% Mizar problem: t75_jordan,jordan,3137,35 fof(t75_jordan,conjecture,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( v1_xreal_0(C) & v2_xreal_0(C) ) => ( r2_hidden(B,k1_topreal9(2,A,C)) => v5_pre_topc(k10_jordan(2,A,B,C),k7_toprealb(2,A,C),k7_toprealb(2,A,C)) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_metric_1,abstractness_v1_pre_topc,antisymmetry_r2_hidden,cc10_isomichi,cc10_membered,cc10_topreal6,cc10_yellow13,cc11_isomichi,cc11_membered,cc11_topreal6,cc11_yellow13,cc12_isomichi,cc12_membered,cc13_isomichi,cc13_membered,cc14_isomichi,cc14_membered,cc15_isomichi,cc15_membered,cc16_isomichi,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_borsuk_4,cc1_funct_1,cc1_funct_2,cc1_isomichi,cc1_jordan,cc1_jordan21,cc1_jordan2c,cc1_membered,cc1_nat_1,cc1_partfun3,cc1_pre_topc,cc1_realset1,cc1_relset_1,cc1_seq_1,cc1_sprect_4,cc1_tex_4,cc1_topreal6,cc1_topreala,cc1_toprealb,cc1_tops_1,cc1_xreal_0,cc1_yellow13,cc20_membered,cc2_funct_1,cc2_funct_2,cc2_isomichi,cc2_jordan,cc2_jordan21,cc2_membered,cc2_nat_1,cc2_partfun3,cc2_pscomp_1,cc2_tex_4,cc2_topgrp_1,cc2_topreal6,cc2_topreala,cc2_tops_1,cc2_xreal_0,cc2_yellow13,cc3_borsuk_2,cc3_funct_2,cc3_isomichi,cc3_jordan,cc3_membered,cc3_nat_1,cc3_pscomp_1,cc3_tex_4,cc3_topreal6,cc3_topreala,cc3_tops_1,cc3_xreal_0,cc3_yellow13,cc4_borsuk_2,cc4_isomichi,cc4_jordan,cc4_membered,cc4_tex_4,cc4_topgrp_1,cc4_topreal6,cc4_topreala,cc4_tops_1,cc4_xreal_0,cc4_yellow13,cc5_funct_2,cc5_isomichi,cc5_jordan,cc5_tex_4,cc5_topreal6,cc5_tops_1,cc5_xreal_0,cc5_yellow13,cc6_funct_2,cc6_isomichi,cc6_membered,cc6_tex_4,cc6_topreal6,cc6_tops_1,cc6_xreal_0,cc6_yellow13,cc7_isomichi,cc7_tex_4,cc7_topreal6,cc7_waybel_3,cc7_xreal_0,cc7_yellow13,cc8_isomichi,cc8_tex_4,cc8_topreal6,cc8_xreal_0,cc8_yellow13,cc9_isomichi,cc9_membered,cc9_topreal6,cc9_yellow13,commutativity_k12_partfun3,commutativity_k14_partfun3,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_seq_1,commutativity_k3_xboole_0,commutativity_k3_xcmplx_0,commutativity_k4_real_1,commutativity_k5_seq_1,connectedness_r1_xreal_0,d16_euclid,d1_euclid,d1_funct_2,d1_jordan,d1_partfun3,d1_tarski,d1_xreal_0,d26_pscomp_1,d2_jordan,d2_topreala,d2_zfmisc_1,d3_jordan,d3_partfun3,d3_seq_1,d3_square_1,d3_tarski,d3_xboole_0,d4_jordan,d4_rfunct_1,d4_seq_1,d4_tarski,d4_tops_2,d5_funct_1,d5_jordan,d5_partfun3,d5_seq_1,d5_tarski,d5_tops_2,d6_jordan,d6_toprealb,d7_euclid,d7_seq_1,d8_euclid,d8_jordan,d9_xcmplx_0,dt_g1_metric_1,dt_g1_pre_topc,dt_k10_finseq_1,dt_k10_jordan,dt_k10_relat_1,dt_k12_mcart_1,dt_k12_partfun3,dt_k13_euclid,dt_k13_funct_3,dt_k13_partfun3,dt_k14_euclid,dt_k14_funct_3,dt_k14_partfun3,dt_k15_euclid,dt_k15_partfun3,dt_k15_pscomp_1,dt_k15_seq_1,dt_k17_partfun3,dt_k1_borsuk_1,dt_k1_euclid,dt_k1_funct_1,dt_k1_jordan,dt_k1_mcart_1,dt_k1_numbers,dt_k1_partfun1,dt_k1_partfun3,dt_k1_pscomp_1,dt_k1_real_1,dt_k1_relat_1,dt_k1_rfunct_1,dt_k1_seq_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_topreal9,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_euclid,dt_k20_partfun3,dt_k21_euclid,dt_k22_euclid,dt_k23_euclid,dt_k2_brouwer,dt_k2_funcop_1,dt_k2_funct_1,dt_k2_funct_2,dt_k2_jordan,dt_k2_mcart_1,dt_k2_pre_topc,dt_k2_real_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_topreal9,dt_k2_topreala,dt_k2_tops_2,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_brouwer,dt_k3_jordan,dt_k3_pre_topc,dt_k3_real_1,dt_k3_seq_1,dt_k3_tarski,dt_k3_topalg_2,dt_k3_topmetr,dt_k3_topreal9,dt_k3_xboole_0,dt_k3_xcmplx_0,dt_k4_finseq_2,dt_k4_jordan,dt_k4_pre_topc,dt_k4_real_1,dt_k4_relset_1,dt_k4_seq_1,dt_k4_tarski,dt_k4_xboole_0,dt_k4_xcmplx_0,dt_k5_jordan,dt_k5_numbers,dt_k5_ordinal2,dt_k5_pcomps_1,dt_k5_real_1,dt_k5_relat_1,dt_k5_seq_1,dt_k5_setfam_1,dt_k5_square_1,dt_k5_toprns_1,dt_k5_xcmplx_0,dt_k6_borsuk_1,dt_k6_jordan,dt_k6_partfun1,dt_k6_relat_1,dt_k6_xcmplx_0,dt_k7_borsuk_1,dt_k7_funct_2,dt_k7_jordan,dt_k7_relat_1,dt_k7_square_1,dt_k7_toprealb,dt_k7_xcmplx_0,dt_k8_borsuk_1,dt_k8_funct_2,dt_k8_jordan,dt_k8_square_1,dt_k9_relat_1,dt_k9_square_1,dt_l1_metric_1,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_finseq_2,dt_m1_pre_topc,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_metric_1,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_metric_1,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_finseq_2,existence_m1_pre_topc,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_subset_1,fc10_jordan,fc10_membered,fc10_partfun3,fc10_pscomp_1,fc10_xreal_0,fc11_membered,fc11_partfun3,fc11_xreal_0,fc12_membered,fc12_partfun3,fc12_xreal_0,fc13_jordan,fc13_membered,fc13_partfun3,fc13_xreal_0,fc14_jordan,fc14_membered,fc14_partfun3,fc14_topreal9,fc14_xreal_0,fc15_membered,fc15_partfun3,fc15_topreal9,fc15_xreal_0,fc16_jordan,fc16_membered,fc16_partfun3,fc16_xreal_0,fc17_jordan,fc17_partfun3,fc17_xreal_0,fc18_jordan,fc18_partfun3,fc18_xreal_0,fc19_jordan,fc19_partfun3,fc19_toprealb,fc19_xreal_0,fc1_euclid,fc1_funct_1,fc1_jordan2c,fc1_jordan5a,fc1_nat_1,fc1_partfun3,fc1_pscomp_1,fc1_seq_1,fc1_square_1,fc1_struct_0,fc1_subset_1,fc1_topreal6,fc1_topreal9,fc1_waybel_2,fc1_xreal_0,fc1_yellow13,fc20_jordan,fc20_partfun3,fc20_toprealb,fc20_xreal_0,fc21_jordan,fc21_partfun3,fc21_toprealb,fc21_xreal_0,fc22_partfun3,fc22_toprealb,fc22_xreal_0,fc23_partfun3,fc23_xreal_0,fc24_partfun3,fc24_xreal_0,fc25_partfun3,fc25_toprealb,fc25_xreal_0,fc26_partfun3,fc26_xreal_0,fc27_membered,fc27_partfun3,fc27_xreal_0,fc28_membered,fc28_partfun3,fc28_xreal_0,fc29_membered,fc29_partfun3,fc29_xreal_0,fc2_borsuk_1,fc2_euclid,fc2_funct_1,fc2_isomichi,fc2_membered,fc2_nat_1,fc2_partfun3,fc2_pre_topc,fc2_pscomp_1,fc2_seq_1,fc2_square_1,fc2_subset_1,fc2_topalg_5,fc2_topmetr,fc2_topreal9,fc2_xreal_0,fc2_yellow13,fc30_membered,fc30_partfun3,fc30_xreal_0,fc31_membered,fc31_partfun3,fc32_membered,fc32_partfun3,fc33_membered,fc33_partfun3,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_brouwer,fc3_jordan,fc3_nat_1,fc3_partfun3,fc3_pre_topc,fc3_pscomp_1,fc3_realset1,fc3_seq_1,fc3_subset_1,fc3_topalg_5,fc3_topgen_3,fc3_topmetr,fc3_topreal9,fc3_xreal_0,fc3_yellow13,fc40_membered,fc41_membered,fc43_partfun3,fc44_partfun3,fc45_partfun3,fc46_partfun3,fc47_partfun3,fc48_partfun3,fc49_partfun3,fc4_borsuk_2,fc4_brouwer,fc4_funct_1,fc4_nat_1,fc4_partfun3,fc4_pre_topc,fc4_seq_1,fc4_subset_1,fc4_topgen_3,fc4_topreal9,fc4_xreal_0,fc50_partfun3,fc51_partfun3,fc52_partfun3,fc58_partfun3,fc59_partfun3,fc5_borsuk_2,fc5_membered,fc5_partfun3,fc5_pre_topc,fc5_seq_1,fc5_topreal9,fc5_xreal_0,fc60_partfun3,fc61_partfun3,fc62_partfun3,fc6_borsuk_2,fc6_funct_1,fc6_membered,fc6_partfun3,fc6_topgrp_1,fc6_topreal9,fc6_xreal_0,fc70_partfun3,fc71_partfun3,fc72_partfun3,fc7_membered,fc7_partfun3,fc7_seq_1,fc7_topreal6,fc7_topreal9,fc7_xreal_0,fc8_membered,fc8_partfun3,fc8_topreal9,fc8_tops_1,fc8_xreal_0,fc9_membered,fc9_partfun3,fc9_pscomp_1,fc9_topreal9,fc9_tops_1,fc9_xreal_0,free_g1_metric_1,free_g1_pre_topc,idempotence_k3_xboole_0,involutiveness_k1_real_1,involutiveness_k2_real_1,involutiveness_k4_xcmplx_0,involutiveness_k5_xcmplx_0,irreflexivity_r1_subset_1,l30_jordan,l31_jordan,l32_jordan,rc10_pscomp_1,rc1_borsuk_2,rc1_borsuk_4,rc1_funct_1,rc1_funct_2,rc1_isomichi,rc1_jordan,rc1_jordan1a,rc1_jordan21,rc1_jordan5a,rc1_membered,rc1_metric_1,rc1_nat_1,rc1_partfun3,rc1_pre_topc,rc1_pscomp_1,rc1_realset1,rc1_seq_1,rc1_subset_1,rc1_tex_4,rc1_topgen_3,rc1_topgrp_1,rc1_topreal6,rc1_topreala,rc1_toprealb,rc1_tops_1,rc1_xreal_0,rc2_borsuk_1,rc2_borsuk_4,rc2_funct_1,rc2_funct_2,rc2_isomichi,rc2_jordan,rc2_jordan1a,rc2_metric_1,rc2_nat_1,rc2_partfun3,rc2_pre_topc,rc2_pscomp_1,rc2_realset1,rc2_subset_1,rc2_tex_4,rc2_topgrp_1,rc2_topreal6,rc2_tops_1,rc2_xreal_0,rc3_borsuk_1,rc3_borsuk_2,rc3_borsuk_4,rc3_funct_1,rc3_isomichi,rc3_jordan,rc3_jordan1a,rc3_metric_1,rc3_nat_1,rc3_partfun3,rc3_pre_topc,rc3_pscomp_1,rc3_struct_0,rc3_tops_1,rc3_xreal_0,rc4_borsuk_1,rc4_isomichi,rc4_partfun3,rc4_pre_topc,rc4_pscomp_1,rc4_rcomp_3,rc4_topgrp_1,rc4_tops_1,rc4_waybel_3,rc4_xreal_0,rc4_yellow13,rc5_funct_1,rc5_partfun3,rc5_pre_topc,rc5_rcomp_3,rc5_struct_0,rc5_topgrp_1,rc5_tops_1,rc6_pre_topc,rc6_topgrp_1,rc7_isomichi,rc7_pre_topc,rc7_pscomp_1,rc8_pscomp_1,rc9_pscomp_1,redefinition_k12_mcart_1,redefinition_k12_partfun3,redefinition_k13_partfun3,redefinition_k14_funct_3,redefinition_k14_partfun3,redefinition_k15_partfun3,redefinition_k17_partfun3,redefinition_k1_borsuk_1,redefinition_k1_jordan,redefinition_k1_partfun1,redefinition_k1_pscomp_1,redefinition_k1_real_1,redefinition_k1_seq_1,redefinition_k1_struct_0,redefinition_k20_partfun3,redefinition_k2_funct_2,redefinition_k2_jordan,redefinition_k2_real_1,redefinition_k3_real_1,redefinition_k3_topalg_2,redefinition_k4_pre_topc,redefinition_k4_real_1,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k5_setfam_1,redefinition_k6_partfun1,redefinition_k7_borsuk_1,redefinition_k7_funct_2,redefinition_k7_square_1,redefinition_k8_borsuk_1,redefinition_k8_funct_2,redefinition_k9_square_1,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r1_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc2_boole,spc2_numerals,symmetry_r1_subset_1,symmetry_r1_xboole_0,t106_zfmisc_1,t116_funct_2,t11_topreal3,t11_xreal_1,t12_pre_topc,t13_funcop_1,t156_relat_1,t16_topreal9,t17_topreal9,t17_xboole_1,t19_topreal9,t1_arithm,t1_jordan1,t1_numerals,t1_partfun3,t1_real,t1_subset,t20_jgraph_2,t21_funct_2,t23_funct_1,t23_mcart_1,t24_topmetr,t25_topgrp_1,t27_xboole_1,t2_arithm,t2_boole,t2_complex1,t2_real,t2_subset,t2_topmetr,t32_tops_2,t33_zfmisc_1,t35_funct_1,t3_boole,t3_brouwer,t3_real,t3_subset,t3_xboole_0,t41_yellow12,t43_funct_2,t45_borsuk_1,t46_jgraph_1,t46_relat_1,t4_arithm,t4_boole,t4_real,t4_subset,t55_relat_1,t56_topreala,t5_arithm,t5_real,t5_subset,t62_tops_2,t65_tops_2,t69_funct_3,t6_boole,t6_real,t70_tops_2,t71_relat_1,t72_funct_1,t77_square_1,t7_boole,t7_funct_2,t7_real,t83_topreal6,t8_boole,t8_brouwer,t8_real,t8_topreal3,t8_topreal9,t92_zfmisc_1,t9_funct_1,t9_xreal_1]), [file(jordan,t75_jordan)]). fof(abstractness_v1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v1_metric_1(A) => A = g1_metric_1(u1_struct_0(A),u1_metric_1(A)) ) ) ), file(metric_1,v1_metric_1), []). 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_isomichi,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) & v4_tops_1(B,A) ) => ( v4_pre_topc(B,A) & v5_tops_1(B,A) ) ) ) ) ), file(isomichi,cc10_isomichi), []). 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(cc10_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v3_compts_1(A) ) => ( v2_pre_topc(A) & v1_urysohn1(A) ) ) ) ), file(yellow13,cc10_yellow13), []). fof(cc11_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_isomichi(B,A) => ( ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc11_isomichi), []). 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(cc11_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_urysohn1(A) ) => ( v2_pre_topc(A) & v2_t_0topsp(A) ) ) ) ), file(yellow13,cc11_yellow13), []). fof(cc12_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_isomichi(B,A) => ( ~ v3_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc12_isomichi), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_isomichi(B,A) => ( ~ v3_isomichi(B,A) & ~ v4_isomichi(B,A) ) ) ) ) ), file(isomichi,cc13_isomichi), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_isomichi(B,A) => ( v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc14_isomichi), []). 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_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => ( v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc15_isomichi), []). 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_isomichi,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_isomichi(B,A) & v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) ), file(isomichi,cc16_isomichi), []). 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_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_xboole_0(A) & ~ v1_realset1(A) & v1_topreal2(A) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) ) ) ) ), file(borsuk_4,cc1_borsuk_4), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) => ( v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) ), file(isomichi,cc1_isomichi), []). fof(cc1_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( ~ v1_xboole_0(A) & v6_compts_1(A,k15_euclid(2)) & v2_sppol_1(A) ) => ( ~ v1_xboole_0(A) & v1_jordan21(A) ) ) ) ), file(jordan,cc1_jordan), []). fof(cc1_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_jordan21(A) => ~ v1_xboole_0(A) ) ) ), file(jordan21,cc1_jordan21), []). 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_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_partfun3(A) ) => ( v1_relat_1(A) & v2_relat_1(A) & v4_partfun3(A) ) ) ), file(partfun3,cc1_partfun3), []). fof(cc1_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_pre_topc(B) ) ) ), file(pre_topc,cc1_pre_topc), []). fof(cc1_realset1,axiom,( ! [A] : ( ~ v1_realset1(A) => ~ v1_xboole_0(A) ) ), file(realset1,cc1_realset1), []). 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_seq_1,axiom,( ! [A,B] : ( v2_membered(B) => ! [C] : ( m1_relset_1(C,A,B) => ( v1_funct_1(C) => ( v1_funct_1(C) & v1_seq_1(C) ) ) ) ) ), file(seq_1,cc1_seq_1), []). fof(cc1_sprect_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_compts_1(B,A) => v4_pre_topc(B,A) ) ) ) ), file(sprect_4,cc1_sprect_4), []). fof(cc1_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_4(B,A) => ( v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) ) ) ) ) ), file(tex_4,cc1_tex_4), []). 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_topreala,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_monoid_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_pre_topc(B) & v1_monoid_0(B) & v2_monoid_0(B) ) ) ) ), file(topreala,cc1_topreala), []). fof(cc1_toprealb,axiom,( ! [A] : ( m1_pre_topc(A,k15_euclid(2)) => ( v1_toprealb(A) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v10_pscomp_1(A) & v1_borsuk_2(A) & v1_monoid_0(A) & v2_monoid_0(A) ) ) ) ), file(toprealb,cc1_toprealb), []). 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(cc1_yellow13,axiom,( ! [A] : ( v1_realset1(A) => v1_finset_1(A) ) ), file(yellow13,cc1_yellow13), []). 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_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). fof(cc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_isomichi(B,A) & v2_isomichi(B,A) ) => v4_tops_1(B,A) ) ) ) ), file(isomichi,cc2_isomichi), []). fof(cc2_jordan,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_xboole_0(B) => v1_jordan2c(B,A) ) ) ) ), file(jordan,cc2_jordan), []). fof(cc2_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & ~ v1_realset1(A) & v1_topreal2(A) & v1_jordan21(A) ) ) ) ), file(jordan21,cc2_jordan21), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_1), []). fof(cc2_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_partfun3(A) ) => ( v1_relat_1(A) & v2_relat_1(A) & v3_partfun3(A) ) ) ), file(partfun3,cc2_partfun3), []). fof(cc2_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v10_pscomp_1(A) ) ) ) ), file(pscomp_1,cc2_pscomp_1), []). fof(cc2_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_tdlat_3(B) => ~ v4_tex_4(B,A) ) ) ) ), file(tex_4,cc2_tex_4), []). fof(cc2_topgrp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_tops_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v3_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v1_t_0topsp(C,A,B) ) ) ) ) ), file(topgrp_1,cc2_topgrp_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_topreala,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v3_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) ) ) ) ), file(topreala,cc2_topreala), []). 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(cc2_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_realset2(A) => v6_group_1(A) ) ) ), file(yellow13,cc2_yellow13), []). fof(cc3_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(A) ) ) ) ), file(borsuk_2,cc3_borsuk_2), []). fof(cc3_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_2), []). fof(cc3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => v1_decomp_1(B,A) ) ) ) ), file(isomichi,cc3_isomichi), []). fof(cc3_jordan,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ~ v1_jordan2c(B,A) => ~ v1_xboole_0(B) ) ) ) ), file(jordan,cc3_jordan), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). fof(cc3_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v10_pscomp_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) ) => ( ~ v1_xboole_0(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_seq_1(B) & v3_seq_2(B) & v1_partfun1(B,u1_struct_0(A),k1_numbers) & v7_pscomp_1(B,u1_struct_0(A)) & v8_pscomp_1(B,u1_struct_0(A)) ) ) ) ) ), file(pscomp_1,cc3_pscomp_1), []). fof(cc3_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_tsep_1(B,A) & v2_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc3_tex_4), []). fof(cc3_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( ~ v1_xboole_0(A) & v1_jordan1(A,2) ) => v2_connsp_1(A,k15_euclid(2)) ) ) ), file(topreal6,cc3_topreal6), []). fof(cc3_topreala,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) ) ) ) ) ), file(topreala,cc3_topreala), []). 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(cc3_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v3_realset2(A) => ~ v3_struct_0(A) ) ) ), file(yellow13,cc3_yellow13), []). fof(cc4_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( v3_struct_0(A) => v2_t_0topsp(A) ) ) ), file(borsuk_2,cc4_borsuk_2), []). fof(cc4_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_decomp_1(B,A) => v2_isomichi(B,A) ) ) ) ), file(isomichi,cc4_isomichi), []). fof(cc4_jordan,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_jordan2c(B,A) => v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) ) ), file(jordan,cc4_jordan), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_tsep_1(B,A) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & ~ v3_realset2(B) & v2_pre_topc(B) & ~ v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc4_tex_4), []). fof(cc4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v1_topgrp_1(A) ) ) ) ), file(topgrp_1,cc4_topgrp_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_topreala,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) ) ) ) ) ), file(topreala,cc4_topreala), []). 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(cc4_yellow13,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v4_pre_topc(B,A) ) ) ) ), file(yellow13,cc4_yellow13), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tops_1(B,A) => v3_pre_topc(B,A) ) ) ) ), file(isomichi,cc5_isomichi), []). fof(cc5_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_struct_0(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v3_compts_1(B) ) ) ) ) ), file(jordan,cc5_jordan), []). fof(cc5_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_tsep_1(B,A) & v2_tex_2(B,A) ) ) ) ) ), file(tex_4,cc5_tex_4), []). 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(cc5_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & v6_group_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) ) ) ) ), file(yellow13,cc5_yellow13), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_tops_1(B,A) => v4_pre_topc(B,A) ) ) ) ), file(isomichi,cc6_isomichi), []). 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_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_borsuk_1(B,A) & v2_tdlat_3(B) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc6_tex_4), []). 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(cc6_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v6_group_1(A) ) => ( v2_pre_topc(A) & v2_compts_1(A) ) ) ) ), file(yellow13,cc6_yellow13), []). fof(cc7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tops_1(B,A) => ( v3_pre_topc(B,A) & v4_tops_1(B,A) & v1_decomp_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) ), file(isomichi,cc7_isomichi), []). fof(cc7_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v1_borsuk_1(B,A) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & ~ v3_realset2(B) & v2_pre_topc(B) & ~ v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) ) ) ) ), file(tex_4,cc7_tex_4), []). 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_waybel_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v3_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v4_compts_1(A) & v5_compts_1(A) & v6_waybel_3(A) ) ) ) ), file(waybel_3,cc7_waybel_3), []). 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(cc7_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) => ( v2_pre_topc(A) & v1_urysohn1(A) & v3_compts_1(A) & v4_compts_1(A) & v5_compts_1(A) ) ) ) ), file(yellow13,cc7_yellow13), []). fof(cc8_isomichi,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_tops_1(B,A) ) => ( v3_pre_topc(B,A) & v6_tops_1(B,A) ) ) ) ) ), file(isomichi,cc8_isomichi), []). fof(cc8_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v3_struct_0(B) & v2_tdlat_3(B) & ~ v4_tex_4(B,A) ) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & ~ v1_borsuk_1(B,A) & v2_tex_2(B,A) ) ) ) ) ), file(tex_4,cc8_tex_4), []). 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(cc8_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & v5_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v4_compts_1(A) ) ) ) ), file(yellow13,cc8_yellow13), []). fof(cc9_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_tops_1(B,A) => ( v4_pre_topc(B,A) & v4_tops_1(B,A) & v1_decomp_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) ), file(isomichi,cc9_isomichi), []). 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(cc9_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_urysohn1(A) & v4_compts_1(A) ) => ( v2_pre_topc(A) & v3_compts_1(A) ) ) ) ), file(yellow13,cc9_yellow13), []). fof(commutativity_k12_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => k12_partfun3(A,B,C) = k12_partfun3(A,C,B) ) ), file(partfun3,k12_partfun3), []). fof(commutativity_k14_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => k14_partfun3(A,B,C) = k14_partfun3(A,C,B) ) ), file(partfun3,k14_partfun3), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(commutativity_k3_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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => k3_seq_1(A,B) = k3_seq_1(B,A) ) ), file(seq_1,k3_seq_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_k5_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => k5_seq_1(A,B) = k5_seq_1(B,A) ) ), file(seq_1,k5_seq_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(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_euclid,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k1_euclid(A) = k4_finseq_2(A,k1_numbers) ) ), file(euclid,d1_euclid), []). 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_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) => ( B = k3_jordan(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2)))) => k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers,B,C) = k5_real_1(k21_euclid(k2_jordan(k15_euclid(2),k15_euclid(2),C)),k21_euclid(A)) ) ) ) ) ), file(jordan,d1_jordan), []). fof(d1_partfun3,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_partfun3(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,k2_relat_1(A)) & r1_xreal_0(B,0) ) ) ) ) ), file(partfun3,d1_partfun3), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) <=> r2_hidden(A,k1_numbers) ) ), file(xreal_0,d1_xreal_0), []). fof(d26_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & m2_relset_1(C,u1_struct_0(A),k1_numbers) ) => k15_pscomp_1(A,B,C) = k7_relat_1(C,B) ) ) ) ), file(pscomp_1,d26_pscomp_1), []). fof(d2_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) => ( B = k4_jordan(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2)))) => k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers,B,C) = k5_real_1(k22_euclid(k2_jordan(k15_euclid(2),k15_euclid(2),C)),k22_euclid(A)) ) ) ) ) ), file(jordan,d2_jordan), []). fof(d2_topreala,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2))) & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2))) ) => ( A = k2_topreala <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) ) ) ), file(topreala,d2_topreala), []). fof(d2_zfmisc_1,axiom,( ! [A,B,C] : ( C = k2_zfmisc_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E,F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k4_tarski(E,F) ) ) ) ), file(zfmisc_1,d2_zfmisc_1), []). fof(d3_jordan,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) => ( A = k5_jordan <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2)))) => k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers,A,B) = k5_real_1(k21_euclid(k1_jordan(k15_euclid(2),k15_euclid(2),B)),k21_euclid(k2_jordan(k15_euclid(2),k15_euclid(2),B))) ) ) ) ), file(jordan,d3_jordan), []). fof(d3_partfun3,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_partfun3(A) <=> ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k2_relat_1(A)) => r1_xreal_0(B,0) ) ) ) ) ), file(partfun3,d3_partfun3), []). fof(d3_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_seq_1(A,B) <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k3_real_1(k1_seq_1(A,D),k1_seq_1(B,D)) ) ) ) ) ) ) ), file(seq_1,d3_seq_1), []). fof(d3_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_square_1(A) = k3_xcmplx_0(A,A) ) ), file(square_1,d3_square_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(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). fof(d4_jordan,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) => ( A = k6_jordan <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2)))) => k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers,A,B) = k5_real_1(k22_euclid(k1_jordan(k15_euclid(2),k15_euclid(2),B)),k22_euclid(k2_jordan(k15_euclid(2),k15_euclid(2),B))) ) ) ) ), file(jordan,d4_jordan), []). fof(d4_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k1_rfunct_1(A,B) <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k4_xboole_0(k1_relat_1(B),k10_relat_1(B,k1_tarski(0)))) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k4_real_1(k1_seq_1(A,D),k2_real_1(k1_seq_1(B,D))) ) ) ) ) ) ) ), file(rfunct_1,d4_rfunct_1), []). fof(d4_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k4_seq_1(A,B) <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k5_real_1(k1_seq_1(A,D),k1_seq_1(B,D)) ) ) ) ) ) ) ), file(seq_1,d4_seq_1), []). fof(d4_tarski,axiom,( ! [A,B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) ), file(tarski,d4_tarski), []). fof(d4_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) ) => k2_tops_2(A,B,C) = k2_funct_1(C) ) ) ) ) ), file(tops_2,d4_tops_2), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_jordan,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) => ( A = k7_jordan <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2)))) => k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers,A,B) = k21_euclid(k2_jordan(k15_euclid(2),k15_euclid(2),B)) ) ) ) ), file(jordan,d5_jordan), []). fof(d5_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k1_partfun3(A) <=> ( k1_relat_1(B) = k1_relat_1(A) & ! [C] : ( r2_hidden(C,k1_relat_1(B)) => k1_funct_1(B,C) = k9_square_1(k1_seq_1(A,C)) ) ) ) ) ) ), file(partfun3,d5_partfun3), []). fof(d5_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k5_seq_1(A,B) <=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B)) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k4_real_1(k1_seq_1(A,D),k1_seq_1(B,D)) ) ) ) ) ) ) ), file(seq_1,d5_seq_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d5_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v3_tops_2(C,A,B) <=> ( k1_relat_1(C) = k2_pre_topc(A) & k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & v5_pre_topc(C,A,B) & v5_pre_topc(k2_tops_2(A,B,C),B,A) ) ) ) ) ) ), file(tops_2,d5_tops_2), []). fof(d6_jordan,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) => ( A = k8_jordan <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2)))) => k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers,A,B) = k22_euclid(k2_jordan(k15_euclid(2),k15_euclid(2),B)) ) ) ) ), file(jordan,d6_jordan), []). fof(d6_toprealb,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k7_toprealb(A,B,C) = k3_pre_topc(k15_euclid(A),k3_topreal9(A,B,C)) ) ) ) ), file(toprealb,d6_toprealb), []). fof(d7_euclid,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k14_euclid(A) = g1_metric_1(k1_euclid(A),k13_euclid(A)) ) ), file(euclid,d7_euclid), []). fof(d7_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k15_seq_1(A) <=> ( k1_relat_1(B) = k1_relat_1(A) & ! [C] : ( r2_hidden(C,k1_relat_1(B)) => k1_funct_1(B,C) = k1_real_1(k1_seq_1(A,C)) ) ) ) ) ) ), file(seq_1,d7_seq_1), []). fof(d8_euclid,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => k15_euclid(A) = k5_pcomps_1(k14_euclid(A)) ) ), file(euclid,d8_euclid), []). fof(d8_jordan,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_subset_1(A,k1_numbers,k5_numbers) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xreal_0(D) ) => ( r2_hidden(C,k1_topreal9(A,B,D)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D))) & m2_relset_1(E,u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D))) ) => ( E = k10_jordan(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(k7_toprealb(A,B,D))) => ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) & F = G & k8_funct_2(u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D)),E,F) = k3_brouwer(A,B,G,C,D) ) ) ) ) ) ) ) ) ) ), file(jordan,d8_jordan), []). fof(d9_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)) ) ) ), file(xcmplx_0,d9_xcmplx_0), []). fof(dt_g1_metric_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) ) => ( v1_metric_1(g1_metric_1(A,B)) & l1_metric_1(g1_metric_1(A,B)) ) ) ), file(metric_1,g1_metric_1), []). 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_k10_jordan,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) & v1_xreal_0(D) & v2_xreal_0(D) ) => ( v1_funct_1(k10_jordan(A,B,C,D)) & v1_funct_2(k10_jordan(A,B,C,D),u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D))) & m2_relset_1(k10_jordan(A,B,C,D),u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D))) ) ) ), file(jordan,k10_jordan), []). fof(dt_k10_relat_1,axiom,( $true ), file(relat_1,k10_relat_1), []). fof(dt_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => m1_subset_1(k12_mcart_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(mcart_1,k12_mcart_1), []). fof(dt_k12_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k12_partfun3(A,B,C)) & v1_funct_2(k12_partfun3(A,B,C),u1_struct_0(A),k1_numbers) & v9_pscomp_1(k12_partfun3(A,B,C),A) & m2_relset_1(k12_partfun3(A,B,C),u1_struct_0(A),k1_numbers) ) ) ), file(partfun3,k12_partfun3), []). fof(dt_k13_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_funct_1(k13_euclid(A)) & v1_funct_2(k13_euclid(A),k2_zfmisc_1(k1_euclid(A),k1_euclid(A)),k1_numbers) & m2_relset_1(k13_euclid(A),k2_zfmisc_1(k1_euclid(A),k1_euclid(A)),k1_numbers) ) ) ), file(euclid,k13_euclid), []). fof(dt_k13_funct_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)) ) ) ), file(funct_3,k13_funct_3), []). fof(dt_k13_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k13_partfun3(A,B,C)) & v1_funct_2(k13_partfun3(A,B,C),u1_struct_0(A),k1_numbers) & v9_pscomp_1(k13_partfun3(A,B,C),A) & m2_relset_1(k13_partfun3(A,B,C),u1_struct_0(A),k1_numbers) ) ) ), file(partfun3,k13_partfun3), []). fof(dt_k14_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_metric_1(k14_euclid(A)) & v6_metric_1(k14_euclid(A)) & v7_metric_1(k14_euclid(A)) & v8_metric_1(k14_euclid(A)) & v9_metric_1(k14_euclid(A)) & l1_metric_1(k14_euclid(A)) ) ) ), file(euclid,k14_euclid), []). fof(dt_k14_funct_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) ) => ( v1_funct_1(k14_funct_3(A,B,C,D,E)) & v1_funct_2(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) & m2_relset_1(k14_funct_3(A,B,C,D,E),A,k2_zfmisc_1(B,C)) ) ) ), file(funct_3,k14_funct_3), []). fof(dt_k14_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k14_partfun3(A,B,C)) & v1_funct_2(k14_partfun3(A,B,C),u1_struct_0(A),k1_numbers) & v9_pscomp_1(k14_partfun3(A,B,C),A) & m2_relset_1(k14_partfun3(A,B,C),u1_struct_0(A),k1_numbers) ) ) ), file(partfun3,k14_partfun3), []). 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_k15_partfun3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k15_partfun3(A,B)) & v1_funct_2(k15_partfun3(A,B),u1_struct_0(A),k1_numbers) & v9_pscomp_1(k15_partfun3(A,B),A) & m2_relset_1(k15_partfun3(A,B),u1_struct_0(A),k1_numbers) ) ) ), file(partfun3,k15_partfun3), []). fof(dt_k15_pscomp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k15_pscomp_1(A,B,C)) & v1_funct_2(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) & m2_relset_1(k15_pscomp_1(A,B,C),u1_struct_0(k3_pre_topc(A,B)),k1_numbers) ) ) ), file(pscomp_1,k15_pscomp_1), []). fof(dt_k15_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k15_seq_1(A)) & v1_funct_1(k15_seq_1(A)) ) ) ), file(seq_1,k15_seq_1), []). fof(dt_k17_partfun3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & v4_partfun3(B) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k17_partfun3(A,B)) & v1_funct_2(k17_partfun3(A,B),u1_struct_0(A),k1_numbers) & v9_pscomp_1(k17_partfun3(A,B),A) & m2_relset_1(k17_partfun3(A,B),u1_struct_0(A),k1_numbers) ) ) ), file(partfun3,k17_partfun3), []). fof(dt_k1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => ( v1_funct_1(k1_borsuk_1(A,B,C)) & v1_funct_2(k1_borsuk_1(A,B,C),B,A) & m2_relset_1(k1_borsuk_1(A,B,C),B,A) ) ) ), file(borsuk_1,k1_borsuk_1), []). fof(dt_k1_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k1_euclid(A)) & m1_finseq_2(k1_euclid(A),k1_numbers) ) ) ), file(euclid,k1_euclid), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_jordan,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) ) => m1_subset_1(k1_jordan(A,B,C),u1_struct_0(A)) ) ), file(jordan,k1_jordan), []). fof(dt_k1_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_partfun1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) ) => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ), file(partfun1,k1_partfun1), []). fof(dt_k1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k1_partfun3(A)) & v1_funct_1(k1_partfun3(A)) ) ) ), file(partfun3,k1_partfun3), []). fof(dt_k1_pscomp_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k1_pscomp_1(A,B,C),k1_zfmisc_1(B)) ) ), file(pscomp_1,k1_pscomp_1), []). fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) ), file(real_1,k1_real_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_rfunct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k1_rfunct_1(A,B)) & v1_funct_1(k1_rfunct_1(A,B)) ) ) ), file(rfunct_1,k1_rfunct_1), []). fof(dt_k1_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => m1_subset_1(k1_seq_1(A,B),k1_numbers) ) ), file(seq_1,k1_seq_1), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_subset_1(k1_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal9,k1_topreal9), []). 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_euclid,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k20_euclid(A,B,C),u1_struct_0(k15_euclid(A))) ) ), file(euclid,k20_euclid), []). fof(dt_k20_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v2_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => ( v1_funct_1(k20_partfun3(A,B,C)) & v1_funct_2(k20_partfun3(A,B,C),u1_struct_0(A),k1_numbers) & v9_pscomp_1(k20_partfun3(A,B,C),A) & m2_relset_1(k20_partfun3(A,B,C),u1_struct_0(A),k1_numbers) ) ) ), file(partfun3,k20_partfun3), []). 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_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_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_k2_brouwer,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_pre_topc(k2_brouwer(A,B,C),k15_euclid(A)) ) ), file(brouwer,k2_brouwer), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)) ) ) ), file(funct_1,k2_funct_1), []). fof(dt_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => m1_subset_1(k2_funct_2(A,B,C,D),k1_zfmisc_1(B)) ) ), file(funct_2,k2_funct_2), []). fof(dt_k2_jordan,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) ) => m1_subset_1(k2_jordan(A,B,C),u1_struct_0(B)) ) ), file(jordan,k2_jordan), []). fof(dt_k2_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), []). fof(dt_k2_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k2_pre_topc), []). fof(dt_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k2_real_1(A),k1_numbers) ) ), file(real_1,k2_real_1), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_subset_1(k2_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal9,k2_topreal9), []). fof(dt_k2_topreala,axiom, ( v1_funct_1(k2_topreala) & v1_funct_2(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2))) & m2_relset_1(k2_topreala,u1_struct_0(k6_borsuk_1(k3_topalg_2,k3_topalg_2)),u1_struct_0(k15_euclid(2))) ), file(topreala,k2_topreala), []). fof(dt_k2_tops_2,axiom,( ! [A,B,C] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_funct_1(k2_tops_2(A,B,C)) & v1_funct_2(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k2_tops_2(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(tops_2,k2_tops_2), []). 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_brouwer,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,u1_struct_0(k15_euclid(A))) & v1_xreal_0(E) & ~ v3_xreal_0(E) ) => m1_subset_1(k3_brouwer(A,B,C,D,E),u1_struct_0(k15_euclid(A))) ) ), file(brouwer,k3_brouwer), []). fof(dt_k3_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( v1_funct_1(k3_jordan(A)) & v1_funct_2(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) ) ), file(jordan,k3_jordan), []). fof(dt_k3_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & m1_pre_topc(k3_pre_topc(A,B),A) ) ) ), file(pre_topc,k3_pre_topc), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k3_seq_1(A,B)) & v1_funct_1(k3_seq_1(A,B)) ) ) ), file(seq_1,k3_seq_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_topalg_2,axiom, ( v1_pre_topc(k3_topalg_2) & v3_topalg_2(k3_topalg_2) & m1_pre_topc(k3_topalg_2,k3_topmetr) ), file(topalg_2,k3_topalg_2), []). fof(dt_k3_topmetr,axiom, ( v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) & l1_pre_topc(k3_topmetr) ), file(topmetr,k3_topmetr), []). fof(dt_k3_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_subset_1(k3_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ), file(topreal9,k3_topreal9), []). 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_finseq_2,axiom,( ! [A,B] : ( v4_ordinal2(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) ), file(finseq_2,k4_finseq_2), []). fof(dt_k4_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( v1_funct_1(k4_jordan(A)) & v1_funct_2(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ) ) ), file(jordan,k4_jordan), []). fof(dt_k4_pre_topc,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ), file(pre_topc,k4_pre_topc), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k4_seq_1(A,B)) & v1_funct_1(k4_seq_1(A,B)) ) ) ), file(seq_1,k4_seq_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(dt_k5_jordan,axiom, ( v1_funct_1(k5_jordan) & v1_funct_2(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ), file(jordan,k5_jordan), []). 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_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => l1_pre_topc(k5_pcomps_1(A)) ) ), file(pcomps_1,k5_pcomps_1), []). fof(dt_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ), file(real_1,k5_real_1), []). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(dt_k5_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k5_seq_1(A,B)) & v1_funct_1(k5_seq_1(A,B)) ) ) ), file(seq_1,k5_seq_1), []). fof(dt_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k5_setfam_1), []). fof(dt_k5_square_1,axiom,( $true ), file(square_1,k5_square_1), []). fof(dt_k5_toprns_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k5_toprns_1(A,B),k1_numbers) ) ), file(toprns_1,k5_toprns_1), []). fof(dt_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A)) ) ), file(xcmplx_0,k5_xcmplx_0), []). fof(dt_k6_borsuk_1,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & l1_pre_topc(k6_borsuk_1(A,B)) ) ) ), file(borsuk_1,k6_borsuk_1), []). fof(dt_k6_jordan,axiom, ( v1_funct_1(k6_jordan) & v1_funct_2(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ), file(jordan,k6_jordan), []). fof(dt_k6_partfun1,axiom,( ! [A] : ( v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A) ) ), file(partfun1,k6_partfun1), []). fof(dt_k6_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_borsuk_1,axiom,( ! [A,B,C,D] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => m1_subset_1(k7_borsuk_1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) ) ), file(borsuk_1,k7_borsuk_1), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_jordan,axiom, ( v1_funct_1(k7_jordan) & v1_funct_2(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ), file(jordan,k7_jordan), []). 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_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k7_square_1(A),k1_numbers) ) ), file(square_1,k7_square_1), []). fof(dt_k7_toprealb,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_pre_topc(k7_toprealb(A,B,C),k15_euclid(A)) ) ), file(toprealb,k7_toprealb), []). fof(dt_k7_xcmplx_0,axiom,( $true ), file(xcmplx_0,k7_xcmplx_0), []). fof(dt_k8_borsuk_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => m1_subset_1(k8_borsuk_1(A,B,C,D),u1_struct_0(k6_borsuk_1(A,B))) ) ), file(borsuk_1,k8_borsuk_1), []). 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_jordan,axiom, ( v1_funct_1(k8_jordan) & v1_funct_2(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & m2_relset_1(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) ), file(jordan,k8_jordan), []). fof(dt_k8_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k8_square_1(A)) ) ), file(square_1,k8_square_1), []). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_k9_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k9_square_1(A),k1_numbers) ) ), file(square_1,k9_square_1), []). fof(dt_l1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => l1_struct_0(A) ) ), file(metric_1,l1_metric_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_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => l1_pre_topc(B) ) ) ), file(pre_topc,m1_pre_topc), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v1_funct_1(u1_metric_1(A)) & v1_funct_2(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) & m2_relset_1(u1_metric_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers) ) ) ), file(metric_1,u1_metric_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_metric_1,axiom,( ? [A] : l1_metric_1(A) ), file(metric_1,l1_metric_1), []). 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_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_pre_topc(B,A) ) ), file(pre_topc,m1_pre_topc), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(fc10_jordan,axiom,( ! [A,B,C,D] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k5_numbers) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ~ v1_xboole_0(k4_xboole_0(k2_topreal9(B,C,A),k1_struct_0(k15_euclid(B),D))) ) ), file(jordan,fc10_jordan), []). 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_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v4_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc10_partfun3), []). fof(fc10_pscomp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & v6_compts_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)) & v2_compts_1(k3_pre_topc(A,B)) ) ) ), file(pscomp_1,fc10_pscomp_1), []). 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_partfun3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k2_funcop_1(A,0)) & ~ v2_relat_1(k2_funcop_1(A,0)) & v1_funct_1(k2_funcop_1(A,0)) & v3_partfun3(k2_funcop_1(A,0)) & v4_partfun3(k2_funcop_1(A,0)) ) ) ), file(partfun3,fc11_partfun3), []). 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_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k3_seq_1(B,C)) & v1_funct_1(k3_seq_1(B,C)) & v1_seq_1(k3_seq_1(B,C)) & v3_partfun3(k3_seq_1(B,C)) ) ) ), file(partfun3,fc12_partfun3), []). 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_jordan,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) ) => ( v2_pre_topc(k2_brouwer(2,A,B)) & v1_borsuk_1(k2_brouwer(2,A,B),k15_euclid(2)) & v1_topalg_2(k2_brouwer(2,A,B),2) ) ) ), file(jordan,fc13_jordan), []). 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_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k3_seq_1(B,C)) & v1_funct_1(k3_seq_1(B,C)) & v1_seq_1(k3_seq_1(B,C)) & v4_partfun3(k3_seq_1(B,C)) ) ) ), file(partfun3,fc13_partfun3), []). fof(fc13_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v3_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc13_xreal_0), []). fof(fc14_jordan,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) ) => ( v2_pre_topc(k2_brouwer(2,A,B)) & v2_compts_1(k2_brouwer(2,A,B)) & v1_borsuk_1(k2_brouwer(2,A,B),k15_euclid(2)) & v1_topalg_2(k2_brouwer(2,A,B),2) ) ) ), file(jordan,fc14_jordan), []). 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(fc14_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k3_seq_1(B,C)) & v2_relat_1(k3_seq_1(B,C)) & v1_funct_1(k3_seq_1(B,C)) & v1_seq_1(k3_seq_1(B,C)) & v1_partfun3(k3_seq_1(B,C)) & v4_partfun3(k3_seq_1(B,C)) ) ) ), file(partfun3,fc14_partfun3), []). fof(fc14_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & v3_xreal_0(C) ) => ( v1_xboole_0(k3_topreal9(A,B,C)) & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ), file(topreal9,fc14_topreal9), []). fof(fc14_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) & ~ v2_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc14_xreal_0), []). 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(fc15_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k3_seq_1(B,C)) & v2_relat_1(k3_seq_1(B,C)) & v1_funct_1(k3_seq_1(B,C)) & v1_seq_1(k3_seq_1(B,C)) & v1_partfun3(k3_seq_1(B,C)) & v4_partfun3(k3_seq_1(B,C)) ) ) ), file(partfun3,fc15_partfun3), []). fof(fc15_topreal9,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ( ~ v1_xboole_0(k3_topreal9(A,B,C)) & v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ), file(topreal9,fc15_topreal9), []). fof(fc15_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc15_xreal_0), []). fof(fc16_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ~ v1_xboole_0(k3_jordan(A)) & v1_relat_1(k3_jordan(A)) & v1_funct_1(k3_jordan(A)) & v1_funct_2(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_partfun1(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_seq_1(k3_jordan(A)) & v9_pscomp_1(k3_jordan(A),k6_borsuk_1(k15_euclid(2),k15_euclid(2))) ) ) ), file(jordan,fc16_jordan), []). 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(fc16_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v2_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k3_seq_1(B,C)) & v2_relat_1(k3_seq_1(B,C)) & v1_funct_1(k3_seq_1(B,C)) & v1_seq_1(k3_seq_1(B,C)) & v2_partfun3(k3_seq_1(B,C)) & v3_partfun3(k3_seq_1(B,C)) ) ) ), file(partfun3,fc16_partfun3), []). fof(fc16_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc16_xreal_0), []). fof(fc17_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ~ v1_xboole_0(k4_jordan(A)) & v1_relat_1(k4_jordan(A)) & v1_funct_1(k4_jordan(A)) & v1_funct_2(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_partfun1(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_seq_1(k4_jordan(A)) & v9_pscomp_1(k4_jordan(A),k6_borsuk_1(k15_euclid(2),k15_euclid(2))) ) ) ), file(jordan,fc17_jordan), []). fof(fc17_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k3_seq_1(B,C)) & v2_relat_1(k3_seq_1(B,C)) & v1_funct_1(k3_seq_1(B,C)) & v1_seq_1(k3_seq_1(B,C)) & v2_partfun3(k3_seq_1(B,C)) & v3_partfun3(k3_seq_1(B,C)) ) ) ), file(partfun3,fc17_partfun3), []). fof(fc17_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v2_xreal_0(k6_xcmplx_0(A,B)) & ~ v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc17_xreal_0), []). fof(fc18_jordan,axiom, ( ~ v1_xboole_0(k5_jordan) & v1_relat_1(k5_jordan) & v1_funct_1(k5_jordan) & v1_funct_2(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_partfun1(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_seq_1(k5_jordan) & v9_pscomp_1(k5_jordan,k6_borsuk_1(k15_euclid(2),k15_euclid(2))) ), file(jordan,fc18_jordan), []). fof(fc18_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k4_seq_1(B,C)) & v1_funct_1(k4_seq_1(B,C)) & v1_seq_1(k4_seq_1(B,C)) & v4_partfun3(k4_seq_1(B,C)) ) ) ), file(partfun3,fc18_partfun3), []). fof(fc18_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & ~ v2_xreal_0(k6_xcmplx_0(B,A)) & v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc18_xreal_0), []). fof(fc19_jordan,axiom, ( ~ v1_xboole_0(k6_jordan) & v1_relat_1(k6_jordan) & v1_funct_1(k6_jordan) & v1_funct_2(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_partfun1(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_seq_1(k6_jordan) & v9_pscomp_1(k6_jordan,k6_borsuk_1(k15_euclid(2),k15_euclid(2))) ), file(jordan,fc19_jordan), []). fof(fc19_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k4_seq_1(B,C)) & v1_funct_1(k4_seq_1(B,C)) & v1_seq_1(k4_seq_1(B,C)) & v3_partfun3(k4_seq_1(B,C)) ) ) ), file(partfun3,fc19_partfun3), []). fof(fc19_toprealb,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) ) => ( ~ v1_xboole_0(k3_topreal9(2,B,A)) & v4_pre_topc(k3_topreal9(2,B,A),k15_euclid(2)) & v1_jordan2c(k3_topreal9(2,B,A),2) & v2_connsp_1(k3_topreal9(2,B,A),k15_euclid(2)) & v6_compts_1(k3_topreal9(2,B,A),k15_euclid(2)) & v1_topreal2(k3_topreal9(2,B,A)) ) ) ), file(toprealb,fc19_toprealb), []). fof(fc19_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(A,B)) & v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & ~ v2_xreal_0(k6_xcmplx_0(A,B)) & v3_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc19_xreal_0), []). fof(fc1_euclid,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v3_struct_0(k14_euclid(A)) & v1_metric_1(k14_euclid(A)) & v6_metric_1(k14_euclid(A)) & v7_metric_1(k14_euclid(A)) & v8_metric_1(k14_euclid(A)) & v9_metric_1(k14_euclid(A)) ) ) ), file(euclid,fc1_euclid), []). fof(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k2_pre_topc(k15_euclid(A))) & v4_pre_topc(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) & v2_connsp_1(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) ) ) ), file(jordan2c,fc1_jordan2c), []). fof(fc1_jordan5a,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)) & v3_compts_1(k15_euclid(A)) & v1_borsuk_2(k15_euclid(A)) ) ) ), file(jordan5a,fc1_jordan5a), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k7_xcmplx_0(A,A)) & v1_xreal_0(k7_xcmplx_0(A,A)) & ~ v3_xreal_0(k7_xcmplx_0(A,A)) ) ) ), file(partfun3,fc1_partfun3), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_xcmplx_0(k1_funct_1(A,B)) & v1_xreal_0(k1_funct_1(A,B)) ) ) ), file(seq_1,fc1_seq_1), []). fof(fc1_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_square_1(A)) ) ), file(square_1,fc1_square_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_topreal6,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & v6_group_1(k3_pre_topc(A,B)) ) ) ), file(topreal6,fc1_topreal6), []). fof(fc1_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v2_xreal_0(C) ) => v1_xboole_0(k1_topreal9(A,B,C)) ) ), file(topreal9,fc1_topreal9), []). fof(fc1_waybel_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ~ v1_xboole_0(k9_relat_1(C,D)) ) ), file(waybel_2,fc1_waybel_2), []). fof(fc1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) ), file(xreal_0,fc1_xreal_0), []). fof(fc1_yellow13,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) ), file(yellow13,fc1_yellow13), []). fof(fc20_jordan,axiom, ( ~ v1_xboole_0(k7_jordan) & v1_relat_1(k7_jordan) & v1_funct_1(k7_jordan) & v1_funct_2(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_partfun1(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_seq_1(k7_jordan) & v9_pscomp_1(k7_jordan,k6_borsuk_1(k15_euclid(2),k15_euclid(2))) ), file(jordan,fc20_jordan), []). fof(fc20_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k4_seq_1(B,C)) & v2_relat_1(k4_seq_1(B,C)) & v1_funct_1(k4_seq_1(B,C)) & v1_seq_1(k4_seq_1(B,C)) & v1_partfun3(k4_seq_1(B,C)) & v4_partfun3(k4_seq_1(B,C)) ) ) ), file(partfun3,fc20_partfun3), []). fof(fc20_toprealb,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ( ~ v3_struct_0(k7_toprealb(A,B,C)) & v1_pre_topc(k7_toprealb(A,B,C)) & v2_pre_topc(k7_toprealb(A,B,C)) & v1_monoid_0(k7_toprealb(A,B,C)) & v2_monoid_0(k7_toprealb(A,B,C)) ) ) ), file(toprealb,fc20_toprealb), []). fof(fc20_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k6_xcmplx_0(B,A)) & v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v2_xreal_0(k6_xcmplx_0(B,A)) & ~ v3_xreal_0(k6_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc20_xreal_0), []). fof(fc21_jordan,axiom, ( ~ v1_xboole_0(k8_jordan) & v1_relat_1(k8_jordan) & v1_funct_1(k8_jordan) & v1_funct_2(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_partfun1(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))),k1_numbers) & v1_seq_1(k8_jordan) & v9_pscomp_1(k8_jordan,k6_borsuk_1(k15_euclid(2),k15_euclid(2))) ), file(jordan,fc21_jordan), []). fof(fc21_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k4_seq_1(B,C)) & v2_relat_1(k4_seq_1(B,C)) & v1_funct_1(k4_seq_1(B,C)) & v1_seq_1(k4_seq_1(B,C)) & v2_partfun3(k4_seq_1(B,C)) & v3_partfun3(k4_seq_1(B,C)) ) ) ), file(partfun3,fc21_partfun3), []). fof(fc21_toprealb,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xboole_0(C) & v1_xreal_0(C) ) => ( v2_pre_topc(k7_toprealb(A,B,C)) & v3_realset2(k7_toprealb(A,B,C)) & v1_monoid_0(k7_toprealb(A,B,C)) & v2_monoid_0(k7_toprealb(A,B,C)) ) ) ), file(toprealb,fc21_toprealb), []). 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_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k4_seq_1(B,C)) & v2_relat_1(k4_seq_1(B,C)) & v1_funct_1(k4_seq_1(B,C)) & v1_seq_1(k4_seq_1(B,C)) & v2_partfun3(k4_seq_1(B,C)) & v3_partfun3(k4_seq_1(B,C)) ) ) ), file(partfun3,fc22_partfun3), []). fof(fc22_toprealb,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) & v2_xreal_0(B) ) => ( ~ v3_struct_0(k7_toprealb(2,A,B)) & v1_pre_topc(k7_toprealb(2,A,B)) & v2_pre_topc(k7_toprealb(2,A,B)) & v2_compts_1(k7_toprealb(2,A,B)) & v10_pscomp_1(k7_toprealb(2,A,B)) & v1_borsuk_2(k7_toprealb(2,A,B)) & v1_monoid_0(k7_toprealb(2,A,B)) & v2_monoid_0(k7_toprealb(2,A,B)) & v1_toprealb(k7_toprealb(2,A,B)) ) ) ), file(toprealb,fc22_toprealb), []). 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_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v2_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k4_seq_1(B,C)) & v2_relat_1(k4_seq_1(B,C)) & v1_funct_1(k4_seq_1(B,C)) & v1_seq_1(k4_seq_1(B,C)) & v1_partfun3(k4_seq_1(B,C)) & v4_partfun3(k4_seq_1(B,C)) ) ) ), file(partfun3,fc23_partfun3), []). 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_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v4_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc24_partfun3), []). 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_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v4_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc25_partfun3), []). fof(fc25_toprealb,axiom,( ! [A,B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v3_struct_0(k7_toprealb(2,A,B)) & v1_pre_topc(k7_toprealb(2,A,B)) & v2_pre_topc(k7_toprealb(2,A,B)) & v1_borsuk_2(k7_toprealb(2,A,B)) & v1_monoid_0(k7_toprealb(2,A,B)) & v2_monoid_0(k7_toprealb(2,A,B)) ) ) ), file(toprealb,fc25_toprealb), []). fof(fc25_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & ~ v2_xreal_0(k5_xcmplx_0(A)) ) ) ), file(xreal_0,fc25_xreal_0), []). fof(fc26_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v3_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc26_partfun3), []). fof(fc26_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) & ~ v3_xreal_0(k5_xcmplx_0(A)) ) ) ), file(xreal_0,fc26_xreal_0), []). fof(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc27_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v3_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc27_partfun3), []). fof(fc27_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v2_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc27_xreal_0), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc28_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v2_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v2_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v2_partfun3(k5_seq_1(B,C)) & v3_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc28_partfun3), []). fof(fc28_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(B,A)) & v1_xreal_0(k7_xcmplx_0(B,A)) & ~ v2_xreal_0(k7_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc28_xreal_0), []). 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(fc29_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v2_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v2_partfun3(k5_seq_1(B,C)) & v3_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc29_partfun3), []). fof(fc29_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc29_xreal_0), []). fof(fc2_borsuk_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) ) ) ), file(borsuk_1,fc2_borsuk_1), []). 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_funct_1,axiom,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) ) ), file(funct_1,fc2_funct_1), []). fof(fc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A) & v1_tops_1(k2_pre_topc(A),A) & v5_tops_1(k2_pre_topc(A),A) & v6_tops_1(k2_pre_topc(A),A) ) ) ), file(isomichi,fc2_isomichi), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k3_xcmplx_0(A,B)) & v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(nat_1,fc2_nat_1), []). fof(fc2_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k3_xcmplx_0(A,A)) & v1_xreal_0(k3_xcmplx_0(A,A)) & ~ v3_xreal_0(k3_xcmplx_0(A,A)) ) ) ), file(partfun3,fc2_partfun3), []). fof(fc2_pre_topc,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k2_pre_topc(A)) ) ), file(pre_topc,fc2_pre_topc), []). 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_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_seq_1(k7_relat_1(A,B)) ) ) ), file(seq_1,fc2_seq_1), []). fof(fc2_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k5_square_1(A)) & v1_xreal_0(k5_square_1(A)) ) ) ), file(square_1,fc2_square_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_topalg_5,axiom,( ! [A] : ( ( ~ v6_group_1(A) & l1_struct_0(A) ) => ~ v1_finset_1(u1_struct_0(A)) ) ), file(topalg_5,fc2_topalg_5), []). fof(fc2_topmetr,axiom, ( ~ v3_struct_0(k3_topmetr) & v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) ), file(topmetr,fc2_topmetr), []). fof(fc2_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & v2_xreal_0(C) ) => ~ v1_xboole_0(k1_topreal9(A,B,C)) ) ), file(topreal9,fc2_topreal9), []). fof(fc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) ) ) ), file(xreal_0,fc2_xreal_0), []). fof(fc2_yellow13,axiom,( ! [A] : ( ( v3_realset2(A) & l1_struct_0(A) ) => v1_realset1(u1_struct_0(A)) ) ), file(yellow13,fc2_yellow13), []). 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(fc30_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v2_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v1_partfun3(k5_seq_1(B,C)) & v4_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc30_partfun3), []). fof(fc30_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) & ~ v3_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc30_xreal_0), []). 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(fc31_partfun3,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v2_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v2_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) & v1_partfun3(k5_seq_1(B,C)) & v4_partfun3(k5_seq_1(B,C)) ) ) ), file(partfun3,fc31_partfun3), []). 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(fc32_partfun3,axiom,( ! [A,B,C] : ( ( v2_relat_1(B) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & v2_relat_1(C) & v1_funct_1(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,C)) & v2_relat_1(k5_seq_1(B,C)) & v1_funct_1(k5_seq_1(B,C)) & v1_seq_1(k5_seq_1(B,C)) ) ) ), file(partfun3,fc32_partfun3), []). 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(fc33_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k5_seq_1(B,B)) & v1_funct_1(k5_seq_1(B,B)) & v1_seq_1(k5_seq_1(B,B)) & v4_partfun3(k5_seq_1(B,B)) ) ) ), file(partfun3,fc33_partfun3), []). 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(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). fof(fc3_brouwer,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ( ~ v3_struct_0(k2_brouwer(A,B,C)) & v2_pre_topc(k2_brouwer(A,B,C)) ) ) ), file(brouwer,fc3_brouwer), []). fof(fc3_jordan,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => ( v1_xreal_0(k5_toprns_1(A,k20_euclid(A,B,C))) & ~ v3_xreal_0(k5_toprns_1(A,k20_euclid(A,B,C))) & v1_xcmplx_0(k5_toprns_1(A,k20_euclid(A,B,C))) ) ) ), file(jordan,fc3_jordan), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(A))) & v1_xreal_0(k3_xcmplx_0(A,k5_xcmplx_0(A))) & ~ v3_xreal_0(k3_xcmplx_0(A,k5_xcmplx_0(A))) ) ) ), file(partfun3,fc3_partfun3), []). fof(fc3_pre_topc,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_pre_topc(A,B)) & v1_pre_topc(k3_pre_topc(A,B)) ) ) ), file(pre_topc,fc3_pre_topc), []). fof(fc3_pscomp_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ~ v1_xboole_0(k9_relat_1(C,A)) ) ), file(pscomp_1,fc3_pscomp_1), []). fof(fc3_realset1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)) ) ), file(realset1,fc3_realset1), []). fof(fc3_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k3_seq_1(A,B)) & v1_funct_1(k3_seq_1(A,B)) & v1_seq_1(k3_seq_1(A,B)) ) ) ), file(seq_1,fc3_seq_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_topalg_5,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)) & v1_tsep_1(k3_pre_topc(A,B),A) ) ) ), file(topalg_5,fc3_topalg_5), []). fof(fc3_topgen_3,axiom, ( ~ v1_xboole_0(k1_numbers) & ~ v1_finset_1(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(topgen_3,fc3_topgen_3), []). fof(fc3_topmetr,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & m1_relset_1(B,A,u1_struct_0(k3_topmetr)) ) => ( v1_xcmplx_0(k1_funct_1(B,C)) & v1_xreal_0(k1_funct_1(B,C)) ) ) ), file(topmetr,fc3_topmetr), []). fof(fc3_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & v3_xreal_0(C) ) => v1_xboole_0(k2_topreal9(A,B,C)) ) ), file(topreal9,fc3_topreal9), []). 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(fc3_yellow13,axiom,( ! [A] : ( ( v2_compts_1(A) & l1_pre_topc(A) ) => ( v1_tops_1(k2_pre_topc(A),A) & v6_compts_1(k2_pre_topc(A),A) ) ) ), file(yellow13,fc3_yellow13), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc43_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v4_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc43_partfun3), []). fof(fc44_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v4_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc44_partfun3), []). fof(fc45_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v4_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v3_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc45_partfun3), []). fof(fc46_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v3_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v3_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc46_partfun3), []). fof(fc47_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v2_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v2_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v2_partfun3(k1_rfunct_1(B,C)) & v3_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc47_partfun3), []). fof(fc48_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v2_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v2_partfun3(k1_rfunct_1(B,C)) & v3_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc48_partfun3), []). fof(fc49_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v1_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v2_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v1_partfun3(k1_rfunct_1(B,C)) & v4_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc49_partfun3), []). fof(fc4_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v2_t_0topsp(k6_borsuk_1(A,B)) ) ) ), file(borsuk_2,fc4_borsuk_2), []). fof(fc4_brouwer,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v2_pre_topc(k2_brouwer(A,B,C)) & v1_topalg_2(k2_brouwer(A,B,C),A) ) ) ), file(brouwer,fc4_brouwer), []). fof(fc4_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_partfun3,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(k8_square_1(A)) & v1_xreal_0(k8_square_1(A)) & ~ v3_xreal_0(k8_square_1(A)) ) ) ), file(partfun3,fc4_partfun3), []). fof(fc4_pre_topc,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_pre_topc(k3_pre_topc(A,B)) & v2_pre_topc(k3_pre_topc(A,B)) ) ) ), file(pre_topc,fc4_pre_topc), []). fof(fc4_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k4_seq_1(A,B)) & v1_funct_1(k4_seq_1(A,B)) & v1_seq_1(k4_seq_1(A,B)) ) ) ), file(seq_1,fc4_seq_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_topgen_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_xboole_0(k1_zfmisc_1(A)) & ~ v1_finset_1(k1_zfmisc_1(A)) ) ) ), file(topgen_3,fc4_topgen_3), []). fof(fc4_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xreal_0(C) ) => ~ v1_xboole_0(k2_topreal9(A,B,C)) ) ), file(topreal9,fc4_topreal9), []). 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(fc50_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) & v1_funct_1(C) & v2_partfun3(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v2_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) & v1_partfun3(k1_rfunct_1(B,C)) & v4_partfun3(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc50_partfun3), []). fof(fc51_partfun3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,B)) & v1_funct_1(k1_rfunct_1(B,B)) & v4_partfun3(k1_rfunct_1(B,B)) ) ) ), file(partfun3,fc51_partfun3), []). fof(fc52_partfun3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & v1_funct_1(B) & m1_relset_1(B,A,k1_numbers) & v2_relat_1(C) & v1_funct_1(C) & m1_relset_1(C,A,k1_numbers) ) => ( v1_relat_1(k1_rfunct_1(B,C)) & v2_relat_1(k1_rfunct_1(B,C)) & v1_funct_1(k1_rfunct_1(B,C)) ) ) ), file(partfun3,fc52_partfun3), []). fof(fc58_partfun3,axiom,( ! [A,B] : ( ( v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k15_seq_1(B)) & v2_relat_1(k15_seq_1(B)) & v1_funct_1(k15_seq_1(B)) & v1_seq_1(k15_seq_1(B)) ) ) ), file(partfun3,fc58_partfun3), []). fof(fc59_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v3_partfun3(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k15_seq_1(B)) & v1_funct_1(k15_seq_1(B)) & v1_seq_1(k15_seq_1(B)) & v4_partfun3(k15_seq_1(B)) ) ) ), file(partfun3,fc59_partfun3), []). fof(fc5_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v1_urysohn1(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v1_urysohn1(k6_borsuk_1(A,B)) ) ) ), file(borsuk_2,fc5_borsuk_2), []). 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_partfun3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(k8_square_1(A)) & v1_xcmplx_0(k8_square_1(A)) & v1_xreal_0(k8_square_1(A)) & v2_xreal_0(k8_square_1(A)) & ~ v3_xreal_0(k8_square_1(A)) ) ) ), file(partfun3,fc5_partfun3), []). fof(fc5_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v4_pre_topc(k2_pre_topc(A),A) ) ), file(pre_topc,fc5_pre_topc), []). fof(fc5_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_seq_1(B) ) => ( v1_relat_1(k5_seq_1(A,B)) & v1_funct_1(k5_seq_1(A,B)) & v1_seq_1(k5_seq_1(A,B)) ) ) ), file(seq_1,fc5_seq_1), []). fof(fc5_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v3_pre_topc(k1_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k1_topreal9(A,B,C),A) ) ) ), file(topreal9,fc5_topreal9), []). fof(fc5_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc5_xreal_0), []). fof(fc60_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k15_seq_1(B)) & v1_funct_1(k15_seq_1(B)) & v1_seq_1(k15_seq_1(B)) & v3_partfun3(k15_seq_1(B)) ) ) ), file(partfun3,fc60_partfun3), []). fof(fc61_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k15_seq_1(B)) & v2_relat_1(k15_seq_1(B)) & v1_funct_1(k15_seq_1(B)) & v1_seq_1(k15_seq_1(B)) & v2_partfun3(k15_seq_1(B)) & v3_partfun3(k15_seq_1(B)) ) ) ), file(partfun3,fc61_partfun3), []). fof(fc62_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v2_partfun3(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k15_seq_1(B)) & v2_relat_1(k15_seq_1(B)) & v1_funct_1(k15_seq_1(B)) & v1_seq_1(k15_seq_1(B)) & v1_partfun3(k15_seq_1(B)) & v4_partfun3(k15_seq_1(B)) ) ) ), file(partfun3,fc62_partfun3), []). fof(fc6_borsuk_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_compts_1(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & v3_compts_1(B) & l1_pre_topc(B) ) => ( ~ v3_struct_0(k6_borsuk_1(A,B)) & v1_pre_topc(k6_borsuk_1(A,B)) & v2_pre_topc(k6_borsuk_1(A,B)) & v2_t_0topsp(k6_borsuk_1(A,B)) & v3_compts_1(k6_borsuk_1(A,B)) & v3_yellow_8(k6_borsuk_1(A,B)) ) ) ), file(borsuk_2,fc6_borsuk_2), []). fof(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_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_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ( v1_xboole_0(k10_relat_1(A,k1_tarski(0))) & v1_funct_1(k10_relat_1(A,k1_tarski(0))) & v1_membered(k10_relat_1(A,k1_tarski(0))) & v2_membered(k10_relat_1(A,k1_tarski(0))) & v3_membered(k10_relat_1(A,k1_tarski(0))) & v4_membered(k10_relat_1(A,k1_tarski(0))) & v5_membered(k10_relat_1(A,k1_tarski(0))) ) ) ), file(partfun3,fc6_partfun3), []). fof(fc6_topgrp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_tops_2(B,A,A) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( v1_relat_1(k2_tops_2(A,A,B)) & v1_funct_1(k2_tops_2(A,A,B)) & v2_funct_1(k2_tops_2(A,A,B)) & ~ v1_xboole_0(k2_tops_2(A,A,B)) & v1_funct_2(k2_tops_2(A,A,B),u1_struct_0(A),u1_struct_0(A)) & v2_funct_2(k2_tops_2(A,A,B),u1_struct_0(A),u1_struct_0(A)) & v3_funct_2(k2_tops_2(A,A,B),u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(k2_tops_2(A,A,B),A,A) & v3_tops_2(k2_tops_2(A,A,B),A,A) & v1_partfun1(k2_tops_2(A,A,B),u1_struct_0(A),u1_struct_0(A)) & v1_t_0topsp(k2_tops_2(A,A,B),A,A) ) ) ), file(topgrp_1,fc6_topgrp_1), []). fof(fc6_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k2_topreal9(A,B,C),A) ) ) ), file(topreal9,fc6_topreal9), []). fof(fc6_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k7_xcmplx_0(A,B)) & v1_xreal_0(k7_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc6_xreal_0), []). fof(fc70_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k1_partfun3(A)) & v1_funct_1(k1_partfun3(A)) & v1_seq_1(k1_partfun3(A)) ) ) ), file(partfun3,fc70_partfun3), []). fof(fc71_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v4_partfun3(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k1_partfun3(B)) & v1_funct_1(k1_partfun3(B)) & v1_seq_1(k1_partfun3(B)) & v4_partfun3(k1_partfun3(B)) ) ) ), file(partfun3,fc71_partfun3), []). fof(fc72_partfun3,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v1_partfun3(B) & m1_relset_1(B,A,k1_numbers) ) => ( v1_relat_1(k1_partfun3(B)) & v2_relat_1(k1_partfun3(B)) & v1_funct_1(k1_partfun3(B)) & v1_seq_1(k1_partfun3(B)) & v1_partfun3(k1_partfun3(B)) & v4_partfun3(k1_partfun3(B)) ) ) ), file(partfun3,fc72_partfun3), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & v2_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc7_partfun3), []). fof(fc7_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => ( v1_relat_1(k15_seq_1(A)) & v1_funct_1(k15_seq_1(A)) & v1_seq_1(k15_seq_1(A)) ) ) ), file(seq_1,fc7_seq_1), []). fof(fc7_topreal6,axiom, ( ~ v3_struct_0(k3_topmetr) & v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) & v3_compts_1(k3_topmetr) ), file(topreal6,fc7_topreal6), []). fof(fc7_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v4_pre_topc(k3_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k3_topreal9(A,B,C),A) ) ) ), file(topreal9,fc7_topreal9), []). 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_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & v3_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc8_partfun3), []). fof(fc8_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v3_pre_topc(k1_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k1_topreal9(A,B,C),A) & v1_jordan1(k1_topreal9(A,B,C),A) ) ) ), file(topreal9,fc8_topreal9), []). fof(fc8_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pre_topc(k2_pre_topc(A),A) & v4_pre_topc(k2_pre_topc(A),A) ) ) ), file(tops_1,fc8_tops_1), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_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_partfun3,axiom,( ! [A,B] : ( ( v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v3_partfun3(k2_funcop_1(A,B)) ) ) ), file(partfun3,fc9_partfun3), []). fof(fc9_pscomp_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_relat_1(k15_pscomp_1(A,C,B)) & v1_funct_1(k15_pscomp_1(A,C,B)) & v1_funct_2(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers) & v1_seq_1(k15_pscomp_1(A,C,B)) & v1_partfun1(k15_pscomp_1(A,C,B),u1_struct_0(k3_pre_topc(A,C)),k1_numbers) & v9_pscomp_1(k15_pscomp_1(A,C,B),k3_pre_topc(A,C)) ) ) ), file(pscomp_1,fc9_pscomp_1), []). fof(fc9_topreal9,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => ( v4_pre_topc(k2_topreal9(A,B,C),k15_euclid(A)) & v1_jordan2c(k2_topreal9(A,B,C),A) & v1_jordan1(k2_topreal9(A,B,C),A) ) ) ), file(topreal9,fc9_topreal9), []). fof(fc9_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_1(k2_pre_topc(A),A) ) ), file(tops_1,fc9_tops_1), []). 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(free_g1_metric_1,axiom,( ! [A,B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & m1_relset_1(B,k2_zfmisc_1(A,A),k1_numbers) ) => ! [C,D] : ( g1_metric_1(A,B) = g1_metric_1(C,D) => ( A = C & B = D ) ) ) ), file(metric_1,g1_metric_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_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) ), file(real_1,k1_real_1), []). fof(involutiveness_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(k2_real_1(A)) = A ) ), file(real_1,k2_real_1), []). fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ), file(xcmplx_0,k4_xcmplx_0), []). fof(involutiveness_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A)) = A ) ), file(xcmplx_0,k5_xcmplx_0), []). fof(irreflexivity_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r1_subset_1(A,A) ) ), file(subset_1,r1_subset_1), []). fof(l30_jordan,axiom,( u1_struct_0(k6_borsuk_1(k15_euclid(2),k15_euclid(2))) = k2_zfmisc_1(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2))) ), file(jordan,l30_jordan), []). fof(l31_jordan,axiom,( k2_pre_topc(k15_euclid(2)) = u1_struct_0(k15_euclid(2)) ), file(jordan,l31_jordan), []). fof(l32_jordan,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => v9_pscomp_1(k1_borsuk_1(k1_numbers,u1_struct_0(A),B),A) ) ) ), file(jordan,l32_jordan), []). fof(rc10_pscomp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v10_pscomp_1(A) ) ), file(pscomp_1,rc10_pscomp_1), []). fof(rc1_borsuk_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(B,A,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ), file(borsuk_2,rc1_borsuk_2), []). fof(rc1_borsuk_4,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) & v2_connsp_1(B,A) & v6_compts_1(B,A) ) ) ), file(borsuk_4,rc1_borsuk_4), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_isomichi,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) ) ), file(isomichi,rc1_isomichi), []). fof(rc1_jordan,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k5_numbers) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(B) & v3_pre_topc(B,k15_euclid(A)) & v4_pre_topc(B,k15_euclid(A)) & ~ v1_jordan2c(B,A) & v1_jordan1(B,A) ) ) ), file(jordan,rc1_jordan), []). fof(rc1_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v1_jordan2c(A,2) & v1_topreal2(A) ) ), file(jordan1a,rc1_jordan1a), []). fof(rc1_jordan21,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & ~ v1_realset1(A) & v1_topreal2(A) & v1_jordan21(A) ) ), file(jordan21,rc1_jordan21), []). fof(rc1_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_pre_topc(B,k15_euclid(A)) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v2_compts_1(B) & v3_compts_1(B) ) ) ), file(jordan5a,rc1_jordan5a), []). 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_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & v1_metric_1(A) ) ), file(metric_1,rc1_metric_1), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_partfun3,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k1_numbers) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v1_seq_1(B) & v2_partfun3(B) & v3_partfun3(B) ) ), file(partfun3,rc1_partfun3), []). 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_realset1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_realset1(A) ) ), file(realset1,rc1_realset1), []). fof(rc1_seq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(seq_1,rc1_seq_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_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) & v4_tex_4(B,A) ) ) ), file(tex_4,rc1_tex_4), []). fof(rc1_topgen_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_finset_1(B) ) ) ), file(topgen_3,rc1_topgen_3), []). fof(rc1_topgrp_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(topgrp_1,rc1_topgrp_1), []). fof(rc1_topreal6,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_compts_1(A) & v6_group_1(A) & v10_pscomp_1(A) ) ), file(topreal6,rc1_topreal6), []). fof(rc1_topreala,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_monoid_0(A) & v2_monoid_0(A) ) ), file(topreala,rc1_topreala), []). fof(rc1_toprealb,axiom,( ? [A] : ( m1_pre_topc(A,k15_euclid(2)) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_compts_1(A) & v10_pscomp_1(A) & v1_borsuk_2(A) & v1_monoid_0(A) & v2_monoid_0(A) & v1_toprealb(A) ) ), file(toprealb,rc1_toprealb), []). 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_borsuk_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ), file(borsuk_1,rc2_borsuk_1), []). fof(rc2_borsuk_4,axiom,( ! [A] : ( ( ~ v3_realset2(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ), file(borsuk_4,rc2_borsuk_4), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). fof(rc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_tops_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ), file(isomichi,rc2_isomichi), []). fof(rc2_jordan,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(B) & v4_pre_topc(B,k15_euclid(A)) & v1_jordan2c(B,A) & v1_jordan1(B,A) ) ) ), file(jordan,rc2_jordan), []). fof(rc2_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & v1_sppol_1(A) & v1_jordan2c(A,2) ) ), file(jordan1a,rc2_jordan1a), []). fof(rc2_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & ~ v3_struct_0(A) & v1_metric_1(A) ) ), file(metric_1,rc2_metric_1), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_partfun3,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,k1_numbers) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v1_seq_1(B) & v1_partfun3(B) & v4_partfun3(B) ) ), file(partfun3,rc2_partfun3), []). 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_realset1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_realset1(A) ) ), file(realset1,rc2_realset1), []). 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_tex_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & ~ v2_tex_2(B,A) ) ) ), file(tex_4,rc2_tex_4), []). fof(rc2_topgrp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v2_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A)) ) ) ), file(topgrp_1,rc2_topgrp_1), []). fof(rc2_topreal6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v2_connsp_1(A,k15_euclid(2)) & v1_jordan1(A,2) ) ), file(topreal6,rc2_topreal6), []). 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_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) ) ) ), file(borsuk_1,rc3_borsuk_1), []). fof(rc3_borsuk_2,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) ) ), file(borsuk_2,rc3_borsuk_2), []). fof(rc3_borsuk_4,axiom,( ! [A] : ( ~ v1_realset1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_realset1(B) ) ) ), file(borsuk_4,rc3_borsuk_4), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_tops_1(B,A) & v6_tops_1(B,A) ) ) ), file(isomichi,rc3_isomichi), []). fof(rc3_jordan,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(B) & v3_pre_topc(B,k15_euclid(A)) & v1_jordan2c(B,A) & v1_jordan1(B,A) ) ) ), file(jordan,rc3_jordan), []). fof(rc3_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v6_compts_1(A,k15_euclid(2)) & v2_sppol_1(A) & v1_jordan2c(A,2) ) ), file(jordan1a,rc3_jordan1a), []). fof(rc3_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & ~ v3_struct_0(A) & v1_metric_1(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) ) ), file(metric_1,rc3_metric_1), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_partfun3,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) ), file(partfun3,rc3_partfun3), []). fof(rc3_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) ) ) ), file(pre_topc,rc3_pre_topc), []). 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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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_borsuk_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) ) ) ), file(borsuk_1,rc4_borsuk_1), []). fof(rc4_isomichi,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_tdlat_3(A) & ~ v3_realset2(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v3_isomichi(B,A) & v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ), file(isomichi,rc4_isomichi), []). fof(rc4_partfun3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_seq_1(B) & v9_pscomp_1(B,A) & v1_partfun3(B) & v4_partfun3(B) ) ) ), file(partfun3,rc4_partfun3), []). fof(rc4_pre_topc,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v3_struct_0(B) & v1_pre_topc(B) ) ) ), file(pre_topc,rc4_pre_topc), []). 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_rcomp_3,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) & v2_connsp_1(B,A) ) ) ), file(rcomp_3,rc4_rcomp_3), []). fof(rc4_topgrp_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) & v1_tops_1(B,A) ) ) ), file(topgrp_1,rc4_topgrp_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_waybel_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v3_compts_1(A) & v4_compts_1(A) & v5_compts_1(A) & v6_waybel_3(A) ) ), file(waybel_3,rc4_waybel_3), []). 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(rc4_yellow13,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) & v6_group_1(A) & v3_realset2(A) ) ), file(yellow13,rc4_yellow13), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_partfun3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_seq_1(B) & v9_pscomp_1(B,A) & v2_partfun3(B) & v3_partfun3(B) ) ) ), file(partfun3,rc5_partfun3), []). fof(rc5_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) ) ) ), file(pre_topc,rc5_pre_topc), []). fof(rc5_rcomp_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(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) & v2_connsp_1(B,A) ) ) ), file(rcomp_3,rc5_rcomp_3), []). 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(rc5_topgrp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v2_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(B,A,A) & v3_tops_2(B,A,A) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v1_t_0topsp(B,A,A) ) ) ), file(topgrp_1,rc5_topgrp_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(rc6_topgrp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v3_realset2(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_topgrp_1(A) ) ), file(topgrp_1,rc6_topgrp_1), []). fof(rc7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ), file(isomichi,rc7_isomichi), []). 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(rc7_pscomp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),k1_numbers) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_seq_1(B) & v1_partfun1(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) ) ) ), file(pscomp_1,rc7_pscomp_1), []). fof(rc8_pscomp_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(B),k1_numbers) & ~ v1_xboole_0(C) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v1_seq_1(C) & v1_partfun1(C,u1_struct_0(B),k1_numbers) & v9_pscomp_1(C,B) ) ) ), file(pscomp_1,rc8_pscomp_1), []). 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_k12_mcart_1,axiom,( ! [A,B,C,D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => k12_mcart_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ), file(mcart_1,k12_mcart_1), []). fof(redefinition_k12_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => k12_partfun3(A,B,C) = k3_seq_1(B,C) ) ), file(partfun3,k12_partfun3), []). fof(redefinition_k13_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => k13_partfun3(A,B,C) = k4_seq_1(B,C) ) ), file(partfun3,k13_partfun3), []). fof(redefinition_k14_funct_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,A,C) & m1_relset_1(E,A,C) ) => k14_funct_3(A,B,C,D,E) = k13_funct_3(D,E) ) ), file(funct_3,k14_funct_3), []). fof(redefinition_k14_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => k14_partfun3(A,B,C) = k5_seq_1(B,C) ) ), file(partfun3,k14_partfun3), []). fof(redefinition_k15_partfun3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => k15_partfun3(A,B) = k15_seq_1(B) ) ), file(partfun3,k15_partfun3), []). fof(redefinition_k17_partfun3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & v4_partfun3(B) & m1_relset_1(B,u1_struct_0(A),k1_numbers) ) => k17_partfun3(A,B) = k1_partfun3(B) ) ), file(partfun3,k17_partfun3), []). fof(redefinition_k1_borsuk_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k1_borsuk_1(A,B,C) = k2_funcop_1(B,C) ) ), file(borsuk_1,k1_borsuk_1), []). fof(redefinition_k1_jordan,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) ) => k1_jordan(A,B,C) = k1_mcart_1(C) ) ), file(jordan,k1_jordan), []). fof(redefinition_k1_partfun1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) ) => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ), file(partfun1,k1_partfun1), []). fof(redefinition_k1_pscomp_1,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k1_pscomp_1(A,B,C) = k2_relat_1(C) ) ), file(pscomp_1,k1_pscomp_1), []). fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) ), file(real_1,k1_real_1), []). fof(redefinition_k1_seq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_seq_1(A) ) => k1_seq_1(A,B) = k1_funct_1(A,B) ) ), file(seq_1,k1_seq_1), []). fof(redefinition_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). fof(redefinition_k20_partfun3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v9_pscomp_1(B,A) & m1_relset_1(B,u1_struct_0(A),k1_numbers) & v2_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v9_pscomp_1(C,A) & m1_relset_1(C,u1_struct_0(A),k1_numbers) ) => k20_partfun3(A,B,C) = k1_rfunct_1(B,C) ) ), file(partfun3,k20_partfun3), []). fof(redefinition_k2_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => k2_funct_2(A,B,C,D) = k9_relat_1(C,D) ) ), file(funct_2,k2_funct_2), []). fof(redefinition_k2_jordan,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) ) => k2_jordan(A,B,C) = k2_mcart_1(C) ) ), file(jordan,k2_jordan), []). fof(redefinition_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(A) = k5_xcmplx_0(A) ) ), file(real_1,k2_real_1), []). fof(redefinition_k3_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ), file(real_1,k3_real_1), []). fof(redefinition_k3_topalg_2,axiom,( k3_topalg_2 = k3_topmetr ), file(topalg_2,k3_topalg_2), []). fof(redefinition_k4_pre_topc,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => k4_pre_topc(A,B,C,D) = k9_relat_1(C,D) ) ), file(pre_topc,k4_pre_topc), []). 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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_real_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ), file(real_1,k5_real_1), []). fof(redefinition_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A,B) = k3_tarski(B) ) ), file(setfam_1,k5_setfam_1), []). fof(redefinition_k6_partfun1,axiom,( ! [A] : k6_partfun1(A) = k6_relat_1(A) ), file(partfun1,k6_partfun1), []). fof(redefinition_k7_borsuk_1,axiom,( ! [A,B,C,D] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => k7_borsuk_1(A,B,C,D) = k2_zfmisc_1(C,D) ) ), file(borsuk_1,k7_borsuk_1), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), []). fof(redefinition_k7_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k7_square_1(A) = k5_square_1(A) ) ), file(square_1,k7_square_1), []). fof(redefinition_k8_borsuk_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => k8_borsuk_1(A,B,C,D) = k4_tarski(C,D) ) ), file(borsuk_1,k8_borsuk_1), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k9_square_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k9_square_1(A) = k8_square_1(A) ) ), file(square_1,k9_square_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r1_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(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(symmetry_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) => r1_subset_1(B,A) ) ) ), file(subset_1,r1_subset_1), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). fof(t106_zfmisc_1,axiom,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), []). fof(t116_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ~ ( r2_hidden(E,k2_funct_2(A,B,D,C)) & ! [F] : ( m1_subset_1(F,A) => ~ ( r2_hidden(F,C) & E = k1_funct_1(D,F) ) ) ) ) ), file(funct_2,t116_funct_2), []). fof(t11_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( k21_euclid(A) = k21_euclid(B) & k22_euclid(A) = k22_euclid(B) ) => A = B ) ) ) ), file(topreal3,t11_topreal3), []). fof(t11_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xreal_0(A,B) <=> r1_xreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t11_xreal_1), []). fof(t12_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => k2_pre_topc(A) = u1_struct_0(A) ) ), file(pre_topc,t12_pre_topc), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t156_relat_1,axiom,( ! [A,B,C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ), file(relat_1,t156_relat_1), []). fof(t16_topreal9,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_tarski(k1_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) ), file(topreal9,t16_topreal9), []). fof(t17_topreal9,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_tarski(k3_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) ), file(topreal9,t17_topreal9), []). fof(t17_xboole_1,axiom,( ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ), file(xboole_1,t17_xboole_1), []). fof(t19_topreal9,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xboole_0(k1_topreal9(A,C,B),k3_topreal9(A,C,B)) ) ) ) ), file(topreal9,t19_topreal9), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_jordan1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => u1_struct_0(k3_pre_topc(A,B)) = B ) ) ), file(jordan1,t1_jordan1), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v2_funct_1(A) & r1_tarski(B,k1_relat_1(k2_funct_1(A))) ) => k9_relat_1(A,k9_relat_1(k2_funct_1(A),B)) = B ) ) ), file(partfun3,t1_partfun3), []). 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(t20_jgraph_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v5_pre_topc(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),E) & v3_pre_topc(E,B) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,F) & v3_pre_topc(F,A) & r1_tarski(k4_pre_topc(A,B,C,F),E) ) ) ) ) ) ) ) ) ) ), file(jgraph_2,t20_jgraph_2), []). fof(t21_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ), file(funct_2,t21_funct_2), []). fof(t23_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), []). fof(t23_mcart_1,axiom,( ! [A,B,C] : ( r2_hidden(A,k2_zfmisc_1(B,C)) => A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ), file(mcart_1,t23_mcart_1), []). fof(t24_topmetr,axiom,( u1_struct_0(k3_topmetr) = k1_numbers ), file(topmetr,t24_topmetr), []). fof(t25_topgrp_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v3_tops_2(C,A,B) <=> ( k1_relat_1(C) = k2_pre_topc(A) & k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(D,A) <=> v3_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ) ), file(topgrp_1,t25_topgrp_1), []). fof(t27_xboole_1,axiom,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ), file(xboole_1,t27_xboole_1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k5_square_1(A),k5_square_1(B)) = 0 <=> ( A = 0 & B = 0 ) ) ) ) ), file(complex1,t2_complex1), []). 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_topmetr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) ), file(topmetr,t2_topmetr), []). fof(t32_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v3_pre_topc(C,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & k3_xboole_0(D,k2_pre_topc(B)) = C ) ) ) ) ) ), file(tops_2,t32_tops_2), []). fof(t33_zfmisc_1,axiom,( ! [A,B,C,D] : ( k4_tarski(A,B) = k4_tarski(C,D) => ( A = C & B = D ) ) ), file(zfmisc_1,t33_zfmisc_1), []). fof(t35_funct_1,axiom,( ! [A,B] : ( r2_hidden(B,A) => k1_funct_1(k6_relat_1(A),B) = B ) ), file(funct_1,t35_funct_1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_brouwer,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => u1_struct_0(k2_brouwer(A,C,B)) = k2_topreal9(A,C,B) ) ) ) ), file(brouwer,t3_brouwer), []). 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_0,axiom,( ! [A,B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) ), file(xboole_0,t3_xboole_0), []). fof(t41_yellow12,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(C)) & v5_pre_topc(E,A,C) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(C)) ) => ( v1_funct_1(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)) & v1_funct_2(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) & v5_pre_topc(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,k6_borsuk_1(B,C)) & m2_relset_1(k14_funct_3(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(k6_borsuk_1(B,C))) ) ) ) ) ) ) ), file(yellow12,t41_yellow12), []). fof(t43_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( B != k1_xboole_0 => ! [E] : ( ? [F] : ( r2_hidden(F,A) & r2_hidden(F,C) & E = k1_funct_1(D,F) ) => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ), file(funct_2,t43_funct_2), []). fof(t45_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B)))) => ( v3_pre_topc(C,k6_borsuk_1(A,B)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k6_borsuk_1(A,B))))) & C = k5_setfam_1(u1_struct_0(k6_borsuk_1(A,B)),D) & ! [E] : ~ ( r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) => ~ ( E = k12_mcart_1(u1_struct_0(A),u1_struct_0(B),F,G) & v3_pre_topc(F,A) & v3_pre_topc(G,B) ) ) ) ) ) ) ) ) ) ), file(borsuk_1,t45_borsuk_1), []). fof(t46_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k7_square_1(k5_toprns_1(2,A)) = k3_real_1(k7_square_1(k21_euclid(A)),k7_square_1(k22_euclid(A))) ) ), file(jgraph_1,t46_jgraph_1), []). fof(t46_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_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(t55_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k5_relat_1(k5_relat_1(A,B),C) = k5_relat_1(A,k5_relat_1(B,C)) ) ) ) ), file(relat_1,t55_relat_1), []). fof(t56_topreala,axiom,( v3_tops_2(k2_topreala,k6_borsuk_1(k3_topalg_2,k3_topalg_2),k15_euclid(2)) ), file(topreala,t56_topreala), []). fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(0,A) = 0 ) ), file(arithm,t5_arithm), []). 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(t62_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) ) => ( k1_relat_1(k2_tops_2(A,B,C)) = k2_pre_topc(B) & k2_relat_1(k2_tops_2(A,B,C)) = k2_pre_topc(A) ) ) ) ) ) ), file(tops_2,t62_tops_2), []). fof(t65_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ( k2_relat_1(C) = k2_pre_topc(B) & v2_funct_1(C) ) => ( k5_relat_1(C,k2_tops_2(A,B,C)) = k6_relat_1(k1_relat_1(C)) & k5_relat_1(k2_tops_2(A,B,C),C) = k6_relat_1(k2_relat_1(C)) ) ) ) ) ) ), file(tops_2,t65_tops_2), []). fof(t69_funct_3,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( k1_relat_1(C) = B & k1_relat_1(D) = B & r2_hidden(A,B) ) => k1_funct_1(k13_funct_3(C,D),A) = k4_tarski(k1_funct_1(C,A),k1_funct_1(D,A)) ) ) ) ), file(funct_3,t69_funct_3), []). 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(t70_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v3_tops_2(C,A,B) => v3_tops_2(k2_tops_2(A,B,C),B,A) ) ) ) ) ), file(tops_2,t70_tops_2), []). fof(t71_relat_1,axiom,( ! [A] : ( k1_relat_1(k6_relat_1(A)) = A & k2_relat_1(k6_relat_1(A)) = A ) ), file(relat_1,t71_relat_1), []). fof(t72_funct_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => k1_funct_1(k7_relat_1(C,A),B) = k1_funct_1(C,B) ) ) ), file(funct_1,t72_funct_1), []). fof(t77_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(0,A) & r1_xreal_0(A,B) ) => r1_xreal_0(k5_square_1(A),k5_square_1(B)) ) ) ) ), file(square_1,t77_square_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),B) ) ) ) ), file(funct_2,t7_funct_2), []). 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(t83_topreal6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & m2_relset_1(B,u1_struct_0(A),k1_numbers) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k3_topmetr)) ) => ( B = C => ( v9_pscomp_1(B,A) <=> v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) ), file(topreal6,t83_topreal6), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_brouwer,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ( ( m1_subset_1(G,u1_struct_0(k2_brouwer(2,I,B))) & m1_subset_1(H,u1_struct_0(k2_brouwer(2,I,B))) & C = k5_real_1(k21_euclid(H),k21_euclid(G)) & D = k5_real_1(k22_euclid(H),k22_euclid(G)) & E = k5_real_1(k21_euclid(G),k21_euclid(I)) & F = k5_real_1(k22_euclid(G),k22_euclid(I)) & A = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(E,C),k3_xcmplx_0(F,D))),k8_square_1(k6_xcmplx_0(k5_square_1(k2_xcmplx_0(k3_xcmplx_0(E,C),k3_xcmplx_0(F,D))),k3_xcmplx_0(k2_xcmplx_0(k5_square_1(C),k5_square_1(D)),k6_xcmplx_0(k2_xcmplx_0(k5_square_1(E),k5_square_1(F)),k5_square_1(B)))))),k2_xcmplx_0(k5_square_1(C),k5_square_1(D))) ) => ( G = H | k3_brouwer(2,I,G,H,B) = k23_euclid(k2_xcmplx_0(k21_euclid(G),k3_xcmplx_0(A,C)),k2_xcmplx_0(k22_euclid(G),k3_xcmplx_0(A,D))) ) ) ) ) ) ) ) ) ) ) ) ), file(brouwer,t8_brouwer), []). 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(t8_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k21_euclid(k20_euclid(2,A,B)) = k5_real_1(k21_euclid(A),k21_euclid(B)) & k22_euclid(k20_euclid(2,A,B)) = k5_real_1(k22_euclid(A),k22_euclid(B)) ) ) ) ), file(topreal3,t8_topreal3), []). fof(t8_topreal9,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(C,k2_topreal9(A,D,B)) <=> r1_xreal_0(k5_toprns_1(A,k20_euclid(A,C,D)),B) ) ) ) ) ) ), file(topreal9,t8_topreal9), []). fof(t92_zfmisc_1,axiom,( ! [A,B] : ( r2_hidden(A,B) => r1_tarski(A,k3_tarski(B)) ) ), file(zfmisc_1,t92_zfmisc_1), []). 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), []). fof(t9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xreal_0(A,B) & r1_xreal_0(C,D) ) => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ), file(xreal_1,t9_xreal_1), []).