% Mizar problem: t35_hahnban,hahnban,1151,43 fof(t35_hahnban,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) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k6_supinf_1) & v1_hahnban(C,A) & v4_hahnban(C,A) & m2_relset_1(C,u1_struct_0(A),k6_supinf_1) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),k6_supinf_1) & v2_hahnban(D,B) & v3_hahnban(D,B) & m2_relset_1(D,u1_struct_0(B),k6_supinf_1) ) => ~ ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( E = F => r1_xreal_0(k8_funct_2(u1_struct_0(B),k6_supinf_1,D,E),k8_funct_2(u1_struct_0(A),k6_supinf_1,C,F)) ) ) ) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),k6_supinf_1) & v2_hahnban(E,A) & v3_hahnban(E,A) & m2_relset_1(E,u1_struct_0(A),k6_supinf_1) ) => ~ ( k2_partfun1(u1_struct_0(A),k6_supinf_1,E,u1_struct_0(B)) = D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r1_xreal_0(k8_funct_2(u1_struct_0(A),k6_supinf_1,E,F),k8_funct_2(u1_struct_0(A),k6_supinf_1,C,F)) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v2_rlvect_1,antisymmetry_r2_hidden,antisymmetry_r2_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_fraenkel,cc1_hahnban,cc1_membered,cc1_relset_1,cc1_supinf_1,cc1_xreal_0,cc20_membered,cc2_hahnban,cc2_membered,cc2_supinf_1,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xboole_0,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k4_rlvect_1,connectedness_r1_xreal_0,d10_xboole_0,d1_funct_2,d1_rlsub_1,d1_rlvect_1,d1_supinf_1,d2_rlsub_1,d3_rlvect_1,d3_supinf_1,d3_tarski,d4_hahnban,d4_rlvect_1,d4_tarski,d5_hahnban,d5_partfun1,d5_tarski,d6_supinf_1,d8_xboole_0,d9_ordinal1,d9_xboole_0,dt_g2_rlvect_1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_realset1,dt_k1_relat_1,dt_k1_rlsub_2,dt_k1_rlvect_3,dt_k1_supinf_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_partfun1,dt_k2_relat_1,dt_k2_rlvect_1,dt_k2_supinf_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_supinf_1,dt_k3_tarski,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k4_partfun1,dt_k4_real_1,dt_k4_relset_1,dt_k4_rfunct_3,dt_k4_rlvect_1,dt_k4_tarski,dt_k6_domain_1,dt_k6_supinf_1,dt_k7_relat_1,dt_k7_rlvect_2,dt_k8_funct_2,dt_k8_relset_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_rlvect_1,dt_l2_struct_0,dt_m1_relset_1,dt_m1_rfunct_3,dt_m1_rlsub_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_rfunct_3,dt_m2_subset_1,dt_u1_rlvect_1,dt_u1_struct_0,dt_u2_rlvect_1,dt_u2_struct_0,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_rlvect_1,existence_l2_struct_0,existence_m1_relset_1,existence_m1_rfunct_3,existence_m1_rlsub_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_rfunct_3,existence_m2_subset_1,fc10_membered,fc10_xreal_0,fc11_membered,fc11_xreal_0,fc12_membered,fc12_xreal_0,fc13_membered,fc14_membered,fc15_membered,fc16_membered,fc1_partfun1,fc1_rlvect_1,fc1_struct_0,fc1_subset_1,fc1_supinf_1,fc21_xreal_0,fc22_membered,fc22_xreal_0,fc23_membered,fc23_xreal_0,fc24_membered,fc24_xreal_0,fc25_membered,fc26_membered,fc27_membered,fc28_membered,fc29_membered,fc2_membered,fc2_subset_1,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc3_subset_1,fc3_xreal_0,fc4_subset_1,fc4_xreal_0,fc6_membered,fc7_membered,fc7_xreal_0,fc8_membered,fc8_xreal_0,fc9_membered,fc9_xreal_0,fraenkel_a_0_0_domain_1,fraenkel_a_1_0_hahnban,fraenkel_a_1_1_hahnban,fraenkel_a_4_0_hahnban,free_g2_rlvect_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,irreflexivity_r2_xboole_0,l44_hahnban,l45_hahnban,l46_hahnban,l47_hahnban,l48_hahnban,rc1_fraenkel,rc1_hahnban,rc1_membered,rc1_rlsub_1,rc1_subset_1,rc1_xreal_0,rc2_partfun1,rc2_rlvect_1,rc2_subset_1,rc2_xreal_0,rc3_rlvect_1,rc3_struct_0,rc3_supinf_1,rc3_xreal_0,rc4_struct_0,rc4_xreal_0,rc5_struct_0,rc6_rlvect_1,redefinition_k1_domain_1,redefinition_k2_partfun1,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k4_relset_1,redefinition_k4_rfunct_3,redefinition_k4_rlvect_1,redefinition_k6_domain_1,redefinition_k6_supinf_1,redefinition_k7_rlvect_2,redefinition_k8_funct_2,redefinition_k8_relset_1,redefinition_m2_relset_1,redefinition_m2_rfunct_3,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_xboole_0,s1_orders_1__e13_42__hahnban,s7_domain_1__e2_42__hahnban,symmetry_r3_xboole_0,t100_relat_1,t119_partfun1,t11_relset_1,t125_partfun1,t12_relset_1,t12_rlvect_4,t13_hahnban,t14_hahnban,t1_boole,t1_real,t1_subset,t1_xboole_1,t21_rlsub_1,t22_rlsub_1,t25_relat_1,t28_rlsub_1,t28_xboole_1,t29_rlsub_1,t2_boole,t2_real,t2_subset,t2_tarski,t36_rlsub_1,t3_real,t3_subset,t3_xboole_1,t40_funct_2,t40_rlsub_1,t43_rlsub_1,t4_hahnban,t4_real,t4_subset,t5_hahnban,t5_real,t5_subset,t60_relat_1,t64_relat_1,t6_boole,t6_real,t77_rlsub_2,t7_boole,t7_real,t88_grfunc_1,t88_relat_1,t8_boole,t8_grfunc_1,t8_real,t92_zfmisc_1,t94_zfmisc_1,t9_rlsub_2]), [file(hahnban,t35_hahnban)]). fof(abstractness_v2_rlvect_1,axiom,( ! [A] : ( l2_rlvect_1(A) => ( v2_rlvect_1(A) => A = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ), file(rlvect_1,v2_rlvect_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(antisymmetry_r2_xboole_0,axiom,( ! [A,B] : ( r2_xboole_0(A,B) => ~ r2_xboole_0(B,A) ) ), file(xboole_0,r2_xboole_0), []). 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_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v2_hahnban(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v1_hahnban(B,A) ) ) ) ) ), file(hahnban,cc1_hahnban), []). 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(cc1_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k3_supinf_1) => v3_supinf_1(A) ) ), file(supinf_1,cc1_supinf_1), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). 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_hahnban,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_relset_1(B,u1_struct_0(A),k6_supinf_1) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v3_hahnban(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & v4_hahnban(B,A) ) ) ) ) ), file(hahnban,cc2_hahnban), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_supinf_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_supinf_1(A) ) ) ), file(supinf_1,cc2_supinf_1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(commutativity_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_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_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_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_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k4_rlvect_1(A,C,B) ) ), file(rlvect_1,k4_rlvect_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(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k4_rlvect_1(A,C,D),B) ) ) ) & ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k3_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) ), file(rlsub_1,d1_rlsub_1), []). fof(d1_rlvect_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( r1_rlvect_1(A,B) <=> r2_hidden(B,u1_struct_0(A)) ) ) ), file(rlvect_1,d1_rlvect_1), []). fof(d1_supinf_1,axiom,( k1_supinf_1 = k1_numbers ), file(supinf_1,d1_supinf_1), []). fof(d2_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ( m1_rlsub_1(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & u2_struct_0(B) = u2_struct_0(A) & u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B)) & u2_rlvect_1(B) = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B))) ) ) ) ) ), file(rlsub_1,d2_rlsub_1), []). 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_supinf_1,axiom,( k2_supinf_1 = k1_tarski(k1_numbers) ), file(supinf_1,d3_supinf_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_hahnban,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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) ) => ( v2_hahnban(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k4_rlvect_1(A,C,D)) = k3_real_1(k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C),k8_funct_2(u1_struct_0(A),k6_supinf_1,B,D)) ) ) ) ) ) ), file(hahnban,d4_hahnban), []). 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(d5_hahnban,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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_supinf_1) & m2_relset_1(B,u1_struct_0(A),k6_supinf_1) ) => ( v3_hahnban(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => k8_funct_2(u1_struct_0(A),k6_supinf_1,B,k3_rlvect_1(A,C,D)) = k4_real_1(D,k8_funct_2(u1_struct_0(A),k6_supinf_1,B,C)) ) ) ) ) ) ), file(hahnban,d5_hahnban), []). fof(d5_partfun1,axiom,( ! [A,B,C] : ( C = k4_partfun1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & D = E & r1_tarski(k1_relat_1(E),A) & r1_tarski(k2_relat_1(E),B) ) ) ) ), file(partfun1,d5_partfun1), []). 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_supinf_1,axiom,( k3_supinf_1 = k2_xboole_0(k1_numbers,k2_tarski(k2_supinf_1,k1_supinf_1)) ), file(supinf_1,d6_supinf_1), []). fof(d8_xboole_0,axiom,( ! [A,B] : ( r2_xboole_0(A,B) <=> ( r1_tarski(A,B) & A != B ) ) ), file(xboole_0,d8_xboole_0), []). 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_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_g2_rlvect_1,axiom,( ! [A,B,C,D] : ( ( 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) ) => ( v2_rlvect_1(g2_rlvect_1(A,B,C,D)) & l2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ), file(rlvect_1,g2_rlvect_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_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_realset1,axiom,( $true ), file(realset1,k1_realset1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_rlsub_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_rlsub_1(B,A) & m1_rlsub_1(C,A) ) => ( v2_rlvect_1(k1_rlsub_2(A,B,C)) & m1_rlsub_1(k1_rlsub_2(A,B,C),A) ) ) ), file(rlsub_2,k1_rlsub_2), []). fof(dt_k1_rlvect_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) & l2_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_rlvect_1(k1_rlvect_3(A,B)) & m1_rlsub_1(k1_rlvect_3(A,B),A) ) ) ), file(rlvect_3,k1_rlvect_3), []). fof(dt_k1_supinf_1,axiom,( $true ), file(supinf_1,k1_supinf_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k2_partfun1(A,B,C,D)) & m2_relset_1(k2_partfun1(A,B,C,D),A,B) ) ) ), file(partfun1,k2_partfun1), []). 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_supinf_1,axiom,( $true ), file(supinf_1,k2_supinf_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_supinf_1,axiom,( $true ), file(supinf_1,k3_supinf_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_partfun1,axiom,( $true ), file(partfun1,k4_partfun1), []). 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_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_rfunct_3,axiom,( ! [A,B] : m1_rfunct_3(k4_rfunct_3(A,B),A,B) ), file(rfunct_3,k4_rfunct_3), []). fof(dt_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_rlvect_1(A,B,C),u1_struct_0(A)) ) ), file(rlvect_1,k4_rlvect_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) ), file(domain_1,k6_domain_1), []). fof(dt_k6_supinf_1,axiom, ( ~ v1_xboole_0(k6_supinf_1) & m1_subset_1(k6_supinf_1,k1_zfmisc_1(k3_supinf_1)) ), file(supinf_1,k6_supinf_1), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). 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_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => m2_relset_1(k8_relset_1(A,B,C,D),A,B) ) ), file(relset_1,k8_relset_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_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_rfunct_3,axiom,( $true ), file(rfunct_3,m1_rfunct_3), []). fof(dt_m1_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlsub_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) & l2_rlvect_1(B) ) ) ) ), file(rlsub_1,m1_rlsub_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) => ( v1_funct_1(D) & m2_relset_1(D,A,B) ) ) ) ), file(rfunct_3,m2_rfunct_3), []). 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_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_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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_rfunct_3,axiom,( ! [A,B] : ? [C] : m1_rfunct_3(C,A,B) ), file(rfunct_3,m1_rfunct_3), []). fof(existence_m1_rlsub_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) & l2_rlvect_1(A) ) => ? [B] : m1_rlsub_1(B,A) ) ), file(rlsub_1,m1_rlsub_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ? [D] : m2_rfunct_3(D,A,B,C) ) ), file(rfunct_3,m2_rfunct_3), []). 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_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(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_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(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(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_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(fc1_partfun1,axiom,( ! [A,B] : ~ v1_xboole_0(k4_partfun1(A,B)) ), file(partfun1,fc1_partfun1), []). fof(fc1_rlvect_1,axiom,( ! [A,B,C,D] : ( ( ~ 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) ) => ( ~ v3_struct_0(g2_rlvect_1(A,B,C,D)) & v2_rlvect_1(g2_rlvect_1(A,B,C,D)) ) ) ), file(rlvect_1,fc1_rlvect_1), []). 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_supinf_1,axiom,( ~ v1_xboole_0(k3_supinf_1) ), file(supinf_1,fc1_supinf_1), []). fof(fc21_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc22_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), []). 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(fc23_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), []). 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(fc24_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), []). 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(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). 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(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_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(fc4_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), []). 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(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_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(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_0_0_domain_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_domain_1) <=> ? [B] : ( m1_subset_1(B,f1_s7_domain_1) & A = B & p1_s7_domain_1(B) ) ) ), file(domain_1,a_0_0_domain_1), []). fof(fraenkel_a_1_0_hahnban,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & v1_fraenkel(B) ) => ( r2_hidden(A,a_1_0_hahnban(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_relat_1(C) ) ) ) ), file(hahnban,a_1_0_hahnban), []). fof(fraenkel_a_1_1_hahnban,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & v1_fraenkel(B) ) => ( r2_hidden(A,a_1_1_hahnban(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k2_relat_1(C) ) ) ) ), file(hahnban,a_1_1_hahnban), []). fof(fraenkel_a_4_0_hahnban,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) & l2_rlvect_1(B) & m1_rlsub_1(C,B) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),k6_supinf_1) & v1_hahnban(D,B) & v4_hahnban(D,B) & m2_relset_1(D,u1_struct_0(B),k6_supinf_1) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),k6_supinf_1) & v2_hahnban(E,C) & v3_hahnban(E,C) & m2_relset_1(E,u1_struct_0(C),k6_supinf_1) ) => ( r2_hidden(A,a_4_0_hahnban(B,C,D,E)) <=> ? [F] : ( m2_rfunct_3(F,u1_struct_0(B),k6_supinf_1,k4_rfunct_3(u1_struct_0(B),k6_supinf_1)) & A = F & ? [G] : ( m1_rlsub_1(G,B) & r1_tarski(u1_struct_0(C),u1_struct_0(G)) & k2_partfun1(u1_struct_0(B),k6_supinf_1,F,u1_struct_0(C)) = E & ? [H] : ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(G),k6_supinf_1) & v2_hahnban(H,G) & v3_hahnban(H,G) & m2_relset_1(H,u1_struct_0(G),k6_supinf_1) & F = H & ! [I] : ( m1_subset_1(I,u1_struct_0(G)) => ! [J] : ( m1_subset_1(J,u1_struct_0(B)) => ( I = J => r1_xreal_0(k8_funct_2(u1_struct_0(G),k6_supinf_1,H,I),k8_funct_2(u1_struct_0(B),k6_supinf_1,D,J)) ) ) ) ) ) ) ) ) ), file(hahnban,a_4_0_hahnban), []). fof(free_g2_rlvect_1,axiom,( ! [A,B,C,D] : ( ( 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) ) => ! [E,F,G,H] : ( g2_rlvect_1(A,B,C,D) = g2_rlvect_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(rlvect_1,g2_rlvect_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(irreflexivity_r2_xboole_0,axiom,( ! [A,B] : ~ r2_xboole_0(A,A) ), file(xboole_0,r2_xboole_0), []). fof(l44_hahnban,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_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r2_hidden(C,u1_struct_0(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k6_supinf_1) & v1_hahnban(D,A) & v4_hahnban(D,A) & m2_relset_1(D,u1_struct_0(A),k6_supinf_1) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),k6_supinf_1) & v2_hahnban(E,B) & v3_hahnban(E,B) & m2_relset_1(E,u1_struct_0(B),k6_supinf_1) ) => ~ ( ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( F = G => r1_xreal_0(k8_funct_2(u1_struct_0(B),k6_supinf_1,E,F),k8_funct_2(u1_struct_0(A),k6_supinf_1,D,G)) ) ) ) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)))),k6_supinf_1) & v2_hahnban(F,k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)))) & v3_hahnban(F,k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)))) & m2_relset_1(F,u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)))),k6_supinf_1) ) => ~ ( k2_partfun1(u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)))),k6_supinf_1,F,u1_struct_0(B)) = E & ! [G] : ( m1_subset_1(G,u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C))))) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( G = H => r1_xreal_0(k8_funct_2(u1_struct_0(k1_rlsub_2(A,B,k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),C)))),k6_supinf_1,F,G),k8_funct_2(u1_struct_0(A),k6_supinf_1,D,H)) ) ) ) ) ) ) ) ) ) ) ) ) ), file(hahnban,l44_hahnban), []). fof(l45_hahnban,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) ) => ( ~ v3_struct_0(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) & v3_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) & v4_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) & v5_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) & v6_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) & v7_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) & l2_rlvect_1(g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A))) ) ) ), file(hahnban,l45_hahnban), []). fof(l46_hahnban,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] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v5_rlvect_1(C) & v6_rlvect_1(C) & v7_rlvect_1(C) & l2_rlvect_1(C) ) => ( B = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( C = g2_rlvect_1(u1_struct_0(D),u2_struct_0(D),u1_rlvect_1(D),u2_rlvect_1(D)) => m1_rlsub_1(C,B) ) ) ) ) ) ) ), file(hahnban,l46_hahnban), []). fof(l47_hahnban,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] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ( B = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k6_supinf_1) & v2_hahnban(C,B) & v3_hahnban(C,B) & m2_relset_1(C,u1_struct_0(B),k6_supinf_1) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k6_supinf_1) & v2_hahnban(C,A) & v3_hahnban(C,A) & m2_relset_1(C,u1_struct_0(A),k6_supinf_1) ) ) ) ) ) ), file(hahnban,l47_hahnban), []). fof(l48_hahnban,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] : ( ( ~ v3_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & l2_rlvect_1(B) ) => ( B = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k6_supinf_1) & v2_hahnban(C,A) & v3_hahnban(C,A) & m2_relset_1(C,u1_struct_0(A),k6_supinf_1) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k6_supinf_1) & v2_hahnban(C,B) & v3_hahnban(C,B) & m2_relset_1(C,u1_struct_0(B),k6_supinf_1) ) ) ) ) ) ), file(hahnban,l48_hahnban), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_hahnban,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v6_ordinal1(B) ) ) ), file(hahnban,rc1_hahnban), []). 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_rlsub_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) & l2_rlvect_1(A) ) => ? [B] : ( m1_rlsub_1(B,A) & ~ v3_struct_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) ) ) ), file(rlsub_1,rc1_rlsub_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_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_rlvect_1,axiom,( ? [A] : ( l2_rlvect_1(A) & v2_rlvect_1(A) ) ), file(rlvect_1,rc2_rlvect_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_rlvect_1,axiom,( ? [A] : ( l2_rlvect_1(A) & ~ v3_struct_0(A) ) ), file(rlvect_1,rc3_rlvect_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_supinf_1,axiom,( ? [A] : v3_supinf_1(A) ), file(supinf_1,rc3_supinf_1), []). fof(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc4_struct_0), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_rlvect_1,axiom,( ? [A] : ( l2_rlvect_1(A) & ~ v3_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) ) ), file(rlvect_1,rc6_rlvect_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_k2_partfun1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => k2_partfun1(A,B,C,D) = k7_relat_1(C,D) ) ), file(partfun1,k2_partfun1), []). 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_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_k4_rfunct_3,axiom,( ! [A,B] : k4_rfunct_3(A,B) = k4_partfun1(A,B) ), file(rfunct_3,k4_rfunct_3), []). fof(redefinition_k4_rlvect_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k4_rlvect_1(A,B,C) = k2_rlvect_1(A,B,C) ) ), file(rlvect_1,k4_rlvect_1), []). fof(redefinition_k6_domain_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) ), file(domain_1,k6_domain_1), []). fof(redefinition_k6_supinf_1,axiom,( k6_supinf_1 = k1_numbers ), file(supinf_1,k6_supinf_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_k8_relset_1,axiom,( ! [A,B,C,D] : ( m1_relset_1(C,A,B) => k8_relset_1(A,B,C,D) = k7_relat_1(C,D) ) ), file(relset_1,k8_relset_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_rfunct_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(rfunct_3,m2_rfunct_3), []). 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(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_xboole_0,axiom,( ! [A,B] : r3_xboole_0(A,A) ), file(xboole_0,r3_xboole_0), []). fof(s1_orders_1__e13_42__hahnban,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) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_rfunct_3(u1_struct_0(A),k6_supinf_1))) ) => ( ( ! [C] : ( m1_subset_1(C,B) => r1_tarski(C,C) ) & ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ( ( r1_tarski(C,D) & r1_tarski(D,C) ) => C = D ) ) ) & ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ( ( r1_tarski(C,D) & r1_tarski(D,E) ) => r1_tarski(C,E) ) ) ) ) & ! [C] : ~ ( r1_tarski(C,B) & ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ~ r1_tarski(D,E) & ~ r1_tarski(E,D) ) ) ) & ! [D] : ( m1_subset_1(D,B) => ? [E] : ( m1_subset_1(E,B) & r2_hidden(E,C) & ~ r1_tarski(E,D) ) ) ) ) => ? [C] : ( m1_subset_1(C,B) & ! [D] : ( m1_subset_1(D,B) => ~ ( C != D & r1_tarski(C,D) ) ) ) ) ) ), file(hahnban,s1_orders_1__e13_42__hahnban), []). fof(s7_domain_1__e2_42__hahnban,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) ) => m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(k4_rfunct_3(u1_struct_0(A),k6_supinf_1))) ) ), file(hahnban,s7_domain_1__e2_42__hahnban), []). 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(t100_relat_1,axiom,( ! [A,B,C] : ( v1_relat_1(C) => k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)) ) ), file(relat_1,t100_relat_1), []). fof(t119_partfun1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => r2_hidden(C,k4_partfun1(A,B)) ) ), file(partfun1,t119_partfun1), []). fof(t11_relset_1,axiom,( ! [A,B,C] : ( v1_relat_1(C) => ( ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) => m2_relset_1(C,A,B) ) ) ), file(relset_1,t11_relset_1), []). fof(t125_partfun1,axiom,( ! [A,B,C] : ( r1_tarski(A,B) => r1_tarski(k4_partfun1(A,C),k4_partfun1(B,C)) ) ), file(partfun1,t125_partfun1), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t12_rlvect_4,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)) => r1_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,B)),B) ) ) ), file(rlvect_4,t12_rlvect_4), []). fof(t13_hahnban,axiom,( ! [A,B,C] : ( ( v6_ordinal1(C) & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(A,B))) ) => r2_hidden(k3_tarski(C),k4_rfunct_3(A,B)) ) ), file(hahnban,t13_hahnban), []). fof(t14_hahnban,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_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => r1_tarski(u1_struct_0(B),u1_struct_0(k1_rlsub_2(A,B,C))) ) ) ) ), file(hahnban,t14_hahnban), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). 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(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(t21_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = B & F = C ) => k4_rlvect_1(D,E,F) = k4_rlvect_1(A,B,C) ) ) ) ) ) ) ) ), file(rlsub_1,t21_rlsub_1), []). fof(t22_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( E = B => k3_rlvect_1(D,E,C) = k3_rlvect_1(A,B,C) ) ) ) ) ) ) ), file(rlsub_1,t22_rlsub_1), []). fof(t25_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) & r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) ) ), file(relat_1,t25_relat_1), []). fof(t28_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( ( r1_rlvect_1(D,B) & r1_rlvect_1(D,C) ) => r1_rlvect_1(D,k4_rlvect_1(A,B,C)) ) ) ) ) ) ), file(rlsub_1,t28_rlsub_1), []). fof(t28_xboole_1,axiom,( ! [A,B] : ( r1_tarski(A,B) => k3_xboole_0(A,B) = A ) ), file(xboole_1,t28_xboole_1), []). fof(t29_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_rlsub_1(D,A) => ( r1_rlvect_1(D,B) => r1_rlvect_1(D,k3_rlvect_1(A,B,C)) ) ) ) ) ) ), file(rlsub_1,t29_rlsub_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). 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(t36_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_rlsub_1(B,C) ) ) ) ) ), file(rlsub_1,t36_rlsub_1), []). 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(t3_xboole_1,axiom,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), []). fof(t40_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( r1_tarski(A,C) => k2_partfun1(A,B,D,C) = D ) ) ), file(funct_2,t40_funct_2), []). fof(t40_rlsub_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_rlvect_1(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] : ( ( v2_rlvect_1(B) & m1_rlsub_1(B,A) ) => ( u1_struct_0(B) = u1_struct_0(A) => B = A ) ) ) ), file(rlsub_1,t40_rlsub_1), []). fof(t43_rlsub_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) & l2_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & v1_rlsub_1(B,A) & ! [C] : ( ( v2_rlvect_1(C) & m1_rlsub_1(C,A) ) => B != u1_struct_0(C) ) ) ) ) ), file(rlsub_1,t43_rlsub_1), []). fof(t4_hahnban,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_rfunct_3(A,B))) ) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(hahnban,t4_hahnban), []). 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_hahnban,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k3_tarski(A) => ( k1_relat_1(B) = k3_tarski(a_1_0_hahnban(A)) & k2_relat_1(B) = k3_tarski(a_1_1_hahnban(A)) ) ) ) ) ), file(hahnban,t5_hahnban), []). 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(t60_relat_1,axiom, ( k1_relat_1(k1_xboole_0) = k1_xboole_0 & k2_relat_1(k1_xboole_0) = k1_xboole_0 ), file(relat_1,t60_relat_1), []). fof(t64_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ( k1_relat_1(A) = k1_xboole_0 | k2_relat_1(A) = k1_xboole_0 ) => A = k1_xboole_0 ) ) ), file(relat_1,t64_relat_1), []). 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(t77_rlsub_2,axiom,( ! [A,B] : ~ ( r2_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,B) & ~ r2_hidden(C,A) ) ) ), file(rlsub_2,t77_rlsub_2), []). 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(t88_grfunc_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(A,k1_relat_1(B)) & r1_tarski(B,C) ) => k7_relat_1(B,A) = k7_relat_1(C,A) ) ) ) ), file(grfunc_1,t88_grfunc_1), []). fof(t88_relat_1,axiom,( ! [A,B] : ( v1_relat_1(B) => r1_tarski(k7_relat_1(B,A),B) ) ), file(relat_1,t88_relat_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) <=> ( r1_tarski(k1_relat_1(A),k1_relat_1(B)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ), file(grfunc_1,t8_grfunc_1), []). 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(t92_zfmisc_1,axiom,( ! [A,B] : ( r2_hidden(A,B) => r1_tarski(A,k3_tarski(B)) ) ), file(zfmisc_1,t92_zfmisc_1), []). fof(t94_zfmisc_1,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) => r1_tarski(C,B) ) => r1_tarski(k3_tarski(A),B) ) ), file(zfmisc_1,t94_zfmisc_1), []). fof(t9_rlsub_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_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k1_rlsub_2(A,B,C) = k1_rlsub_2(A,C,B) ) ) ) ), file(rlsub_2,t9_rlsub_2), []).