% Mizar problem: t38_gobrd14,gobrd14,1323,58 fof(t38_gobrd14,conjecture,( ! [A] : ( ( v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k6_pre_topc(k15_euclid(2),k3_goboard9(k1_sprect_1(A))) = k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),1,2,k1_rcomp_1(k18_pscomp_1(k5_topreal1(2,k1_sprect_1(A))),k20_pscomp_1(k5_topreal1(2,k1_sprect_1(A)))),k1_rcomp_1(k21_pscomp_1(k5_topreal1(2,k1_sprect_1(A))),k19_pscomp_1(k5_topreal1(2,k1_sprect_1(A)))))) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_membered,cc10_topreal6,cc11_membered,cc11_topreal6,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_jordan2c,cc1_membered,cc1_relset_1,cc1_sprect_1,cc1_sprect_3,cc1_topreal6,cc1_tops_1,cc1_xreal_0,cc20_membered,cc2_int_1,cc2_membered,cc2_sprect_1,cc2_topreal6,cc2_tops_1,cc2_xreal_0,cc3_int_1,cc3_membered,cc3_sprect_1,cc3_tops_1,cc3_xreal_0,cc4_int_1,cc4_membered,cc4_sprect_1,cc4_topreal6,cc4_tops_1,cc4_xreal_0,cc5_sprect_1,cc5_topreal6,cc5_tops_1,cc5_xreal_0,cc6_membered,cc6_sprect_1,cc6_topreal6,cc6_tops_1,cc6_xreal_0,cc7_topreal6,cc7_xreal_0,cc8_topreal6,cc8_xreal_0,cc9_membered,cc9_topreal6,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k4_subset_1,connectedness_r1_xreal_0,d10_xboole_0,d16_euclid,d1_rcomp_1,d1_sprect_1,d2_tarski,d2_xboole_0,d3_tarski,d5_card_3,dt_g1_pre_topc,dt_k10_finseq_1,dt_k11_finseq_1,dt_k15_euclid,dt_k18_pscomp_1,dt_k19_pscomp_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_rcomp_1,dt_k1_relat_1,dt_k1_sprect_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_pscomp_1,dt_k21_euclid,dt_k21_pscomp_1,dt_k22_euclid,dt_k22_pscomp_1,dt_k23_euclid,dt_k23_pscomp_1,dt_k24_pscomp_1,dt_k25_pscomp_1,dt_k2_finseq_1,dt_k2_finseq_4,dt_k2_goboard9,dt_k2_relat_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_4,dt_k3_goboard9,dt_k4_card_3,dt_k4_finseq_1,dt_k4_funct_4,dt_k4_subset_1,dt_k5_funct_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_topreal1,dt_k6_pre_topc,dt_k7_finseq_1,dt_k8_finseq_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_membered,fc10_sprect_1,fc11_membered,fc11_sprect_1,fc12_membered,fc12_sprect_1,fc13_membered,fc13_sprect_1,fc14_membered,fc15_membered,fc16_membered,fc1_pscomp_1,fc1_revrot_1,fc1_sprect_1,fc1_sprect_3,fc1_subset_1,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc2_euclid,fc2_membered,fc2_pscomp_1,fc2_sprect_1,fc2_sprect_3,fc2_subset_1,fc2_tops_1,fc3_jordan2c,fc3_revrot_1,fc3_sprect_1,fc3_sprect_3,fc3_subset_1,fc4_gobrd14,fc4_subset_1,fc5_membered,fc5_sprect_1,fc6_membered,fc6_sprect_1,fc7_membered,fc7_sprect_1,fc8_membered,fc8_topreal6,fc9_membered,fc9_sprect_1,fraenkel_a_1_5_gobrd14,fraenkel_a_1_5_sprect_3,fraenkel_a_1_6_gobrd14,fraenkel_a_1_6_sprect_3,fraenkel_a_1_7_gobrd14,fraenkel_a_2_0_rcomp_1,free_g1_pre_topc,idempotence_k2_xboole_0,idempotence_k4_subset_1,rc1_int_1,rc1_membered,rc1_pre_topc,rc1_pscomp_1,rc1_revrot_1,rc1_sprect_1,rc1_sprect_3,rc1_subset_1,rc1_tops_1,rc1_xreal_0,rc2_int_1,rc2_pre_topc,rc2_pscomp_1,rc2_sprect_1,rc2_sprect_3,rc2_subset_1,rc2_tops_1,rc2_xreal_0,rc3_pscomp_1,rc3_sprect_1,rc3_tops_1,rc3_xreal_0,rc4_pscomp_1,rc4_sprect_1,rc4_tops_1,rc4_xreal_0,rc5_pscomp_1,rc5_tops_1,rc6_pre_topc,rc7_pre_topc,rc9_pscomp_1,redefinition_k2_finseq_1,redefinition_k2_finseq_4,redefinition_k3_finseq_1,redefinition_k3_finseq_4,redefinition_k4_finseq_1,redefinition_k4_subset_1,redefinition_k5_funct_4,redefinition_k5_numbers,redefinition_k8_finseq_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,t18_card_3,t1_boole,t1_numerals,t1_real,t1_subset,t26_gobrd14,t29_finseq_3,t2_real,t2_subset,t2_tarski,t31_gobrd14,t33_gobrd14,t34_gobrd14,t35_gobrd14,t36_gobrd14,t3_real,t3_subset,t48_rcomp_1,t4_finseq_1,t4_real,t4_subset,t54_sprect_3,t55_euclid,t56_euclid,t5_real,t5_subset,t61_finseq_1,t65_funct_4,t66_funct_4,t6_boole,t6_real,t71_pscomp_1,t7_boole,t7_real,t8_boole,t8_real,t9_funct_1]), [file(gobrd14,t38_gobrd14)]). fof(abstractness_v1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(A) => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ), file(pre_topc,v1_pre_topc), []). 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(cc10_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => v2_connsp_1(A,k15_euclid(2)) ) ) ), file(topreal6,cc10_topreal6), []). 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(cc11_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_finset_1(A) => ( v1_membered(A) & v2_membered(A) & v1_rcomp_1(A) ) ) ) ), file(topreal6,cc11_topreal6), []). 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_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v6_compts_1(B,k15_euclid(A)) => v1_jordan2c(B,A) ) ) ) ), file(jordan2c,cc1_jordan2c), []). 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_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v5_seqm_3(A) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & ~ v1_realset1(A) ) ) ), file(sprect_1,cc1_sprect_1), []). fof(cc1_sprect_3,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ( ~ v1_xboole_0(A) & v1_sprect_1(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) ) => ( ~ v1_xboole_0(A) & v1_sprect_2(A) & v1_sprect_1(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) ) ) ) ), file(sprect_3,cc1_sprect_3), []). fof(cc1_topreal6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_connsp_1(B,A) ) ) ) ), file(topreal6,cc1_topreal6), []). fof(cc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => ( v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ) ) ), file(tops_1,cc1_tops_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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_realset1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) ) ), file(sprect_1,cc2_sprect_1), []). fof(cc2_topreal6,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v6_compts_1(B,A) ) ) ) ), file(topreal6,cc2_topreal6), []). fof(cc2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_tops_1(B,A) ) ) ) ), file(tops_1,cc2_tops_1), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_seq_4(A) => ( v1_membered(A) & v2_membered(A) & v1_seq_4(A) & v2_seq_4(A) ) ) ) ), file(sprect_1,cc3_sprect_1), []). fof(cc3_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_tops_1(B,A) ) ) ) ), file(tops_1,cc3_tops_1), []). 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_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( v1_seq_4(A) & v2_seq_4(A) ) => ( v1_membered(A) & v2_membered(A) & v3_seq_4(A) ) ) ) ), file(sprect_1,cc4_sprect_1), []). fof(cc4_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_sppol_1(A) => ~ v1_xboole_0(A) ) ) ), file(topreal6,cc4_topreal6), []). fof(cc4_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) => v2_tops_1(B,A) ) ) ) ), file(tops_1,cc4_tops_1), []). 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_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_sprect_1(A) => ~ v5_seqm_3(A) ) ) ), file(sprect_1,cc5_sprect_1), []). fof(cc5_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v2_sppol_1(A) => ~ v1_xboole_0(A) ) ) ), file(topreal6,cc5_topreal6), []). fof(cc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_pre_topc(B,A) & v2_tops_1(B,A) ) => ( v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ) ) ), file(tops_1,cc5_tops_1), []). 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_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ( ~ v1_xboole_0(A) & v1_sprect_1(A) ) => ( ~ v1_xboole_0(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) ) ) ) ), file(sprect_1,cc6_sprect_1), []). fof(cc6_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v2_topreal4(A,k15_euclid(2)) => ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) ) ) ), file(topreal6,cc6_topreal6), []). fof(cc6_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(B,A) & v3_tops_1(B,A) ) => ( v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ) ) ), file(tops_1,cc6_tops_1), []). 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_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v3_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) ) => v2_topreal4(A,k15_euclid(2)) ) ) ), file(topreal6,cc7_topreal6), []). 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_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v1_sppol_1(A) ) ) ), file(topreal6,cc8_topreal6), []). 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(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(cc9_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v2_sppol_1(A) ) ) ), file(topreal6,cc9_topreal6), []). 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_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(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(d16_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k23_euclid(A,B) = k10_finseq_1(A,B) ) ) ), file(euclid,d16_euclid), []). fof(d1_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_rcomp_1(A,B) = a_2_0_rcomp_1(A,B) ) ) ), file(rcomp_1,d1_rcomp_1), []). fof(d1_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k1_sprect_1(A) = k8_finseq_1(u1_struct_0(k15_euclid(2)),k3_finseq_4(u1_struct_0(k15_euclid(2)),k23_pscomp_1(A),k24_pscomp_1(A),k25_pscomp_1(A)),k2_finseq_4(u1_struct_0(k15_euclid(2)),k22_pscomp_1(A),k23_pscomp_1(A))) ) ), file(sprect_1,d1_sprect_1), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). 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_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k4_card_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & C = D & k1_relat_1(D) = k1_relat_1(A) & ! [E] : ( r2_hidden(E,k1_relat_1(A)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ), file(card_3,d5_card_3), []). fof(dt_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(pre_topc,g1_pre_topc), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k11_finseq_1,axiom,( $true ), file(finseq_1,k11_finseq_1), []). fof(dt_k15_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & l1_pre_topc(k15_euclid(A)) ) ) ), file(euclid,k15_euclid), []). fof(dt_k18_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k18_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k18_pscomp_1), []). fof(dt_k19_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k19_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k19_pscomp_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_rcomp_1,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) ), file(rcomp_1,k1_rcomp_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m2_finseq_1(k1_sprect_1(A),u1_struct_0(k15_euclid(2))) ) ), file(sprect_1,k1_sprect_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_k20_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k20_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k20_pscomp_1), []). fof(dt_k21_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k21_euclid(A),k1_numbers) ) ), file(euclid,k21_euclid), []). fof(dt_k21_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k21_pscomp_1(A),k1_numbers) ) ), file(pscomp_1,k21_pscomp_1), []). fof(dt_k22_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k22_euclid(A),k1_numbers) ) ), file(euclid,k22_euclid), []). fof(dt_k22_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k22_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k22_pscomp_1), []). fof(dt_k23_euclid,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k23_euclid(A,B),u1_struct_0(k15_euclid(2))) ) ), file(euclid,k23_euclid), []). fof(dt_k23_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k23_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k23_pscomp_1), []). fof(dt_k24_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k24_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k24_pscomp_1), []). fof(dt_k25_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(k25_pscomp_1(A),u1_struct_0(k15_euclid(2))) ) ), file(pscomp_1,k25_pscomp_1), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_finseq_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k2_finseq_4(A,B,C),A) ) ), file(finseq_4,k2_finseq_4), []). fof(dt_k2_goboard9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(k2_goboard9(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard9,k2_goboard9), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_finseq_4,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) ) => m2_finseq_1(k3_finseq_4(A,B,C,D),A) ) ), file(finseq_4,k3_finseq_4), []). fof(dt_k3_goboard9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(k3_goboard9(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ), file(goboard9,k3_goboard9), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_funct_4,axiom,( $true ), file(funct_4,k4_funct_4), []). 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_k5_funct_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( v1_funct_1(k5_funct_4(A,B,C,D,E)) & v1_funct_2(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) & m2_relset_1(k5_funct_4(A,B,C,D,E),k2_tarski(B,C),A) ) ) ), file(funct_4,k5_funct_4), []). 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_topreal1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k5_topreal1(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal1,k5_topreal1), []). fof(dt_k6_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k6_pre_topc), []). fof(dt_k7_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pre_topc,u1_pre_topc), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_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_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k1_sprect_1(A)) & v1_relat_1(k1_sprect_1(A)) & v1_funct_1(k1_sprect_1(A)) & v1_finset_1(k1_sprect_1(A)) & v1_finseq_1(k1_sprect_1(A)) & ~ v1_realset1(k1_sprect_1(A)) & ~ v5_seqm_3(k1_sprect_1(A)) & v1_topreal1(k1_sprect_1(A)) & v2_topreal1(k1_sprect_1(A)) & v1_finseq_6(k1_sprect_1(A),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_sprect_1(A)) & v2_goboard5(k1_sprect_1(A)) & v1_sprect_1(k1_sprect_1(A)) ) ) ), file(sprect_1,fc10_sprect_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(fc11_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k5_topreal1(2,A)) & v2_jordan1(k5_topreal1(2,A)) & v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) ) ) ), file(sprect_1,fc11_sprect_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(fc12_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ v1_xboole_0(k2_goboard9(A)) ) ), file(sprect_1,fc12_sprect_1), []). 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(fc13_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ v1_xboole_0(k3_goboard9(A)) ) ), file(sprect_1,fc13_sprect_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(fc1_pscomp_1,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) & ~ v1_setfam_1(k1_numbers) ), file(pscomp_1,fc1_pscomp_1), []). fof(fc1_revrot_1,axiom,( ! [A] : ( ( ~ v3_realset2(A) & l1_struct_0(A) ) => ( ~ v1_xboole_0(u1_struct_0(A)) & ~ v1_realset1(u1_struct_0(A)) ) ) ), file(revrot_1,fc1_revrot_1), []). fof(fc1_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) => v1_realset1(k2_relat_1(A)) ) ), file(sprect_1,fc1_sprect_1), []). fof(fc1_sprect_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k5_topreal1(2,A)) & ~ v1_sppol_1(k5_topreal1(2,A)) & ~ v2_sppol_1(k5_topreal1(2,A)) & v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) & v1_topreal2(k5_topreal1(2,A)) ) ) ), file(sprect_3,fc1_sprect_3), []). 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_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) ) ) ), file(euclid,fc2_euclid), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_pscomp_1,axiom, ( ~ v1_xboole_0(k5_ordinal2) & v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) & ~ v1_setfam_1(k5_ordinal2) ), file(pscomp_1,fc2_pscomp_1), []). fof(fc2_sprect_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & ~ v1_realset1(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) ) => ~ v1_xboole_0(k5_topreal1(A,B)) ) ), file(sprect_1,fc2_sprect_1), []). fof(fc2_sprect_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k2_goboard9(A)) & v2_topreal4(k2_goboard9(A),k15_euclid(2)) ) ) ), file(sprect_3,fc2_sprect_3), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_tops_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v4_pre_topc(k6_pre_topc(A,B),A) ) ), file(tops_1,fc2_tops_1), []). fof(fc3_jordan2c,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_tops_1(k5_topreal1(2,A),k15_euclid(2)) & v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) & v1_jordan2c(k5_topreal1(2,A),2) ) ) ), file(jordan2c,fc3_jordan2c), []). fof(fc3_revrot_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ( ~ v3_struct_0(k15_euclid(A)) & v1_pre_topc(k15_euclid(A)) & v2_pre_topc(k15_euclid(A)) & ~ v3_realset2(k15_euclid(A)) ) ) ), file(revrot_1,fc3_revrot_1), []). fof(fc3_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) ) ), file(sprect_1,fc3_sprect_1), []). fof(fc3_sprect_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k3_goboard9(A)) & v2_topreal4(k3_goboard9(A),k15_euclid(2)) ) ) ), file(sprect_3,fc3_sprect_3), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc4_gobrd14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k5_topreal1(2,A)) & v6_compts_1(k5_topreal1(2,A),k15_euclid(2)) & v2_connsp_1(k5_topreal1(2,A),k15_euclid(2)) & v2_jordan1(k5_topreal1(2,A)) & v1_jordan2c(k5_topreal1(2,A),2) & ~ v1_sppol_1(k5_topreal1(2,A)) & ~ v2_sppol_1(k5_topreal1(2,A)) & v1_topreal2(k5_topreal1(2,A)) & v2_tops_1(k5_topreal1(2,A),k15_euclid(2)) ) ) ), file(gobrd14,fc4_gobrd14), []). 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(fc5_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v2_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k1_sprect_1(A)) & v1_relat_1(k1_sprect_1(A)) & v1_funct_1(k1_sprect_1(A)) & v1_finset_1(k1_sprect_1(A)) & v1_finseq_1(k1_sprect_1(A)) & ~ v1_realset1(k1_sprect_1(A)) & ~ v5_seqm_3(k1_sprect_1(A)) ) ) ), file(sprect_1,fc5_sprect_1), []). 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(fc6_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k1_sprect_1(A)) & v1_relat_1(k1_sprect_1(A)) & v1_funct_1(k1_sprect_1(A)) & v1_finset_1(k1_sprect_1(A)) & v1_finseq_1(k1_sprect_1(A)) & ~ v1_realset1(k1_sprect_1(A)) & ~ v5_seqm_3(k1_sprect_1(A)) ) ) ), file(sprect_1,fc6_sprect_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ~ v1_xboole_0(k1_sprect_1(A)) & v1_relat_1(k1_sprect_1(A)) & v1_funct_1(k1_sprect_1(A)) & v1_finset_1(k1_sprect_1(A)) & v1_finseq_1(k1_sprect_1(A)) & ~ v1_realset1(k1_sprect_1(A)) & ~ v5_seqm_3(k1_sprect_1(A)) & v1_topreal1(k1_sprect_1(A)) & v2_topreal1(k1_sprect_1(A)) & v1_finseq_6(k1_sprect_1(A),u1_struct_0(k15_euclid(2))) & v1_goboard5(k1_sprect_1(A)) & v2_goboard5(k1_sprect_1(A)) ) ) ), file(sprect_1,fc7_sprect_1), []). 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_topreal6,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k1_rcomp_1(A,B)) & v2_membered(k1_rcomp_1(A,B)) & v1_seq_4(k1_rcomp_1(A,B)) & v2_seq_4(k1_rcomp_1(A,B)) & v3_seq_4(k1_rcomp_1(A,B)) & v1_rcomp_1(k1_rcomp_1(A,B)) & v2_rcomp_1(k1_rcomp_1(A,B)) ) ) ), file(topreal6,fc8_topreal6), []). 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_sprect_1,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k1_rcomp_1(A,B)) & v2_membered(k1_rcomp_1(A,B)) & v3_seq_4(k1_rcomp_1(A,B)) ) ) ), file(sprect_1,fc9_sprect_1), []). fof(fraenkel_a_1_5_gobrd14,axiom,( ! [A,B] : ( ( v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_5_gobrd14(B)) <=> ? [C] : ( m1_subset_1(C,k1_numbers) & A = C & r1_xreal_0(k18_pscomp_1(k5_topreal1(2,k1_sprect_1(B))),C) & r1_xreal_0(C,k20_pscomp_1(k5_topreal1(2,k1_sprect_1(B)))) ) ) ) ), file(gobrd14,a_1_5_gobrd14), []). fof(fraenkel_a_1_5_sprect_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & v1_sprect_1(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_5_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ ( r1_xreal_0(k18_pscomp_1(k5_topreal1(2,B)),k21_euclid(C)) & r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(2,B))) & r1_xreal_0(k21_pscomp_1(k5_topreal1(2,B)),k22_euclid(C)) & r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(2,B))) ) ) ) ) ), file(sprect_3,a_1_5_sprect_3), []). fof(fraenkel_a_1_6_gobrd14,axiom,( ! [A,B] : ( ( v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_6_gobrd14(B)) <=> ? [C] : ( m1_subset_1(C,k1_numbers) & A = C & r1_xreal_0(k21_pscomp_1(k5_topreal1(2,k1_sprect_1(B))),C) & r1_xreal_0(C,k19_pscomp_1(k5_topreal1(2,k1_sprect_1(B)))) ) ) ) ), file(gobrd14,a_1_6_gobrd14), []). fof(fraenkel_a_1_6_sprect_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & v1_sprect_1(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_6_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xreal_0(k21_euclid(C),k18_pscomp_1(k5_topreal1(2,B))) & ~ r1_xreal_0(k20_pscomp_1(k5_topreal1(2,B)),k21_euclid(C)) & ~ r1_xreal_0(k22_euclid(C),k21_pscomp_1(k5_topreal1(2,B))) & ~ r1_xreal_0(k19_pscomp_1(k5_topreal1(2,B)),k22_euclid(C)) ) ) ) ), file(sprect_3,a_1_6_sprect_3), []). fof(fraenkel_a_1_7_gobrd14,axiom,( ! [A,B] : ( ( v6_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_7_gobrd14(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ ( r1_xreal_0(k18_pscomp_1(k5_topreal1(2,k1_sprect_1(B))),k21_euclid(C)) & r1_xreal_0(k21_euclid(C),k20_pscomp_1(k5_topreal1(2,k1_sprect_1(B)))) & r1_xreal_0(k21_pscomp_1(k5_topreal1(2,k1_sprect_1(B))),k22_euclid(C)) & r1_xreal_0(k22_euclid(C),k19_pscomp_1(k5_topreal1(2,k1_sprect_1(B)))) ) ) ) ) ), file(gobrd14,a_1_7_gobrd14), []). fof(fraenkel_a_2_0_rcomp_1,axiom,( ! [A,B,C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_rcomp_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & A = D & r1_xreal_0(B,D) & r1_xreal_0(D,C) ) ) ) ), file(rcomp_1,a_2_0_rcomp_1), []). fof(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). 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(rc1_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_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_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) ), file(pre_topc,rc1_pre_topc), []). fof(rc1_pscomp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(pscomp_1,rc1_pscomp_1), []). fof(rc1_revrot_1,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & ~ v5_seqm_3(B) & v1_finset_1(B) & v1_finseq_1(B) & v1_finseq_6(B,A) & ~ v1_realset1(B) ) ) ), file(revrot_1,rc1_revrot_1), []). fof(rc1_sprect_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v5_seqm_3(A) ) ), file(sprect_1,rc1_sprect_1), []). fof(rc1_sprect_3,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_realset1(A) & v1_sprect_1(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) ) ), file(sprect_3,rc1_sprect_3), []). 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_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) ) ) ), file(tops_1,rc1_tops_1), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) ), file(pre_topc,rc2_pre_topc), []). fof(rc2_pscomp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) ), file(pscomp_1,rc2_pscomp_1), []). fof(rc2_sprect_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v6_compts_1(A,k15_euclid(2)) ) ), file(sprect_1,rc2_sprect_1), []). fof(rc2_sprect_3,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_sprect_2(A) & ~ v1_realset1(A) & v1_sprect_1(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) ) ), file(sprect_3,rc2_sprect_3), []). 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_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc2_tops_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_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v1_setfam_1(A) ) ), file(pscomp_1,rc3_pscomp_1), []). fof(rc3_sprect_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v1_seq_4(A) & v2_seq_4(A) ) ), file(sprect_1,rc3_sprect_1), []). fof(rc3_tops_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc3_tops_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_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & ~ v1_setfam_1(A) ) ), file(pscomp_1,rc4_pscomp_1), []). fof(rc4_sprect_1,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_sprect_1(A) ) ), file(sprect_1,rc4_sprect_1), []). fof(rc4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) ) ) ), file(tops_1,rc4_tops_1), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_pscomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_seq_4(A) & v2_rcomp_1(A) ) ), file(pscomp_1,rc5_pscomp_1), []). fof(rc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ), file(tops_1,rc5_tops_1), []). fof(rc6_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) ) ) ), file(pre_topc,rc6_pre_topc), []). fof(rc7_pre_topc,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v4_pre_topc(B,A) ) ) ), file(pre_topc,rc7_pre_topc), []). fof(rc9_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v6_compts_1(B,A) ) ) ), file(pscomp_1,rc9_pscomp_1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_finseq_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k2_finseq_4(A,B,C) = k10_finseq_1(B,C) ) ), file(finseq_4,k2_finseq_4), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_finseq_4,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) ) => k3_finseq_4(A,B,C,D) = k11_finseq_1(B,C,D) ) ), file(finseq_4,k3_finseq_4), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_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_funct_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => k5_funct_4(A,B,C,D,E) = k4_funct_4(B,C,D,E) ) ), file(funct_4,k5_funct_4), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(t18_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k4_card_3(B)) <=> ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(B)) => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ), file(card_3,t18_card_3), []). 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_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(t26_gobrd14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k5_topreal1(2,A)) <=> ( ~ r2_hidden(B,k2_goboard9(A)) & ~ r2_hidden(B,k3_goboard9(A)) ) ) ) ) ), file(gobrd14,t26_gobrd14), []). fof(t29_finseq_3,axiom,( ! [A,B] : k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(2) ), file(finseq_3,t29_finseq_3), []). 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(t31_gobrd14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v5_seqm_3(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & v2_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k6_pre_topc(k15_euclid(2),k3_goboard9(A)) = k4_subset_1(u1_struct_0(k15_euclid(2)),k3_goboard9(A),k5_topreal1(2,A)) ) ), file(gobrd14,t31_gobrd14), []). fof(t33_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & v1_sprect_2(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ~ ( r2_hidden(A,k3_goboard9(B)) & r1_xreal_0(k21_euclid(A),k18_pscomp_1(k5_topreal1(2,B))) ) ) ) ), file(gobrd14,t33_gobrd14), []). fof(t34_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & v1_sprect_2(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ~ ( r2_hidden(A,k3_goboard9(B)) & r1_xreal_0(k20_pscomp_1(k5_topreal1(2,B)),k21_euclid(A)) ) ) ) ), file(gobrd14,t34_gobrd14), []). fof(t35_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & v1_sprect_2(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ~ ( r2_hidden(A,k3_goboard9(B)) & r1_xreal_0(k19_pscomp_1(k5_topreal1(2,B)),k22_euclid(A)) ) ) ) ), file(gobrd14,t35_gobrd14), []). fof(t36_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v5_seqm_3(B) & v1_topreal1(B) & v2_topreal1(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_goboard5(B) & v2_goboard5(B) & v1_sprect_2(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ~ ( r2_hidden(A,k3_goboard9(B)) & r1_xreal_0(k22_euclid(A),k21_pscomp_1(k5_topreal1(2,B))) ) ) ) ), file(gobrd14,t36_gobrd14), []). 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(t48_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k1_rcomp_1(A,B)) <=> ( r1_xreal_0(A,C) & r1_xreal_0(C,B) ) ) ) ) ) ), file(rcomp_1,t48_rcomp_1), []). fof(t4_finseq_1,axiom, ( k2_finseq_1(0) = k1_xboole_0 & k2_finseq_1(1) = k1_tarski(1) & k2_finseq_1(2) = k2_tarski(1,2) ), file(finseq_1,t4_finseq_1), []). 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(t54_sprect_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_sprect_1(A) & v1_topreal1(A) & v2_topreal1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( k2_goboard9(A) = a_1_5_sprect_3(A) & k3_goboard9(A) = a_1_6_sprect_3(A) ) ) ), file(sprect_3,t54_sprect_3), []). fof(t55_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & A = k10_finseq_1(B,C) ) ) ) ), file(euclid,t55_euclid), []). fof(t56_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k21_euclid(k23_euclid(A,B)) = A & k22_euclid(k23_euclid(A,B)) = B ) ) ) ), file(euclid,t56_euclid), []). 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(t61_finseq_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k10_finseq_1(A,B) <=> ( k3_finseq_1(C) = 2 & k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) ) ) ), file(finseq_1,t61_finseq_1), []). fof(t65_funct_4,axiom,( ! [A,B,C,D] : ( k1_relat_1(k4_funct_4(A,B,C,D)) = k2_tarski(A,B) & r1_tarski(k2_relat_1(k4_funct_4(A,B,C,D)),k2_tarski(C,D)) ) ), file(funct_4,t65_funct_4), []). fof(t66_funct_4,axiom,( ! [A,B,C,D] : ( A != B => ( k1_funct_1(k4_funct_4(A,B,C,D),A) = C & k1_funct_1(k4_funct_4(A,B,C,D),B) = D ) ) ), file(funct_4,t66_funct_4), []). 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(t71_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & v6_compts_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,B) => ( r1_xreal_0(k18_pscomp_1(B),k21_euclid(A)) & r1_xreal_0(k21_euclid(A),k20_pscomp_1(B)) & r1_xreal_0(k21_pscomp_1(B),k22_euclid(A)) & r1_xreal_0(k22_euclid(A),k19_pscomp_1(B)) ) ) ) ) ), file(pscomp_1,t71_pscomp_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( 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) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []).