k2_nat_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_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_orders_2(k2_yellow_2(A,B,C)) & v4_yellow_0(k2_yellow_2(A,B,C),B) & m1_yellow_0(k2_yellow_2(A,B,C),B) ) ) ), file(yellow_2,k2_yellow_2), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A)) ) ) ), file(lattice3,k3_lattice3), []). fof(dt_k3_relat_1,axiom,( $true ), file(relat_1,k3_relat_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_lattice5,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => m1_subset_1(k4_lattice5(A,B,C,D,E),u1_struct_0(B)) ) ), file(lattice5,k4_lattice5), []). 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_k5_eqrel_1,axiom,( ! [A,B,C] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) ) => ( v3_relat_2(k5_eqrel_1(A,B,C)) & v8_relat_2(k5_eqrel_1(A,B,C)) & v1_partfun1(k5_eqrel_1(A,B,C),A,A) & m2_relset_1(k5_eqrel_1(A,B,C),A,A) ) ) ), file(eqrel_1,k5_eqrel_1), []). fof(dt_k5_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k5_finsop_1(A),k5_finsub_1(k5_numbers)) ) ), file(finsop_1,k5_finsop_1), []). fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) ), file(finsub_1,k5_finsub_1), []). fof(dt_k5_lattice5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & v1_lattice5(C,A,B) & v2_lattice5(C,A,B) & v3_lattice5(C,A,B) & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) ) => ( v1_funct_1(k5_lattice5(A,B,C)) & v1_funct_2(k5_lattice5(A,B,C),u1_struct_0(B),u1_struct_0(k1_lattice5(A))) & m2_relset_1(k5_lattice5(A,B,C),u1_struct_0(B),u1_struct_0(k1_lattice5(A))) ) ) ), file(lattice5,k5_lattice5), []). 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_k5_yellow_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_orders_2(k5_yellow_0(A,B)) & v4_yellow_0(k5_yellow_0(A,B),A) & m1_yellow_0(k5_yellow_0(A,B),A) ) ) ), file(yellow_0,k5_yellow_0), []). fof(dt_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_2,k7_yellow_2), []). fof(dt_k8_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ), file(yellow_2,k8_yellow_2), []). fof(dt_k9_filter_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => v1_relat_1(k9_filter_1(A)) ) ), file(filter_1,k9_filter_1), []). fof(dt_l1_lattices,axiom,( ! [A] : ( l1_lattices(A) => l1_struct_0(A) ) ), file(lattices,l1_lattices), []). 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_l2_lattices,axiom,( ! [A] : ( l2_lattices(A) => l1_struct_0(A) ) ), file(lattices,l2_lattices), []). fof(dt_l3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( l1_lattices(A) & l2_lattices(A) ) ) ), file(lattices,l3_lattices), []). 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) ) ) ), file(finseq_1,m1_finseq_1), []). 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_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) ), file(yellow_0,m1_yellow_0), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_lattice5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & v1_lattice5(C,A,B) & v2_lattice5(C,A,B) & v3_lattice5(C,A,B) & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) ) => ! [D] : ( m2_lattice5(D,A,B,C) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) ), file(lattice5,m2_lattice5), []). 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_lattices,axiom,( ! [A] : ( l1_lattices(A) => ( v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(lattices,u1_lattices), []). 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(dt_u2_lattices,axiom,( ! [A] : ( l2_lattices(A) => ( v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(lattices,u2_lattices), []). fof(existence_l1_lattices,axiom,( ? [A] : l1_lattices(A) ), file(lattices,l1_lattices), []). 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_l2_lattices,axiom,( ? [A] : l2_lattices(A) ), file(lattices,l2_lattices), []). fof(existence_l3_lattices,axiom,( ? [A] : l3_lattices(A) ), file(lattices,l3_lattices), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). 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_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) ), file(yellow_0,m1_yellow_0), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_lattice5,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & v1_lattice5(C,A,B) & v2_lattice5(C,A,B) & v3_lattice5(C,A,B) & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) ) => ? [D] : m2_lattice5(D,A,B,C) ) ), file(lattice5,m2_lattice5), []). 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_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & ~ v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc10_abian), []). fof(fc11_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) & ~ v1_abian(k2_xcmplx_0(B,A)) ) ) ), file(abian,fc11_abian), []). 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(fc12_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc12_abian), []). fof(fc17_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_zfmisc_1(A)) & ~ v2_setfam_1(k1_zfmisc_1(A)) ) ) ), file(abian,fc17_abian), []). 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_abian,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k3_xcmplx_0(2,A)) & v1_xreal_0(k3_xcmplx_0(2,A)) & v1_int_1(k3_xcmplx_0(2,A)) & v1_abian(k3_xcmplx_0(2,A)) ) ) ), file(abian,fc1_abian), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_1), []). fof(fc1_lattice5,axiom,( ! [A] : ( ~ v3_struct_0(k1_lattice5(A)) & v2_orders_2(k1_lattice5(A)) & v3_orders_2(k1_lattice5(A)) & v4_orders_2(k1_lattice5(A)) & v1_lattice3(k1_lattice5(A)) & v2_lattice3(k1_lattice5(A)) ) ), file(lattice5,fc1_lattice5), []). fof(fc1_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). 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(fc1_yellow_0,axiom,( ! [A,B] : ( m1_relset_1(B,k1_tarski(A),k1_tarski(A)) => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ), file(yellow_0,fc1_yellow_0), []). fof(fc1_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ~ v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) ) ) ), file(yellow_1,fc1_yellow_1), []). fof(fc2_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,1)) & v1_xreal_0(k2_xcmplx_0(A,1)) & v1_int_1(k2_xcmplx_0(A,1)) & ~ v1_abian(k2_xcmplx_0(A,1)) ) ) ), file(abian,fc2_abian), []). fof(fc2_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_ordinal1(k1_card_1(A)) & v2_ordinal1(k1_card_1(A)) & v3_ordinal1(k1_card_1(A)) & v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) ), file(card_1,fc2_card_1), []). 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_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). fof(fc2_lattice5,axiom,( ! [A] : ( ~ v3_struct_0(k1_lattice5(A)) & v2_orders_2(k1_lattice5(A)) & v3_orders_2(k1_lattice5(A)) & v4_orders_2(k1_lattice5(A)) & v1_yellow_0(k1_lattice5(A)) & v2_yellow_0(k1_lattice5(A)) & v3_yellow_0(k1_lattice5(A)) & v1_lattice3(k1_lattice5(A)) & v2_lattice3(k1_lattice5(A)) & v3_lattice3(k1_lattice5(A)) ) ), file(lattice5,fc2_lattice5), []). 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_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,1)) & v1_xreal_0(k2_xcmplx_0(A,1)) & v1_int_1(k2_xcmplx_0(A,1)) & v1_abian(k2_xcmplx_0(A,1)) ) ) ), file(abian,fc3_abian), []). fof(fc3_lattices,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) ) => ( ~ v3_struct_0(g3_lattices(A,B,C)) & v3_lattices(g3_lattices(A,B,C)) ) ) ), file(lattices,fc3_lattices), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc4_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ~ v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) ) ) ), file(lattice3,fc4_lattice3), []). 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_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(fc6_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & v1_abian(k3_xcmplx_0(A,B)) ) ) ), file(abian,fc6_abian), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_1), []). fof(fc7_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) & v1_abian(k3_xcmplx_0(B,A)) ) ) ), file(abian,fc7_abian), []). fof(fc7_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). fof(fc8_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) & ~ v1_abian(k3_xcmplx_0(A,B)) ) ) ), file(abian,fc8_abian), []). fof(fc9_abian,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & v1_abian(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) & v1_abian(k2_xcmplx_0(A,B)) ) ) ), file(abian,fc9_abian), []). fof(fraenkel_a_0_0_lattice5,axiom,( ! [A] : ( r2_hidden(A,a_0_0_lattice5) <=> ? [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) & A = B & r1_xreal_0(1,B) & r1_xreal_0(B,5) ) ) ), file(lattice5,a_0_0_lattice5), []). fof(fraenkel_a_1_0_finseq_1,axiom,( ! [A,B] : ( v4_ordinal2(B) => ( r2_hidden(A,a_1_0_finseq_1(B)) <=> ? [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) & A = C & r1_xreal_0(1,C) & r1_xreal_0(C,B) ) ) ) ), file(finseq_1,a_1_0_finseq_1), []). fof(fraenkel_a_2_5_lattice5,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) ) => ( r2_hidden(A,a_2_5_lattice5(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k1_mcart_1(k1_funct_1(C,D)) ) ) ) ), file(lattice5,a_2_5_lattice5), []). fof(fraenkel_a_2_6_lattice5,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & m2_lattice5(C,u1_struct_0(B),B,k17_lattice5(B)) ) => ( r2_hidden(A,a_2_6_lattice5(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) & A = k2_mcart_1(k1_funct_1(C,D)) ) ) ) ), file(lattice5,a_2_6_lattice5), []). 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(free_g3_lattices,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) ) => ! [D,E,F] : ( g3_lattices(A,B,C) = g3_lattices(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(lattices,g3_lattices), []). fof(idempotence_k5_eqrel_1,axiom,( ! [A,B,C] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) & v3_relat_2(C) & v8_relat_2(C) & v1_partfun1(C,A,A) & m1_relset_1(C,A,A) ) => k5_eqrel_1(A,B,B) = B ) ), file(eqrel_1,k5_eqrel_1), []). fof(l67_lattice5,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ~ ( r1_xreal_0(1,A) & ~ r1_xreal_0(5,A) & A != 1 & A != 2 & A != 3 & A != 4 ) ) ), file(lattice5,l67_lattice5), []). fof(l68_lattice5,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ~ ( r2_hidden(A,k2_finseq_1(5)) & A != 1 & A != 2 & A != 3 & A != 4 & A != 5 ) ) ), file(lattice5,l68_lattice5), []). fof(rc1_abian,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_int_1(A) & v1_abian(A) ) ), file(abian,rc1_abian), []). fof(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) ), file(card_1,rc1_card_1), []). 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_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_lattice3,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) & v3_lattice3(A) ) ), file(lattice3,rc1_lattice3), []). fof(rc1_lattice5,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v20_waybel_0(C,A,B) ) ) ), file(lattice5,rc1_lattice5), []). fof(rc1_ordinal1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc1_ordinal1), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(pralg_1,rc1_pralg_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_yellow_0,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) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) ), file(yellow_0,rc1_yellow_0), []). fof(rc2_abian,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_int_1(A) & ~ v1_abian(A) ) ), file(abian,rc2_abian), []). 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_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_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_lattice3,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) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ), file(lattice3,rc2_lattice3), []). fof(rc2_lattice5,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v5_yellow_0(B,A) & v6_yellow_0(B,A) ) ) ), file(lattice5,rc2_lattice5), []). 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_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). 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_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ), file(yellow_0,rc2_yellow_0), []). fof(rc3_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) ), file(abian,rc3_abian), []). 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_lattice5,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & v1_lattice5(C,A,B) & v2_lattice5(C,A,B) & v3_lattice5(C,A,B) ) ) ), file(lattice5,rc3_lattice5), []). fof(rc3_lattices,axiom,( ? [A] : ( l3_lattices(A) & v3_lattices(A) ) ), file(lattices,rc3_lattices), []). fof(rc3_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) ), file(ordinal1,rc3_ordinal1), []). fof(rc3_partfun1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) ) ), file(partfun1,rc3_partfun1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc3_yellow_0), []). fof(rc4_abian,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) ), file(abian,rc4_abian), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc4_yellow_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(rc6_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v3_struct_0(A) & v3_lattices(A) ) ), file(lattices,rc6_lattices), []). 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(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(rc9_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v3_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) ) ), file(lattices,rc9_lattices), []). fof(redefinition_k13_lattice3,axiom,( ! [A,B,C] : ( ( v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k13_lattice3(A,B,C) = k10_lattice3(A,B,C) ) ), file(lattice3,k13_lattice3), []). 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_k1_yellow_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => k1_yellow_2(A,B,C) = k2_relat_1(C) ) ), file(yellow_2,k1_yellow_2), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k2_lattice3(A) = k9_filter_1(A) ) ), file(lattice3,k2_lattice3), []). fof(redefinition_k2_lattice5,axiom,( ! [A,B,C] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v20_waybel_0(C,A,B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => k2_lattice5(A,B,C) = k2_yellow_2(A,B,C) ) ), file(lattice5,k2_lattice5), []). fof(redefinition_k2_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) ), file(nat_1,k2_nat_1), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_lattice5,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & m1_relset_1(C,k2_zfmisc_1(A,A),u1_struct_0(B)) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => k4_lattice5(A,B,C,D,E) = k1_binop_1(C,D,E) ) ), file(lattice5,k4_lattice5), []). 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_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k5_finsop_1(A) = k1_relat_1(A) ) ), file(finsop_1,k5_finsop_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_2,k7_yellow_2), []). fof(redefinition_k8_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => k8_yellow_2(A,B,C) = k2_relat_1(C) ) ), file(yellow_2,k8_yellow_2), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). 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_finseq_1__e35_82__lattice5,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) & m1_subset_1(F,A) ) => ( ( ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H,I] : ( ( r2_hidden(G,k2_finseq_1(5)) & ( G = 1 => H = B ) & ( G = 2 => H = D ) & ( G = 3 => H = E ) & ( G = 4 => H = F ) & ( G = 5 => H = C ) & ( G = 1 => I = B ) & ( G = 2 => I = D ) & ( G = 3 => I = E ) & ( G = 4 => I = F ) & ( G = 5 => I = C ) ) => H = I ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r2_hidden(G,k2_finseq_1(5)) & ! [H] : ~ ( ( G = 1 => H = B ) & ( G = 2 => H = D ) & ( G = 3 => H = E ) & ( G = 4 => H = F ) & ( G = 5 => H = C ) ) ) ) ) => ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) & k4_finseq_1(G) = k2_finseq_1(5) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k2_finseq_1(5)) => ( ( H = 1 => k1_funct_1(G,H) = B ) & ( H = 2 => k1_funct_1(G,H) = D ) & ( H = 3 => k1_funct_1(G,H) = E ) & ( H = 4 => k1_funct_1(G,H) = F ) & ( H = 5 => k1_funct_1(G,H) = C ) ) ) ) ) ) ) ), file(lattice5,s1_finseq_1__e35_82__lattice5), []). 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(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc4_boole,axiom,( ~ v1_xboole_0(4) ), file(boole,spc4_boole), []). fof(spc4_numerals,axiom, ( v2_xreal_0(4) & m1_subset_1(4,k5_numbers) ), file(numerals,spc4_numerals), []). fof(spc5_boole,axiom,( ~ v1_xboole_0(5) ), file(boole,spc5_boole), []). fof(spc5_numerals,axiom, ( v2_xreal_0(5) & m1_subset_1(5,k5_numbers) ), file(numerals,spc5_numerals), []). fof(t10_lattice5,axiom,( ! [A,B] : ( m1_subset_1(B,u1_struct_0(k1_lattice5(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_lattice5(A))) => ! [D] : ( ( v1_partfun1(D,A,A) & v3_relat_2(D) & v8_relat_2(D) & m2_relset_1(D,A,A) ) => ! [E] : ( ( v1_partfun1(E,A,A) & v3_relat_2(E) & v8_relat_2(E) & m2_relset_1(E,A,A) ) => ( ( B = D & C = E ) => k13_lattice3(k1_lattice5(A),B,C) = k5_eqrel_1(A,D,E) ) ) ) ) ) ), file(lattice5,t10_lattice5), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). 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(t25_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) = 0 <=> A = k1_xboole_0 ) ) ), file(finseq_1,t25_finseq_1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). 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(t2_waybel_6,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v20_waybel_0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k7_yellow_2(u1_struct_0(A),B,C,k13_lattice3(A,D,E)) = k13_lattice3(B,k7_yellow_2(u1_struct_0(A),B,C,D),k7_yellow_2(u1_struct_0(A),B,C,E)) ) ) ) ) ) ) ), file(waybel_6,t2_waybel_6), []). fof(t30_relat_1,axiom,( ! [A,B,C] : ( v1_relat_1(C) => ( r2_hidden(k4_tarski(A,B),C) => ( r2_hidden(A,k3_relat_1(C)) & r2_hidden(B,k3_relat_1(C)) ) ) ) ), file(relat_1,t30_relat_1), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). 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(t45_lattice5,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m2_lattice5(B,u1_struct_0(A),A,k17_lattice5(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(C,C),u1_struct_0(A)) & v1_lattice5(D,C,A) & v2_lattice5(D,C,A) & v3_lattice5(D,C,A) & m2_relset_1(D,k2_zfmisc_1(C,C),u1_struct_0(A)) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( m1_subset_1(F,C) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( C = k3_tarski(a_2_5_lattice5(A,B)) & D = k3_tarski(a_2_6_lattice5(A,B)) & r3_orders_2(A,k4_lattice5(C,A,D,E,F),k13_lattice3(A,G,H)) & ! [I] : ( m1_subset_1(I,C) => ! [J] : ( m1_subset_1(J,C) => ! [K] : ( m1_subset_1(K,C) => ~ ( k4_lattice5(C,A,D,E,I) = G & k4_lattice5(C,A,D,J,K) = G & k4_lattice5(C,A,D,I,J) = H & k4_lattice5(C,A,D,K,F) = H ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(lattice5,t45_lattice5), []). 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), []). fof(t97_orders_1,axiom,( ! [A,B] : ( ( v1_partfun1(B,A,A) & m2_relset_1(B,A,A) ) => k3_relat_1(B) = A ) ), file(orders_1,t97_orders_1), []).