% Mizar problem: t5_msscyc_2,msscyc_2,768,77 fof(t5_msscyc_2,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & v1_pre_circ(B,u1_struct_0(A)) & m1_pboole(B,u1_struct_0(A)) ) => ( v5_msscyc_1(A) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => v1_finset_1(a_4_0_msscyc_2(A,B,C,D)) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc10_membered,cc10_trees_3,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_dtconstr,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_membered,cc1_msafree2,cc1_msaterm,cc1_msualg_1,cc1_nat_1,cc1_pre_circ,cc1_relset_1,cc1_trees_9,cc1_xreal_0,cc20_membered,cc2_dtconstr,cc2_finset_1,cc2_membered,cc2_msualg_1,cc2_nat_1,cc2_trees_9,cc2_xreal_0,cc3_membered,cc3_msafree2,cc3_nat_1,cc3_trees_9,cc3_xreal_0,cc4_membered,cc4_msafree2,cc4_trees_3,cc4_trees_9,cc4_xreal_0,cc5_trees_3,cc5_trees_9,cc5_xreal_0,cc6_membered,cc6_trees_3,cc6_trees_9,cc6_xreal_0,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d11_finseq_1,d13_msafree,d14_msafree2,d16_msafree,d1_trees_9,d3_finseq_1,d3_tarski,d4_card_3,d4_tarski,d5_card_3,d5_funct_1,d5_msaterm,d5_tarski,d6_msscyc_1,d6_tarski,dt_g1_lang1,dt_g3_msualg_1,dt_k10_msafree,dt_k11_msafree,dt_k12_msafree,dt_k13_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_msaterm,dt_k1_msualg_1,dt_k1_msualg_2,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_msaterm,dt_k2_msualg_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_1,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_tarski,dt_k4_card_3,dt_k4_dtconstr,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_tarski,dt_k4_trees_4,dt_k5_msafree,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_trees_3,dt_k6_lang1,dt_k6_msafree,dt_k6_pboole,dt_k6_trees_1,dt_k7_dtconstr,dt_k7_msafree,dt_k7_msaterm,dt_k7_pboole,dt_k8_msafree,dt_k8_pboole,dt_k9_msafree2,dt_l1_lang1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_msaterm,dt_m1_pboole,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m1_trees_4,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_m3_trees_2,dt_m4_trees_3,dt_m5_trees_3,dt_u1_lang1,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_lang1,existence_l1_msualg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_msaterm,existence_m1_pboole,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m1_trees_4,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc10_membered,fc10_xreal_0,fc11_finseq_1,fc11_membered,fc11_xreal_0,fc12_membered,fc12_xreal_0,fc13_membered,fc14_finset_1,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc17_finseq_1,fc1_dtconstr,fc1_finseq_1,fc1_finset_1,fc1_msaterm,fc1_msualg_1,fc1_nat_1,fc1_ordinal2,fc1_struct_0,fc22_membered,fc22_trees_3,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc26_trees_3,fc2_dtconstr,fc2_finseq_1,fc2_finset_1,fc2_membered,fc2_msafree,fc2_msaterm,fc2_trees_9,fc3_dtconstr,fc3_msafree,fc3_msscyc_1,fc3_nat_1,fc3_pre_circ,fc3_trees_9,fc3_xreal_0,fc4_msafree,fc4_nat_1,fc5_membered,fc5_msafree,fc6_membered,fc6_msafree,fc6_trees_3,fc7_membered,fc7_msafree,fc7_xreal_0,fc8_membered,fc8_msafree,fc8_xreal_0,fc9_finseq_1,fc9_finset_1,fc9_membered,fc9_msafree,fc9_trees_9,fc9_xreal_0,fraenkel_a_0_0_topreal1,fraenkel_a_0_1_topreal1,fraenkel_a_0_2_topreal1,fraenkel_a_0_4_fraenkel,fraenkel_a_0_5_fraenkel,fraenkel_a_2_0_msscyc_1,fraenkel_a_2_0_msscyc_2,fraenkel_a_3_1_msscyc_2,fraenkel_a_3_2_msscyc_1,fraenkel_a_3_2_msscyc_2,fraenkel_a_4_0_msscyc_2,fraenkel_a_4_1_msscyc_2,fraenkel_a_4_2_msscyc_2,fraenkel_a_4_3_msscyc_2,fraenkel_a_5_0_msscyc_2,fraenkel_a_5_1_msscyc_2,fraenkel_a_5_2_msscyc_2,fraenkel_a_5_3_msscyc_2,fraenkel_a_6_0_msscyc_2,fraenkel_a_6_1_msscyc_2,free_g1_lang1,free_g3_msualg_1,idempotence_k2_xboole_0,rc1_dtconstr,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_membered,rc1_nat_1,rc1_pre_circ,rc1_trees_9,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_nat_1,rc2_pre_circ,rc2_trees_3,rc2_trees_9,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_nat_1,rc3_struct_0,rc3_trees_9,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_trees_3,rc4_trees_9,rc4_xreal_0,rc5_msafree2,rc5_msualg_1,rc5_struct_0,rc5_trees_9,rc6_finseq_1,rc6_msafree2,rc6_msualg_1,rc6_trees_3,rc6_trees_9,rc7_finseq_1,rc8_finseq_1,rc8_trees_3,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k2_msaterm,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k7_dtconstr,redefinition_k7_pboole,redefinition_k8_pboole,redefinition_m1_dtconstr,redefinition_m1_struct_0,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,redefinition_r2_wellord2,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r2_wellord2,s1_nat_1__e5_8__msscyc_2,s1_topreal1__e6_8_2__msscyc_2,s2_finseq_1__e10_8_2__msscyc_2,s2_finseq_1__e8_8_2_1__msscyc_2,s3_fraenkel__e5_8_2__msscyc_2,spc0_boole,spc1_boole,spc1_numerals,symmetry_r2_wellord2,t10_msaterm,t12_msaterm,t13_finset_1,t14_finset_1,t15_trees_4,t17_msaterm,t1_arithm,t1_boole,t1_msscyc_1,t1_numerals,t1_real,t1_subset,t20_msscyc_1,t22_msaterm,t23_msaterm,t26_msscyc_1,t26_nat_1,t27_msscyc_1,t28_msscyc_1,t2_real,t2_subset,t2_tarski,t33_zfmisc_1,t37_nat_1,t38_nat_1,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t63_card_4,t68_card_1,t6_boole,t6_real,t73_finseq_1,t79_trees_1,t7_boole,t7_real,t8_boole,t8_real]), [file(msscyc_2,t5_msscyc_2)]). fof(abstractness_v1_lang1,axiom,( ! [A] : ( l1_lang1(A) => ( v1_lang1(A) => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) ), file(lang1,v1_lang1), []). fof(abstractness_v4_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(B,A) => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ), file(msualg_1,v4_msualg_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). fof(cc10_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v6_trees_3(B) ) ) ), file(trees_3,cc10_trees_3), []). fof(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_dtconstr,axiom,( ! [A,B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) ), file(dtconstr,cc1_dtconstr), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_msafree2,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v3_struct_0(A) & v2_msualg_1(A) ) => ( ~ v3_struct_0(A) & v2_msafree2(A) ) ) ) ), file(msafree2,cc1_msafree2), []). fof(cc1_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k1_msaterm(A,B)) => v1_finset_1(C) ) ) ), file(msaterm,cc1_msaterm), []). fof(cc1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc1_msualg_1), []). 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_pre_circ,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_trees_3(A)) => v1_finset_1(B) ) ) ), file(pre_circ,cc1_pre_circ), []). 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_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ) ), file(trees_9,cc1_trees_9), []). fof(cc1_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_dtconstr,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m4_trees_3(B,A) ) => ! [C] : ( m1_finseq_1(C,B) => v6_trees_3(C) ) ) ), file(dtconstr,cc2_dtconstr), []). fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc2_msualg_1), []). 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_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v1_trees_9(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ) ), file(trees_9,cc2_trees_9), []). fof(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) => ( ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) ), file(msafree2,cc3_msafree2), []). 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_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v2_trees_9(A) ) ) ), file(trees_9,cc3_trees_9), []). fof(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) => ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) ) ) ) ) ), file(msafree2,cc4_msafree2), []). fof(cc4_trees_3,axiom,( ! [A] : ( v3_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_trees_3(B) ) ) ), file(trees_3,cc4_trees_3), []). fof(cc4_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) ) ), file(trees_9,cc4_trees_9), []). fof(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). fof(cc5_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_trees_3(B,A) => v3_trees_3(B) ) ) ), file(trees_3,cc5_trees_3), []). fof(cc5_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v4_trees_9(A) ) ) ), file(trees_9,cc5_trees_9), []). fof(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(cc6_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(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_funct_2(C,A,B) & v3_trees_2(C) ) ) ) ) ), file(trees_3,cc6_trees_3), []). fof(cc6_trees_9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A))) ) => ! [C] : ( m1_subset_1(C,B) => v1_finset_1(C) ) ) ), file(trees_9,cc6_trees_9), []). fof(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). fof(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(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(d11_finseq_1,axiom,( ! [A,B] : ( B = k13_finseq_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m2_finseq_1(C,A) ) ) ), file(finseq_1,d11_finseq_1), []). fof(d13_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_pboole(C,u1_struct_0(A)) => ( C = k8_msafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k7_msafree(A,B,D) ) ) ) ) ) ), file(msafree,d13_msafree), []). fof(d14_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( E = k9_msafree2(A,B,C,D) <=> ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finset_1(F) & v3_trees_2(F) & ? [G] : ( ~ v1_xboole_0(G) & v1_finset_1(G) & v1_trees_1(G) & F = D & G = k1_relat_1(F) & E = k6_trees_1(G) ) ) ) ) ) ) ) ) ), file(msafree2,d14_msafree2), []). fof(d16_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => k11_msafree(A,B) = g3_msualg_1(A,k8_msafree(A,B),k10_msafree(A,B)) ) ) ), file(msafree,d16_msafree), []). fof(d1_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( v1_trees_9(A) <=> k1_relat_1(A) = k2_trees_1(0) ) ) ), file(trees_9,d1_trees_9), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ), file(card_3,d4_card_3), []). fof(d4_tarski,axiom,( ! [A,B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) ), file(tarski,d4_tarski), []). fof(d5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k4_card_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & C = D & k1_relat_1(D) = k1_relat_1(A) & ! [E] : ( r2_hidden(E,k1_relat_1(A)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ), file(card_3,d5_card_3), []). fof(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_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k7_msaterm(A,B,C) <=> r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) ) ), file(msaterm,d5_msaterm), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_msscyc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ( v5_msscyc_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_finset_1(a_2_0_msscyc_1(A,B)) ) ) ) ), file(msscyc_1,d6_msscyc_1), []). fof(d6_tarski,axiom,( ! [A,B] : ( r2_tarski(A,B) <=> ? [C] : ( ! [D] : ~ ( r2_hidden(D,A) & ! [E] : ~ ( r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C) ) ) & ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ~ ( r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C) ) ) & ! [D,E,F,G] : ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) ) => ( D = F <=> E = G ) ) ) ) ), file(tarski,d6_tarski), []). fof(dt_g1_lang1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k3_finseq_2(A)) => ( v1_lang1(g1_lang1(A,B)) & l1_lang1(g1_lang1(A,B)) ) ) ), file(lang1,g1_lang1), []). fof(dt_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ( v4_msualg_1(g3_msualg_1(A,B,C),A) & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ), file(msualg_1,g3_msualg_1), []). fof(dt_k10_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m3_pboole(k10_msafree(A,B),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B))) ) ), file(msafree,k10_msafree), []). fof(dt_k11_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => l3_msualg_1(k11_msafree(A,B),A) ) ), file(msafree,k11_msafree), []). fof(dt_k12_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k12_msafree(A,B,C),k1_zfmisc_1(k1_funct_1(k8_msafree(A,B),C))) ) ), file(msafree,k12_msafree), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => m1_subset_1(k1_msaterm(A,B),k1_zfmisc_1(k5_trees_3(u1_struct_0(k5_msafree(A,B))))) ) ), file(msaterm,k1_msaterm), []). fof(dt_k1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(msualg_1,k1_msualg_1), []). fof(dt_k1_msualg_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k1_msualg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) ) ), file(msualg_2,k1_msualg_2), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). fof(dt_k2_msaterm,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => m1_struct_0(k2_msaterm(A,B,C),k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B))) ) ), file(msaterm,k2_msaterm), []). fof(dt_k2_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,k2_msualg_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_trees_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k2_trees_1(A)) & v1_finset_1(k2_trees_1(A)) & v1_trees_1(k2_trees_1(A)) ) ) ), file(trees_1,k2_trees_1), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_card_3,axiom,( $true ), file(card_3,k3_card_3), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_lang1(A) ) => m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) ), file(dtconstr,k4_dtconstr), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k4_trees_4(A,B)) & v1_funct_1(k4_trees_4(A,B)) & v3_trees_2(k4_trees_4(A,B)) ) ) ), file(trees_4,k4_trees_4), []). fof(dt_k5_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => l1_lang1(k5_msafree(A,B)) ) ), file(msafree,k5_msafree), []). 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_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_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m4_trees_3(k5_trees_3(A),A) ) ), file(trees_3,k5_trees_3), []). fof(dt_k6_lang1,axiom,( $true ), file(lang1,k6_lang1), []). fof(dt_k6_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => m1_subset_1(k6_msafree(A,B,C),u1_struct_0(k5_msafree(A,B))) ) ), file(msafree,k6_msafree), []). fof(dt_k6_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ), file(pboole,k6_pboole), []). fof(dt_k6_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => m2_subset_1(k6_trees_1(A),k1_numbers,k5_numbers) ) ), file(trees_1,k6_trees_1), []). fof(dt_k7_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k7_dtconstr(A)) & m1_subset_1(k7_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(dtconstr,k7_dtconstr), []). fof(dt_k7_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k7_msafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k5_msafree(A,B)))) ) ), file(msafree,k7_msafree), []). fof(dt_k7_msaterm,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k1_msaterm(A,B)) ) => m1_subset_1(k7_msaterm(A,B,C),u1_struct_0(A)) ) ), file(msaterm,k7_msaterm), []). fof(dt_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => m1_pboole(k7_pboole(A,B,C,D),A) ) ), file(pboole,k7_pboole), []). fof(dt_k8_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m1_pboole(k8_msafree(A,B),u1_struct_0(A)) ) ), file(msafree,k8_msafree), []). fof(dt_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => ( v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ), file(pboole,k8_pboole), []). fof(dt_k9_msafree2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) ) => m2_subset_1(k9_msafree2(A,B,C,D),k1_numbers,k5_numbers) ) ), file(msafree2,k9_msafree2), []). fof(dt_l1_lang1,axiom,( ! [A] : ( l1_lang1(A) => l1_struct_0(A) ) ), file(lang1,l1_lang1), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_dtconstr(D,A,B,C) => m5_trees_3(D,A,B) ) ) ), file(dtconstr,m1_dtconstr), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_msaterm,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) ) => ! [D] : ( m1_msaterm(D,A,B,C) => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ), file(msaterm,m1_msaterm), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) => m2_finseq_1(C,A) ) ) ), file(trees_4,m1_trees_4), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). 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_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => m1_pboole(D,A) ) ) ), file(pboole,m3_pboole), []). fof(dt_m3_trees_2,axiom,( ! [A,B] : ( m3_trees_2(B,A) => v1_relat_1(B) ) ), file(trees_2,m3_trees_2), []). fof(dt_m4_trees_3,axiom,( $true ), file(trees_3,m4_trees_3), []). fof(dt_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ! [C] : ( m5_trees_3(C,A,B) => ( v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) ) ) ) ), file(trees_3,m5_trees_3), []). fof(dt_u1_lang1,axiom,( ! [A] : ( l1_lang1(A) => m2_relset_1(u1_lang1(A),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(lang1,u1_lang1), []). fof(dt_u1_msualg_1,axiom,( $true ), file(msualg_1,u1_msualg_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u2_msualg_1(A)) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ), file(msualg_1,u2_msualg_1), []). fof(dt_u3_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u3_msualg_1(A)) & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ), file(msualg_1,u3_msualg_1), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(dt_u5_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ), file(msualg_1,u5_msualg_1), []). fof(existence_l1_lang1,axiom,( ? [A] : l1_lang1(A) ), file(lang1,l1_lang1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : m1_dtconstr(D,A,B,C) ) ), file(dtconstr,m1_dtconstr), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_msaterm,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,k7_dtconstr(k5_msafree(A,B))) ) => ? [D] : m1_msaterm(D,A,B,C) ) ), file(msaterm,m1_msaterm), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m1_trees_4(C,A,B) ) ), file(trees_4,m1_trees_4), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). 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(existence_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m3_pboole(D,A,B,C) ) ), file(pboole,m3_pboole), []). fof(existence_m3_trees_2,axiom,( ! [A] : ? [B] : m3_trees_2(B,A) ), file(trees_2,m3_trees_2), []). fof(existence_m4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m4_trees_3(B,A) ) ), file(trees_3,m4_trees_3), []). fof(existence_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ? [C] : m5_trees_3(C,A,B) ) ), file(trees_3,m5_trees_3), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc1_dtconstr,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,k3_finseq_2(A)) ) => ( ~ v3_struct_0(g1_lang1(A,B)) & v1_lang1(g1_lang1(A,B)) ) ) ), file(dtconstr,fc1_dtconstr), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_msaterm,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(msaterm,fc1_msaterm), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_1), []). 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_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc22_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ~ v1_xboole_0(k2_xboole_0(A,B)) & v1_trees_1(k2_xboole_0(A,B)) ) ) ), file(trees_3,fc22_trees_3), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc26_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_trees_3(A)) ) => ( ~ v1_xboole_0(k1_relat_1(B)) & v1_finset_1(k1_relat_1(B)) & v1_trees_1(k1_relat_1(B)) ) ) ), file(trees_3,fc26_trees_3), []). fof(fc2_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k4_dtconstr(A)) & v3_trees_3(k4_dtconstr(A)) ) ) ), file(dtconstr,fc2_dtconstr), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_msafree,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ~ v1_xboole_0(k3_card_3(B)) ) ), file(msafree,fc2_msafree), []). fof(fc2_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k1_msaterm(A,B)) & v3_trees_3(k1_msaterm(A,B)) ) ) ), file(msaterm,fc2_msaterm), []). fof(fc2_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) & v1_trees_2(k1_relat_1(A)) & v2_trees_9(k1_relat_1(A)) ) ) ), file(trees_9,fc2_trees_9), []). fof(fc3_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k4_dtconstr(A)) & v3_trees_3(k4_dtconstr(A)) ) ) ), file(dtconstr,fc3_dtconstr), []). fof(fc3_msafree,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(u1_msualg_1(A)) ) ), file(msafree,fc3_msafree), []). fof(fc3_msscyc_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & v1_pre_circ(B,u1_struct_0(A)) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k12_msafree(A,B,C)) & v1_finset_1(k12_msafree(A,B,C)) ) ) ), file(msscyc_1,fc3_msscyc_1), []). 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_pre_circ,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v2_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) ) ) ), file(pre_circ,fc3_pre_circ), []). fof(fc3_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v4_trees_9(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) & v2_trees_9(k1_relat_1(A)) ) ) ), file(trees_9,fc3_trees_9), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc4_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_msafree(A,B)) & v1_lang1(k5_msafree(A,B)) ) ) ), file(msafree,fc4_msafree), []). 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(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_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_msafree(A,B)) & v1_lang1(k5_msafree(A,B)) & v1_dtconstr(k5_msafree(A,B)) & v2_dtconstr(k5_msafree(A,B)) & v3_dtconstr(k5_msafree(A,B)) ) ) ), file(msafree,fc5_msafree), []). 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_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k7_msafree(A,B,C)) & v3_trees_3(k7_msafree(A,B,C)) ) ) ), file(msafree,fc6_msafree), []). fof(fc6_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k5_trees_3(A)) & v3_trees_3(k5_trees_3(A)) ) ) ), file(trees_3,fc6_trees_3), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_relat_1(k8_msafree(A,B)) & v2_relat_1(k8_msafree(A,B)) & ~ v3_relat_1(k8_msafree(A,B)) & v1_funct_1(k8_msafree(A,B)) ) ) ), file(msafree,fc7_msafree), []). 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_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k11_msafree(A,B),A) & v5_msualg_1(k11_msafree(A,B),A) ) ) ), file(msafree,fc8_msafree), []). 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_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ~ v1_xboole_0(k12_msafree(A,B,C)) ) ), file(msafree,fc9_msafree), []). fof(fc9_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v3_trees_3(k1_tarski(A)) ) ) ), file(trees_9,fc9_trees_9), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_0_0_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topreal1) <=> ? [B] : ( m1_subset_1(B,f1_s1_topreal1) & A = B & ( p1_s1_topreal1(B) | p2_s1_topreal1(B) ) ) ) ), file(topreal1,a_0_0_topreal1), []). fof(fraenkel_a_0_1_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_topreal1) <=> ? [B] : ( m1_subset_1(B,f1_s1_topreal1) & A = B & p1_s1_topreal1(B) ) ) ), file(topreal1,a_0_1_topreal1), []). fof(fraenkel_a_0_2_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_2_topreal1) <=> ? [B] : ( m1_subset_1(B,f1_s1_topreal1) & A = B & p2_s1_topreal1(B) ) ) ), file(topreal1,a_0_2_topreal1), []). fof(fraenkel_a_0_4_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_4_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p1_s3_fraenkel(B) ) ) ), file(fraenkel,a_0_4_fraenkel), []). fof(fraenkel_a_0_5_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_5_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p2_s3_fraenkel(B) ) ) ), file(fraenkel,a_0_5_fraenkel), []). fof(fraenkel_a_2_0_msscyc_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_msscyc_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_msualg_1(B)) & A = D & k2_msualg_1(B,D) = C ) ) ) ), file(msscyc_1,a_2_0_msscyc_1), []). fof(fraenkel_a_2_0_msscyc_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_msscyc_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_msualg_1(B)) & A = D & k2_msualg_1(B,D) = C ) ) ) ), file(msscyc_2,a_2_0_msscyc_2), []). fof(fraenkel_a_3_1_msscyc_2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_msscyc_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),D)) & A = E & r1_xreal_0(k9_msafree2(B,C,D,E),0) ) ) ) ), file(msscyc_2,a_3_1_msscyc_2), []). fof(fraenkel_a_3_2_msscyc_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_msscyc_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),D)) & A = E & k9_msafree2(B,C,D,E) = 0 ) ) ) ), file(msscyc_1,a_3_2_msscyc_1), []). fof(fraenkel_a_3_2_msscyc_2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_msscyc_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),D)) & A = E & k9_msafree2(B,C,D,E) = 0 ) ) ) ), file(msscyc_2,a_3_2_msscyc_2), []). fof(fraenkel_a_4_0_msscyc_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_msscyc_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & A = F & r1_xreal_0(k9_msafree2(B,C,E,F),D) ) ) ) ), file(msscyc_2,a_4_0_msscyc_2), []). fof(fraenkel_a_4_1_msscyc_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_msscyc_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & A = F & r1_xreal_0(k9_msafree2(B,C,E,F),k1_nat_1(D,1)) ) ) ) ), file(msscyc_2,a_4_1_msscyc_2), []). fof(fraenkel_a_4_2_msscyc_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_2_msscyc_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & A = F & ( r1_xreal_0(k9_msafree2(B,C,E,F),D) | k9_msafree2(B,C,E,F) = k1_nat_1(D,1) ) ) ) ) ), file(msscyc_2,a_4_2_msscyc_2), []). fof(fraenkel_a_4_3_msscyc_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_3_msscyc_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & A = F & k9_msafree2(B,C,E,F) = k1_nat_1(D,1) ) ) ) ), file(msscyc_2,a_4_3_msscyc_2), []). fof(fraenkel_a_5_0_msscyc_2,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_msualg_1(B)) ) => ( r2_hidden(A,a_5_0_msscyc_2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k13_finseq_1(k1_msaterm(B,C))) & A = k4_trees_4(k4_tarski(F,u1_struct_0(B)),G) & m1_msaterm(G,B,C,k2_msaterm(B,C,F)) & ? [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & k9_msafree2(B,C,E,H) = k1_nat_1(D,1) & H = k4_trees_4(k4_tarski(F,u1_struct_0(B)),G) ) ) ) ) ), file(msscyc_2,a_5_0_msscyc_2), []). fof(fraenkel_a_5_1_msscyc_2,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_msualg_1(B)) ) => ( r2_hidden(A,a_5_1_msscyc_2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k13_finseq_1(k1_msaterm(B,C))) & A = G & m1_msaterm(G,B,C,k2_msaterm(B,C,F)) & ? [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & k9_msafree2(B,C,E,H) = k1_nat_1(D,1) & H = k4_trees_4(k4_tarski(F,u1_struct_0(B)),G) ) ) ) ) ), file(msscyc_2,a_5_1_msscyc_2), []). fof(fraenkel_a_5_2_msscyc_2,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_msualg_1(B)) ) => ( r2_hidden(A,a_5_2_msscyc_2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k13_finseq_1(k1_msaterm(B,C))) & A = k4_tarski(G,k4_trees_4(k4_tarski(F,u1_struct_0(B)),G)) & m1_msaterm(G,B,C,k2_msaterm(B,C,F)) & ? [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & k9_msafree2(B,C,E,H) = k1_nat_1(D,1) & H = k4_trees_4(k4_tarski(F,u1_struct_0(B)),G) ) ) ) ) ), file(msscyc_2,a_5_2_msscyc_2), []). fof(fraenkel_a_5_3_msscyc_2,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_msualg_1(B)) & m2_subset_1(F,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_5_3_msscyc_2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),k4_finseq_4(k5_numbers,u1_struct_0(B),k1_msualg_1(B,E),F))) & A = G & r1_xreal_0(k9_msafree2(B,C,k4_finseq_4(k5_numbers,u1_struct_0(B),k1_msualg_1(B,E),F),G),D) ) ) ) ), file(msscyc_2,a_5_3_msscyc_2), []). fof(fraenkel_a_6_0_msscyc_2,axiom,( ! [A,B,C,D,E,F,G] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) & v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & m2_subset_1(G,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_6_0_msscyc_2(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & A = H & k9_msafree2(B,C,E,H) = k1_nat_1(D,1) & k1_funct_1(H,k1_xboole_0) = k4_tarski(k1_funct_1(F,G),u1_struct_0(B)) ) ) ) ), file(msscyc_2,a_6_0_msscyc_2), []). fof(fraenkel_a_6_1_msscyc_2,axiom,( ! [A,B,C,D,E,F,G] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_1(B) & v2_relat_1(C) & v1_pre_circ(C,u1_struct_0(B)) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_numbers,k5_numbers) & m1_subset_1(E,u1_struct_0(B)) & v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ( r2_hidden(A,a_6_1_msscyc_2(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(B,k11_msafree(B,C)),E)) & A = H & k9_msafree2(B,C,E,H) = k1_nat_1(D,1) & k1_funct_1(H,k1_xboole_0) = k4_tarski(k1_funct_1(F,G),u1_struct_0(B)) ) ) ) ), file(msscyc_2,a_6_1_msscyc_2), []). fof(free_g1_lang1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k3_finseq_2(A)) => ! [C,D] : ( g1_lang1(A,B) = g1_lang1(C,D) => ( A = C & B = D ) ) ) ), file(lang1,g1_lang1), []). fof(free_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ! [D,E,F] : ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(msualg_1,g3_msualg_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(rc1_dtconstr,axiom,( ? [A] : ( l1_lang1(A) & ~ v3_struct_0(A) & v1_lang1(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_dtconstr(A) ) ), file(dtconstr,rc1_dtconstr), []). fof(rc1_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). 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_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_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v1_trees_9(A) ) ), file(trees_9,rc1_trees_9), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_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_pre_circ,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_pre_circ(B,A) ) ), file(pre_circ,rc2_pre_circ), []). fof(rc2_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) ), file(trees_3,rc2_trees_3), []). fof(rc2_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & ~ v1_trees_9(A) ) ), file(trees_9,rc2_trees_9), []). 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_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_trees_9,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & v1_trees_2(A) & v2_trees_9(A) ) ), file(trees_9,rc3_trees_9), []). 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_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m4_trees_3(B,A) & ~ v1_xboole_0(B) & v1_finset_1(B) & v3_trees_3(B) ) ) ), file(trees_3,rc4_trees_3), []). fof(rc4_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v3_trees_9(A) & v4_trees_9(A) ) ), file(trees_9,rc4_trees_9), []). fof(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). fof(rc5_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ? [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) & ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ), file(msafree2,rc5_msafree2), []). fof(rc5_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) ), file(msualg_1,rc5_msualg_1), []). 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_trees_9,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(trees_9,rc5_trees_9), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc6_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ? [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) & ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) ) ) ), file(msafree2,rc6_msafree2), []). fof(rc6_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) ) ) ), file(msualg_1,rc6_msualg_1), []). fof(rc6_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) ), file(trees_3,rc6_trees_3), []). fof(rc6_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(trees_9,rc6_trees_9), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(rc8_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v6_trees_3(A) ) ), file(trees_3,rc8_trees_3), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_msaterm,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => k2_msaterm(A,B,C) = k6_msafree(A,B,C) ) ), file(msaterm,k2_msaterm), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k7_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & l1_lang1(A) ) => k7_dtconstr(A) = k6_lang1(A) ) ), file(dtconstr,k7_dtconstr), []). fof(redefinition_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k7_pboole), []). fof(redefinition_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k8_pboole), []). fof(redefinition_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_dtconstr(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(dtconstr,m1_dtconstr), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). fof(redefinition_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) <=> m1_finseq_1(C,B) ) ) ), file(trees_4,m1_trees_4), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). 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_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ! [C] : ( m5_trees_3(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(trees_3,m5_trees_3), []). fof(redefinition_r2_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) <=> r2_tarski(A,B) ) ), file(wellord2,r2_wellord2), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(reflexivity_r2_wellord2,axiom,( ! [A,B] : r2_wellord2(A,A) ), file(wellord2,r2_wellord2), []). fof(s1_nat_1__e5_8__msscyc_2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & v1_pre_circ(B,u1_struct_0(A)) & m1_pboole(B,u1_struct_0(A)) ) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v1_finset_1(a_3_1_msscyc_2(A,B,C)) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => v1_finset_1(a_4_0_msscyc_2(A,B,D,E)) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => v1_finset_1(a_4_1_msscyc_2(A,B,D,F)) ) ) ) ) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => v1_finset_1(a_4_0_msscyc_2(A,B,D,G)) ) ) ) ) ), file(msscyc_2,s1_nat_1__e5_8__msscyc_2), []). fof(s1_topreal1__e6_8_2__msscyc_2,axiom,( a_0_0_topreal1 = k2_xboole_0(a_0_1_topreal1,a_0_2_topreal1) ), file(msscyc_2,s1_topreal1__e6_8_2__msscyc_2), []). fof(s2_finseq_1__e10_8_2__msscyc_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & v1_pre_circ(B,u1_struct_0(A)) & m1_pboole(B,u1_struct_0(A)) & m2_subset_1(C,k1_numbers,k5_numbers) & m1_subset_1(D,u1_struct_0(A)) & v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & k3_finseq_1(F) = k3_finseq_1(E) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r2_hidden(G,k2_finseq_1(k3_finseq_1(E))) => k1_funct_1(F,G) = a_6_0_msscyc_2(A,B,C,D,E,G) ) ) ) ) ), file(msscyc_2,s2_finseq_1__e10_8_2__msscyc_2), []). fof(s2_finseq_1__e8_8_2_1__msscyc_2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & v1_pre_circ(B,u1_struct_0(A)) & m1_pboole(B,u1_struct_0(A)) & m2_subset_1(C,k1_numbers,k5_numbers) & m1_subset_1(D,u1_msualg_1(A)) ) => ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & k3_finseq_1(E) = k3_finseq_1(k1_msualg_1(A,D)) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(k1_msualg_1(A,D)))) => k1_funct_1(E,F) = a_5_3_msscyc_2(A,B,C,D,F) ) ) ) ) ), file(msscyc_2,s2_finseq_1__e8_8_2_1__msscyc_2), []). fof(s3_fraenkel__e5_8_2__msscyc_2,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & v1_pre_circ(B,u1_struct_0(A)) & m1_pboole(B,u1_struct_0(A)) & m2_subset_1(C,k1_numbers,k5_numbers) & m1_subset_1(D,u1_struct_0(A)) ) => ( ! [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),D)) => ( r1_xreal_0(k9_msafree2(A,B,D,E),k1_nat_1(C,1)) <=> ( r1_xreal_0(k9_msafree2(A,B,D,E),C) | k9_msafree2(A,B,D,E) = k1_nat_1(C,1) ) ) ) => a_0_4_fraenkel = a_0_5_fraenkel ) ) ), file(msscyc_2,s3_fraenkel__e5_8_2__msscyc_2), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(symmetry_r2_wellord2,axiom,( ! [A,B] : ( r2_wellord2(A,B) => r2_wellord2(B,A) ) ), file(wellord2,r2_wellord2), []). fof(t10_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ~ ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A)) & ! [E] : ( m1_msaterm(E,A,B,k2_msaterm(A,B,D)) => C != k4_trees_4(k4_tarski(D,u1_struct_0(A)),E) ) ) ) ) ) ) ), file(msaterm,t10_msaterm), []). fof(t12_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k7_msafree(A,B,C),k1_msaterm(A,B)) ) ) ) ), file(msaterm,t12_msaterm), []). fof(t13_finset_1,axiom,( ! [A,B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) ), file(finset_1,t13_finset_1), []). fof(t14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,t14_finset_1), []). fof(t15_trees_4,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) ) => ( k4_trees_4(A,C) = k4_trees_4(B,D) => ( A = B & C = D ) ) ) ) ), file(trees_4,t15_trees_4), []). fof(t17_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A)) => k7_msaterm(A,B,C) = k2_msualg_1(A,D) ) ) ) ) ) ), file(msaterm,t17_msaterm), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_msscyc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( ! [B] : ( r2_hidden(B,k1_relat_1(A)) => v1_finset_1(k1_funct_1(A,B)) ) => v1_finset_1(k4_card_3(A)) ) ) ), file(msscyc_1,t1_msscyc_1), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_msscyc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ~ ( ~ v1_trees_9(C) & ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => k1_funct_1(C,k1_xboole_0) != k4_tarski(D,u1_struct_0(A)) ) ) ) ) ) ), file(msscyc_1,t20_msscyc_1), []). fof(t22_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m1_msaterm(D,A,B,k2_msaterm(A,B,C)) => ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C)) & k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_finseq_1(D)) => m1_dtconstr(k1_funct_1(D,E),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ) ) ) ), file(msaterm,t22_msaterm), []). fof(t23_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m1_msaterm(D,A,B,k2_msaterm(A,B,C)) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ( F = k1_funct_1(D,E) => ( F = k4_finseq_4(k5_numbers,k1_msaterm(A,B),D,E) & k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) & k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) ) ) ) ) ) ), file(msaterm,t23_msaterm), []). fof(t26_msscyc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v5_msscyc_1(A) => v1_finset_1(k1_msualg_2(A,B,C)) ) ) ) ) ), file(msscyc_1,t26_msscyc_1), []). fof(t26_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( r1_xreal_0(A,k2_xcmplx_0(B,1)) & ~ r1_xreal_0(A,B) & A != k2_xcmplx_0(B,1) ) ) ) ), file(nat_1,t26_nat_1), []). fof(t27_msscyc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => a_3_2_msscyc_1(A,B,C) = k2_xboole_0(k12_msafree(A,B,C),k1_msualg_2(A,k11_msafree(A,B),C)) ) ) ) ), file(msscyc_1,t27_msscyc_1), []). fof(t28_msscyc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_msualg_1(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) => ! [G] : ( m1_msaterm(G,A,B,k2_msaterm(A,B,E)) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ! [I] : ( m1_subset_1(I,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),D)) => ~ ( F = k4_trees_4(k4_tarski(E,u1_struct_0(A)),G) & r2_hidden(H,k4_finseq_1(G)) & I = k1_funct_1(G,H) & r1_xreal_0(k9_msafree2(A,B,C,F),k9_msafree2(A,B,D,I)) ) ) ) ) ) ) ) ) ) ) ), file(msscyc_1,t28_msscyc_1), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(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(t37_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ! [C] : ( v4_ordinal2(C) => ( r1_xreal_0(A,B) => r1_xreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ), file(nat_1,t37_nat_1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t63_card_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_finset_1(k1_relat_1(A)) & ! [B] : ( r2_hidden(B,k1_relat_1(A)) => v1_finset_1(k1_funct_1(A,B)) ) ) => v1_finset_1(k3_card_3(A)) ) ) ), file(card_4,t63_card_4), []). fof(t68_card_1,axiom,( ! [A,B] : ( ( r2_wellord2(A,B) & v1_finset_1(A) ) => v1_finset_1(B) ) ), file(card_1,t68_card_1), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t73_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) <=> ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & A = k2_relat_1(B) ) ) ), file(finseq_1,t73_finseq_1), []). fof(t79_trees_1,axiom,( k6_trees_1(k2_trees_1(0)) = 0 ), file(trees_1,t79_trees_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []).