% Mizar problem: t11_rusub_3,rusub_3,510,60 fof(t11_rusub_3,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,C) & v1_rlvect_3(C,A) & k1_rusub_3(A,C) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_bhsp_1,antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_finseq_1,cc1_finset_1,cc1_funct_2,cc1_membered,cc1_relset_1,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc5_funct_2,cc6_funct_2,cc6_membered,cc9_membered,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_subset_1,d11_rlvect_1,d11_rlvect_2,d14_rlvect_2,d15_rlvect_2,d1_orders_1,d1_rlvect_3,d1_tarski,d2_rlvect_1,d2_xboole_0,d3_rlvect_1,d3_rusub_1,d3_tarski,d4_rlvect_1,d4_tarski,d4_xboole_0,d5_funct_1,d5_rlvect_2,d5_tarski,d6_rlvect_2,d7_xcmplx_0,d8_rlvect_2,d9_ordinal1,d9_rlvect_1,d9_xboole_0,dt_g1_bhsp_1,dt_k10_rlvect_2,dt_k13_rlvect_2,dt_k14_rlvect_2,dt_k15_rlvect_2,dt_k16_rlvect_2,dt_k17_rlvect_2,dt_k1_domain_1,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_numbers,dt_k1_real_1,dt_k1_relat_1,dt_k1_rlvect_1,dt_k1_rusub_3,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_real_1,dt_k2_relat_1,dt_k2_rlvect_1,dt_k2_rusub_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_real_1,dt_k3_rlvect_1,dt_k3_tarski,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_rlvect_2,dt_k4_subset_1,dt_k4_tarski,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_rlvect_1,dt_k5_xcmplx_0,dt_k6_rlvect_1,dt_k6_xcmplx_0,dt_k7_rlvect_2,dt_k8_funct_2,dt_l1_bhsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m1_fraenkel,dt_m1_orders_1,dt_m1_relset_1,dt_m1_rlvect_2,dt_m1_rusub_1,dt_m1_subset_1,dt_m2_fraenkel,dt_m2_relset_1,dt_m2_rlvect_2,dt_u1_bhsp_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u2_rlvect_1,dt_u2_struct_0,existence_l1_bhsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m1_fraenkel,existence_m1_orders_1,existence_m1_relset_1,existence_m1_rlvect_2,existence_m1_rusub_1,existence_m1_subset_1,existence_m2_fraenkel,existence_m2_relset_1,existence_m2_rlvect_2,fc10_membered,fc11_finseq_1,fc11_membered,fc12_finset_1,fc12_membered,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc17_finseq_1,fc1_bhsp_1,fc1_finset_1,fc1_funct_2,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_finseq_1,fc2_finset_1,fc2_funct_2,fc2_membered,fc2_subset_1,fc37_membered,fc38_membered,fc39_membered,fc3_subset_1,fc40_membered,fc41_membered,fc4_subset_1,fc5_membered,fc6_membered,fc7_membered,fc8_membered,fc9_finset_1,fc9_membered,fraenkel_a_2_0_rlvect_2,fraenkel_a_2_1_rusub_3,fraenkel_a_3_0_rusub_3,fraenkel_a_4_0_rusub_3,free_g1_bhsp_1,idempotence_k2_xboole_0,idempotence_k4_subset_1,involutiveness_k1_real_1,involutiveness_k2_real_1,involutiveness_k4_xcmplx_0,involutiveness_k5_xcmplx_0,rc1_arytm_3,rc1_bhsp_1,rc1_finseq_1,rc1_finset_1,rc1_funct_2,rc1_membered,rc1_rlvect_3,rc1_rusub_1,rc1_subset_1,rc2_bhsp_1,rc2_finseq_1,rc2_finset_1,rc2_subset_1,rc3_bhsp_1,rc3_finseq_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc4_struct_0,rc5_struct_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,redefinition_k1_domain_1,redefinition_k1_fraenkel,redefinition_k1_real_1,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_rlvect_2,redefinition_k4_subset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k7_rlvect_2,redefinition_k8_funct_2,redefinition_m2_fraenkel,redefinition_m2_relset_1,redefinition_r1_rlvect_2,reflexivity_r1_rlvect_2,reflexivity_r1_tarski,reflexivity_r3_xboole_0,s10_funct_2__e10_17_2_1_1_1__rusub_3,s10_funct_2__e2_17_2_1_1_1__rusub_3,s1_xboole_0__e2_17__rusub_3,s3_funct_1__e3_17_1_2__rusub_3,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_rlvect_2,symmetry_r3_xboole_0,t10_rlvect_1,t11_funct_2,t15_rusub_1,t177_orders_1,t1_arithm,t1_boole,t1_numerals,t1_rusub_3,t1_subset,t1_xboole_1,t25_rusub_1,t26_finset_1,t28_rlvect_2,t2_arithm,t2_rusub_3,t2_subset,t2_tarski,t35_rlvect_3,t3_arithm,t3_boole,t3_rlvect_1,t3_subset,t4_arithm,t4_boole,t4_rlvect_3,t4_subset,t50_rlvect_2,t5_subset,t65_relat_1,t6_boole,t78_rlsub_2,t79_rlvect_2,t7_boole,t7_xboole_1,t81_card_2,t8_boole,t92_zfmisc_1]), [file(rusub_3,t11_rusub_3)]). fof(abstractness_v1_bhsp_1,axiom,( ! [A] : ( l1_bhsp_1(A) => ( v1_bhsp_1(A) => A = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ) ), file(bhsp_1,v1_bhsp_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). 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_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_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_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). 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_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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). 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_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). 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(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_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) ), file(real_1,k3_real_1), []). 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_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) ), file(real_1,k4_real_1), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(d11_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_rlvect_1(A,B,C) = k2_rlvect_1(A,B,k5_rlvect_1(A,C)) ) ) ) ), file(rlvect_1,d11_rlvect_1), []). fof(d11_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ( r1_rlvect_2(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),k1_numbers,B,D) = k8_funct_2(u1_struct_0(A),k1_numbers,C,D) ) ) ) ) ) ), file(rlvect_2,d11_rlvect_2), []). fof(d14_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => k16_rlvect_2(A,B) = k15_rlvect_2(A,k1_real_1(1),B) ) ) ), file(rlvect_2,d14_rlvect_2), []). fof(d15_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => k17_rlvect_2(A,B,C) = k14_rlvect_2(A,B,k16_rlvect_2(A,C)) ) ) ) ), file(rlvect_2,d15_rlvect_2), []). fof(d1_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ r2_hidden(k1_xboole_0,A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) ) => ( m1_orders_1(B,A) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) ) ), file(orders_1,d1_orders_1), []). fof(d1_rlvect_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) <=> ! [C] : ( m2_rlvect_2(C,A,B) => ( k13_rlvect_2(A,C) = k1_rlvect_1(A) => k10_rlvect_2(A,C) = k1_xboole_0 ) ) ) ) ) ), file(rlvect_3,d1_rlvect_3), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d2_rlvect_1,axiom,( ! [A] : ( l2_struct_0(A) => k1_rlvect_1(A) = u2_struct_0(A) ) ), file(rlvect_1,d2_rlvect_1), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_rlvect_1(A),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ), file(rlvect_1,d3_rlvect_1), []). fof(d3_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => k2_rusub_1(A) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ), file(rusub_1,d3_rusub_1), []). 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_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_numbers) => k3_rlvect_1(A,B,C) = k8_funct_2(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k1_domain_1(k1_numbers,u1_struct_0(A),C,B)) ) ) ) ), file(rlvect_1,d4_rlvect_1), []). fof(d4_tarski,axiom,( ! [A,B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) ), file(tarski,d4_tarski), []). 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_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_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)) => ( m1_rlvect_2(B,A) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r2_hidden(D,C) => k8_funct_2(u1_struct_0(A),k1_numbers,B,D) = 0 ) ) ) ) ) ) ), file(rlvect_2,d5_rlvect_2), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => k10_rlvect_2(A,B) = a_2_0_rlvect_2(A,B) ) ) ), file(rlvect_2,d6_rlvect_2), []). fof(d7_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( A != 0 => ( B = k5_xcmplx_0(A) <=> k3_xcmplx_0(A,B) = 1 ) ) & ( A = 0 => ( B = k5_xcmplx_0(A) <=> B = 0 ) ) ) ) ) ), file(xcmplx_0,d7_xcmplx_0), []). fof(d8_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlvect_2(C,A) => ( m2_rlvect_2(C,A,B) <=> r1_tarski(k10_rlvect_2(A,C),B) ) ) ) ) ), file(rlvect_2,d8_rlvect_2), []). fof(d9_ordinal1,axiom,( ! [A] : ( v6_ordinal1(A) <=> ! [B,C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r3_xboole_0(B,C) ) ) ), file(ordinal1,d9_ordinal1), []). fof(d9_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) ) => ( v7_rlvect_1(A) <=> ( ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,k2_rlvect_1(A,C,D),B) = k2_rlvect_1(A,k3_rlvect_1(A,C,B),k3_rlvect_1(A,D,B)) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,D,k3_real_1(B,C)) = k2_rlvect_1(A,k3_rlvect_1(A,D,B),k3_rlvect_1(A,D,C)) ) ) ) & ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,D,k4_real_1(B,C)) = k3_rlvect_1(A,k3_rlvect_1(A,D,C),B) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_rlvect_1(A,B,1) = B ) ) ) ) ), file(rlvect_1,d9_rlvect_1), []). fof(d9_xboole_0,axiom,( ! [A,B] : ( r3_xboole_0(A,B) <=> ( r1_tarski(A,B) | r1_tarski(B,A) ) ) ), file(xboole_0,d9_xboole_0), []). fof(dt_g1_bhsp_1,axiom,( ! [A,B,C,D,E] : ( ( m1_subset_1(B,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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(E,k2_zfmisc_1(A,A),k1_numbers) ) => ( v1_bhsp_1(g1_bhsp_1(A,B,C,D,E)) & l1_bhsp_1(g1_bhsp_1(A,B,C,D,E)) ) ) ), file(bhsp_1,g1_bhsp_1), []). fof(dt_k10_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) ) => ( v1_finset_1(k10_rlvect_2(A,B)) & m1_subset_1(k10_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(rlvect_2,k10_rlvect_2), []). fof(dt_k13_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_rlvect_2(B,A) ) => m1_subset_1(k13_rlvect_2(A,B),u1_struct_0(A)) ) ), file(rlvect_2,k13_rlvect_2), []). fof(dt_k14_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) ) => m1_rlvect_2(k14_rlvect_2(A,B,C),A) ) ), file(rlvect_2,k14_rlvect_2), []). fof(dt_k15_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_subset_1(B,k1_numbers) & m1_rlvect_2(C,A) ) => m1_rlvect_2(k15_rlvect_2(A,B,C),A) ) ), file(rlvect_2,k15_rlvect_2), []). fof(dt_k16_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_rlvect_2(B,A) ) => m1_rlvect_2(k16_rlvect_2(A,B),A) ) ), file(rlvect_2,k16_rlvect_2), []). fof(dt_k17_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) ) => m1_rlvect_2(k17_rlvect_2(A,B,C),A) ) ), file(rlvect_2,k17_rlvect_2), []). 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_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_rlvect_1,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ), file(rlvect_1,k1_rlvect_1), []). fof(dt_k1_rusub_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_bhsp_1(k1_rusub_3(A,B)) & m1_rusub_1(k1_rusub_3(A,B),A) ) ) ), file(rusub_3,k1_rusub_3), []). 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_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k2_real_1(A),k1_numbers) ) ), file(real_1,k2_real_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k2_rlvect_1), []). fof(dt_k2_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ( v1_bhsp_1(k2_rusub_1(A)) & m1_rusub_1(k2_rusub_1(A),A) ) ) ), file(rusub_1,k2_rusub_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ), file(real_1,k3_real_1), []). fof(dt_k3_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l2_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_numbers) ) => m1_subset_1(k3_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k3_rlvect_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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ), file(real_1,k4_real_1), []). fof(dt_k4_rlvect_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_finset_1(k4_rlvect_2(A,B,C)) & m1_subset_1(k4_rlvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(rlvect_2,k4_rlvect_2), []). fof(dt_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_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_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). 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_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_rlvect_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k5_rlvect_1(A,B),u1_struct_0(A)) ) ), file(rlvect_1,k5_rlvect_1), []). fof(dt_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A)) ) ), file(xcmplx_0,k5_xcmplx_0), []). fof(dt_k6_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k6_rlvect_1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_finset_1(k7_rlvect_2(A,B)) & m1_subset_1(k7_rlvect_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(rlvect_2,k7_rlvect_2), []). 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_bhsp_1,axiom,( ! [A] : ( l1_bhsp_1(A) => l2_rlvect_1(A) ) ), file(bhsp_1,l1_bhsp_1), []). fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_struct_0(A) ) ), file(rlvect_1,l1_rlvect_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => l1_rlvect_1(A) ) ), file(rlvect_1,l2_rlvect_1), []). fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) ), file(struct_0,l2_struct_0), []). fof(dt_m1_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), []). fof(dt_m1_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_orders_1(B,A) => ( v1_funct_1(B) & v1_funct_2(B,A,k3_tarski(A)) & m2_relset_1(B,A,k3_tarski(A)) ) ) ) ), file(orders_1,m1_orders_1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => m2_fraenkel(B,u1_struct_0(A),k1_numbers,k1_fraenkel(u1_struct_0(A),k1_numbers)) ) ) ), file(rlvect_2,m1_rlvect_2), []). fof(dt_m1_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v2_bhsp_1(B) & l1_bhsp_1(B) ) ) ) ), file(rusub_1,m1_rusub_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ! [D] : ( m2_fraenkel(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) ) ) ), file(fraenkel,m2_fraenkel), []). 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_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_rlvect_2(C,A,B) => m1_rlvect_2(C,A) ) ) ), file(rlvect_2,m2_rlvect_2), []). fof(dt_u1_bhsp_1,axiom,( ! [A] : ( l1_bhsp_1(A) => ( v1_funct_1(u1_bhsp_1(A)) & v1_funct_2(u1_bhsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_bhsp_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) ) ) ), file(bhsp_1,u1_bhsp_1), []). fof(dt_u1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => ( v1_funct_1(u1_rlvect_1(A)) & v1_funct_2(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_rlvect_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u1_rlvect_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => ( v1_funct_1(u2_rlvect_1(A)) & v1_funct_2(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(rlvect_1,u2_rlvect_1), []). fof(dt_u2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) ), file(struct_0,u2_struct_0), []). fof(existence_l1_bhsp_1,axiom,( ? [A] : l1_bhsp_1(A) ), file(bhsp_1,l1_bhsp_1), []). fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) ), file(rlvect_1,l1_rlvect_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_rlvect_1,axiom,( ? [A] : l2_rlvect_1(A) ), file(rlvect_1,l2_rlvect_1), []). fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) ), file(struct_0,l2_struct_0), []). fof(existence_m1_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), []). fof(existence_m1_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m1_orders_1(B,A) ) ), file(orders_1,m1_orders_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_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l2_struct_0(A) ) => ? [B] : m1_rlvect_2(B,A) ) ), file(rlvect_2,m1_rlvect_2), []). fof(existence_m1_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : m1_rusub_1(B,A) ) ), file(rusub_1,m1_rusub_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ? [D] : m2_fraenkel(D,A,B,C) ) ), file(fraenkel,m2_fraenkel), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_rlvect_2(C,A,B) ) ), file(rlvect_2,m2_rlvect_2), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). 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_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). 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_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). 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_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). 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_bhsp_1,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(E,k2_zfmisc_1(A,A),k1_numbers) ) => ( ~ v3_struct_0(g1_bhsp_1(A,B,C,D,E)) & v1_bhsp_1(g1_bhsp_1(A,B,C,D,E)) ) ) ), file(bhsp_1,fc1_bhsp_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_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_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(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). 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_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). 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_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc6_membered,axiom, ( v1_xboole_0(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) ), file(membered,fc6_membered), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fraenkel_a_2_0_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_rlvect_1(B) & m1_rlvect_2(C,B) ) => ( r2_hidden(A,a_2_0_rlvect_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k8_funct_2(u1_struct_0(B),k1_numbers,C,D) != 0 ) ) ) ), file(rlvect_2,a_2_0_rlvect_2), []). fof(fraenkel_a_2_1_rusub_3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m1_rlvect_2(C,B) ) => ( r2_hidden(A,a_2_1_rusub_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k8_funct_2(u1_struct_0(B),k1_numbers,C,D) != 0 ) ) ) ), file(rusub_3,a_2_1_rusub_3), []). fof(fraenkel_a_3_0_rusub_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v2_bhsp_1(B) & l1_bhsp_1(B) ) => ( r2_hidden(A,a_3_0_rusub_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(D,E) & r2_hidden(E,C) ) ) ) ), file(rusub_3,a_3_0_rusub_3), []). fof(fraenkel_a_4_0_rusub_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & m2_rlvect_2(E,B,k4_subset_1(u1_struct_0(B),C,k7_rlvect_2(B,D))) ) => ( r2_hidden(A,a_4_0_rusub_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k8_funct_2(u1_struct_0(B),k1_numbers,E,F) != 0 ) ) ) ), file(rusub_3,a_4_0_rusub_3), []). fof(free_g1_bhsp_1,axiom,( ! [A,B,C,D,E] : ( ( m1_subset_1(B,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) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A) & m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(E,k2_zfmisc_1(A,A),k1_numbers) ) => ! [F,G,H,I,J] : ( g1_bhsp_1(A,B,C,D,E) = g1_bhsp_1(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) ), file(bhsp_1,g1_bhsp_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), []). fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(k2_real_1(A)) = A ) ), file(real_1,k2_real_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(involutiveness_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A)) = A ) ), file(xcmplx_0,k5_xcmplx_0), []). 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_bhsp_1,axiom,( ? [A] : ( l1_bhsp_1(A) & v1_bhsp_1(A) ) ), file(bhsp_1,rc1_bhsp_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_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_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_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_rlvect_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_rlvect_3(B,A) ) ) ), file(rlvect_3,rc1_rlvect_3), []). fof(rc1_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : ( m1_rusub_1(B,A) & ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v1_bhsp_1(B) & v2_bhsp_1(B) ) ) ), file(rusub_1,rc1_rusub_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(rc2_bhsp_1,axiom,( ? [A] : ( l1_bhsp_1(A) & ~ v3_struct_0(A) & v1_bhsp_1(A) ) ), file(bhsp_1,rc2_bhsp_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_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_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc3_bhsp_1,axiom,( ? [A] : ( l1_bhsp_1(A) & ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v1_bhsp_1(A) & v2_bhsp_1(A) ) ), file(bhsp_1,rc3_bhsp_1), []). 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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_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_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_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(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_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). fof(redefinition_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(A) = k5_xcmplx_0(A) ) ), file(real_1,k2_real_1), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). fof(redefinition_k4_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ), file(real_1,k4_real_1), []). fof(redefinition_k4_rlvect_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => k4_rlvect_2(A,B,C) = k4_xboole_0(B,C) ) ), file(rlvect_2,k4_rlvect_2), []). fof(redefinition_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k7_rlvect_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k7_rlvect_2(A,B) = k1_tarski(B) ) ), file(rlvect_2,k7_rlvect_2), []). 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_fraenkel,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_fraenkel(C,A,B) ) => ! [D] : ( m2_fraenkel(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(fraenkel,m2_fraenkel), []). 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_r1_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) ) => ( r1_rlvect_2(A,B,C) <=> B = C ) ) ), file(rlvect_2,r1_rlvect_2), []). fof(reflexivity_r1_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) ) => r1_rlvect_2(A,B,B) ) ), file(rlvect_2,r1_rlvect_2), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r3_xboole_0,axiom,( ! [A,B] : r3_xboole_0(A,A) ), file(xboole_0,r3_xboole_0), []). fof(s10_funct_2__e10_17_2_1_1_1__rusub_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) & m2_rlvect_2(D,A,k4_subset_1(u1_struct_0(A),B,k7_rlvect_2(A,C))) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),k1_numbers) & m2_relset_1(E,u1_struct_0(A),k1_numbers) & k8_funct_2(u1_struct_0(A),k1_numbers,E,C) = k1_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,D,C)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F != C => k8_funct_2(u1_struct_0(A),k1_numbers,E,F) = 0 ) ) ) ) ), file(rusub_3,s10_funct_2__e10_17_2_1_1_1__rusub_3), []). fof(s10_funct_2__e2_17_2_1_1_1__rusub_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) & m2_rlvect_2(D,A,k4_subset_1(u1_struct_0(A),B,k7_rlvect_2(A,C))) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),k1_numbers) & m2_relset_1(E,u1_struct_0(A),k1_numbers) & k8_funct_2(u1_struct_0(A),k1_numbers,E,C) = 0 & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F != C => k8_funct_2(u1_struct_0(A),k1_numbers,E,F) = k8_funct_2(u1_struct_0(A),k1_numbers,D,F) ) ) ) ) ), file(rusub_3,s10_funct_2__e2_17_2_1_1_1__rusub_3), []). fof(s1_xboole_0__e2_17__rusub_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & E = D & r1_tarski(B,E) & v1_rlvect_3(E,A) ) ) ) ) ), file(rusub_3,s1_xboole_0__e2_17__rusub_3), []). fof(s3_funct_1__e3_17_1_2__rusub_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m2_rlvect_2(D,A,C) ) => ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & k1_relat_1(E) = k10_rlvect_2(A,D) & ! [F] : ( r2_hidden(F,k10_rlvect_2(A,D)) => k1_funct_1(E,F) = a_3_0_rusub_3(A,B,F) ) ) ) ), file(rusub_3,s3_funct_1__e3_17_1_2__rusub_3), []). 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(symmetry_r1_rlvect_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) ) => ( r1_rlvect_2(A,B,C) => r1_rlvect_2(A,C,B) ) ) ), file(rlvect_2,r1_rlvect_2), []). fof(symmetry_r3_xboole_0,axiom,( ! [A,B] : ( r3_xboole_0(A,B) => r3_xboole_0(B,A) ) ), file(xboole_0,r3_xboole_0), []). fof(t10_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ), file(rlvect_1,t10_rlvect_1), []). fof(t11_funct_2,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => r2_hidden(C,k1_funct_2(A,B)) ) ) ), file(funct_2,t11_funct_2), []). fof(t15_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( r1_rlvect_1(B,C) => r1_rlvect_1(B,k3_rlvect_1(A,C,D)) ) ) ) ) ) ), file(rusub_1,t15_rusub_1), []). fof(t177_orders_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ( ( r1_tarski(B,A) & v6_ordinal1(B) ) => ( B = k1_xboole_0 | r2_hidden(k3_tarski(B),A) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(B,C) ) ) ) ), file(orders_1,t177_orders_1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_rusub_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r1_rlvect_1(k1_rusub_3(A,B),C) <=> ? [D] : ( m2_rlvect_2(D,A,B) & C = k13_rlvect_2(A,D) ) ) ) ) ), file(rusub_3,t1_rusub_3), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t25_rusub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_rlvect_1(B,D) <=> r1_rlvect_1(C,D) ) ) => B = C ) ) ) ) ), file(rusub_1,t25_rusub_1), []). fof(t26_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_finset_1(k1_relat_1(A)) => v1_finset_1(k2_relat_1(A)) ) ) ), file(finset_1,t26_finset_1), []). fof(t28_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k8_funct_2(u1_struct_0(A),k1_numbers,B,C) = 0 <=> ~ r2_hidden(C,k10_rlvect_2(A,B)) ) ) ) ) ), file(rlvect_2,t28_rlvect_2), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_rusub_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,B) => r1_rlvect_1(k1_rusub_3(A,B),C) ) ) ) ), file(rusub_3,t2_rusub_3), []). 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(t35_rlvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_orders_1(B,A) => ( ~ r2_hidden(k1_xboole_0,A) => ( k1_relat_1(B) = A & r1_tarski(k2_relat_1(B),k3_tarski(A)) ) ) ) ) ), file(rlvect_3,t35_rlvect_3), []). fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_rlvect_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_rlvect_1(A,B) ) ) ), file(rlvect_1,t3_rlvect_1), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_rlvect_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => k13_rlvect_2(A,k17_rlvect_2(A,B,C)) = k6_rlvect_1(A,k13_rlvect_2(A,B),k13_rlvect_2(A,C)) ) ) ) ), file(rlvect_3,t4_rlvect_3), []). 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(t50_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_rlvect_2(C,A,k7_rlvect_2(A,B)) => k13_rlvect_2(A,C) = k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,C,B)) ) ) ) ), file(rlvect_2,t50_rlvect_2), []). 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(t65_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( k1_relat_1(A) = k1_xboole_0 <=> k2_relat_1(A) = k1_xboole_0 ) ) ), file(relat_1,t65_relat_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t78_rlsub_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k2_rlvect_1(A,C,D) <=> C = k6_rlvect_1(A,B,D) ) ) ) ) ) ), file(rlsub_2,t78_rlsub_2), []). fof(t79_rlvect_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( m1_rlvect_2(D,A) => k8_funct_2(u1_struct_0(A),k1_numbers,k17_rlvect_2(A,C,D),B) = k5_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,C,B),k8_funct_2(u1_struct_0(A),k1_numbers,D,B)) ) ) ) ) ), file(rlvect_2,t79_rlvect_2), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_xboole_1,axiom,( ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ), file(xboole_1,t7_xboole_1), []). fof(t81_card_2,axiom,( ! [A] : ( ( v1_finset_1(A) & ! [B,C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ~ r1_tarski(B,C) & ~ r1_tarski(C,B) ) ) => ( A = k1_xboole_0 | r2_hidden(k3_tarski(A),A) ) ) ), file(card_2,t81_card_2), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t92_zfmisc_1,axiom,( ! [A,B] : ( r2_hidden(A,B) => r1_tarski(A,k3_tarski(B)) ) ), file(zfmisc_1,t92_zfmisc_1), []).