% Mizar problem: t14_scm_comp,scm_comp,901,56 fof(t14_scm_comp,conjecture,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_scm_1(E,k15_scm_comp(A,B),k2_lang1(k4_numbers),C,C,D) => ~ ( ~ r1_xreal_0(B,k17_scm_comp(A)) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ~ ( G = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k1_nat_1(F,1)) & k1_nat_1(F,1) = k3_finseq_1(k15_scm_comp(A,B)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),F)) = k16_ami_3(k1_nat_1(C,F)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,G) = k16_ami_3(k1_nat_1(C,k1_nat_1(F,1))) & k2_ami_3(G,k15_ami_3(B)) = k13_scm_comp(E,A) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(B,H) => k2_ami_3(E,k15_ami_3(H)) = k2_ami_3(G,k15_ami_3(H)) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,abstractness_v1_lang1,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_fraenkel,cc1_funct_1,cc1_funct_2,cc1_int_1,cc1_membered,cc1_nat_1,cc1_relset_1,cc1_setfam_1,cc20_membered,cc2_bintree1,cc2_dtconstr,cc2_funct_1,cc2_int_1,cc2_membered,cc2_nat_1,cc3_int_1,cc3_membered,cc3_nat_1,cc4_int_1,cc4_membered,cc4_trees_3,cc5_funct_2,cc5_trees_3,cc6_funct_2,cc6_membered,cc6_trees_3,cc7_trees_3,cc8_membered,cc9_membered,commutativity_k1_limfunc1,commutativity_k1_nat_1,commutativity_k2_square_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,connectedness_r1_xreal_0,d10_scm_comp,d19_ami_1,d1_scm_1,d2_scm_comp,d2_tarski,d3_finseq_1,d5_tarski,d7_finseq_1,d8_scm_comp,dt_g1_ami_1,dt_g1_lang1,dt_k10_ami_1,dt_k10_finseq_1,dt_k10_scm_comp,dt_k10_trees_4,dt_k11_ami_1,dt_k11_scm_comp,dt_k13_ami_1,dt_k13_finseq_1,dt_k13_scm_comp,dt_k14_scm_comp,dt_k15_ami_3,dt_k15_scm_comp,dt_k16_ami_3,dt_k17_scm_comp,dt_k1_ami_3,dt_k1_bintree1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_funct_2,dt_k1_limfunc1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_scm_comp,dt_k1_tarski,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_3,dt_k2_finseq_1,dt_k2_lang1,dt_k2_scm_comp,dt_k2_square_1,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_ami_3,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_lang1,dt_k3_scm_comp,dt_k3_tarski,dt_k3_xcmplx_0,dt_k4_ami_3,dt_k4_card_3,dt_k4_dtconstr,dt_k4_finseq_1,dt_k4_lang1,dt_k4_numbers,dt_k4_scm_comp,dt_k4_tarski,dt_k5_ami_3,dt_k5_finseq_1,dt_k5_int_1,dt_k5_lang1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_trees_3,dt_k6_ami_1,dt_k6_ami_3,dt_k6_dtconstr,dt_k6_finseq_1,dt_k6_int_1,dt_k6_lang1,dt_k6_trees_4,dt_k6_xcmplx_0,dt_k7_ami_3,dt_k7_dtconstr,dt_k7_finseq_1,dt_k8_dtconstr,dt_k8_finseq_1,dt_k8_funct_2,dt_k9_ami_1,dt_k9_finseq_1,dt_l1_ami_1,dt_l1_lang1,dt_l1_struct_0,dt_m1_ami_3,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_scm_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_trees_2,dt_m4_trees_3,dt_m5_trees_3,dt_u1_ami_1,dt_u1_lang1,dt_u1_struct_0,dt_u2_ami_1,dt_u3_ami_1,dt_u4_ami_1,dt_u5_ami_1,dt_u6_ami_1,existence_l1_ami_1,existence_l1_lang1,existence_l1_struct_0,existence_m1_ami_3,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_scm_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc10_membered,fc10_trees_3,fc11_membered,fc11_trees_3,fc12_membered,fc13_membered,fc13_trees_3,fc14_membered,fc14_trees_3,fc15_membered,fc16_membered,fc16_trees_3,fc17_trees_3,fc1_ami_3,fc1_dtconstr,fc1_fraenkel,fc1_funct_2,fc1_int_1,fc1_nat_1,fc1_ordinal2,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc22_membered,fc22_trees_3,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc26_trees_3,fc2_ami_1,fc2_ami_3,fc2_dtconstr,fc2_fraenkel,fc2_funct_2,fc2_int_1,fc2_membered,fc2_nat_1,fc2_setfam_1,fc2_subset_1,fc2_xboole_0,fc3_ami_1,fc3_ami_3,fc3_dtconstr,fc3_nat_1,fc3_setfam_1,fc3_subset_1,fc3_xboole_0,fc4_ami_1,fc4_int_1,fc4_membered,fc4_nat_1,fc4_setfam_1,fc4_subset_1,fc5_ami_3,fc5_membered,fc6_int_1,fc6_membered,fc6_trees_3,fc7_int_1,fc7_membered,fc7_trees_3,fc8_int_1,fc8_membered,fc8_trees_3,fc9_int_1,fc9_membered,fc9_trees_3,free_g1_ami_1,free_g1_lang1,idempotence_k1_limfunc1,idempotence_k2_square_1,idempotence_k2_xboole_0,rc1_ami_1,rc1_dtconstr,rc1_fraenkel,rc1_funct_1,rc1_funct_2,rc1_int_1,rc1_membered,rc1_nat_1,rc1_setfam_1,rc1_subset_1,rc1_xboole_0,rc2_ami_1,rc2_bintree1,rc2_funct_1,rc2_int_1,rc2_nat_1,rc2_subset_1,rc2_trees_3,rc2_xboole_0,rc3_ami_1,rc3_bintree1,rc3_funct_1,rc3_nat_1,rc3_struct_0,rc4_bintree1,rc4_trees_3,rc5_ami_1,rc5_struct_0,rc5_trees_3,rc6_ami_1,rc6_trees_3,rc7_ami_1,rc7_trees_3,rc8_ami_1,rc8_trees_3,rc9_ami_1,redefinition_k10_trees_4,redefinition_k11_ami_1,redefinition_k11_scm_comp,redefinition_k13_ami_1,redefinition_k1_limfunc1,redefinition_k1_nat_1,redefinition_k2_ami_3,redefinition_k2_finseq_1,redefinition_k2_lang1,redefinition_k2_scm_comp,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_lang1,redefinition_k3_scm_comp,redefinition_k4_finseq_1,redefinition_k4_lang1,redefinition_k5_numbers,redefinition_k6_dtconstr,redefinition_k7_dtconstr,redefinition_k8_dtconstr,redefinition_k8_finseq_1,redefinition_k8_funct_2,redefinition_k9_finseq_1,redefinition_m1_dtconstr,redefinition_m1_struct_0,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s2_bintree1__e3_30__scm_comp,spc0_boole,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,t10_scm_comp,t12_scm_comp,t13_scm_comp,t18_scm_1,t19_scm_1,t1_arithm,t1_boole,t1_numerals,t1_real,t1_scm_comp,t1_subset,t20_scm_1,t21_scm_1,t22_scm_1,t2_arithm,t2_real,t2_scm_comp,t2_subset,t2_xreal_1,t35_finseq_1,t38_nat_1,t3_arithm,t3_real,t3_scm_comp,t3_subset,t45_finseq_1,t46_square_1,t4_arithm,t4_finseq_1,t4_real,t4_subset,t51_ami_1,t52_ami_3,t57_finseq_1,t59_finseq_1,t5_real,t5_subset,t61_finseq_1,t6_boole,t6_real,t6_scm_comp,t7_boole,t7_real,t7_scm_comp,t8_boole,t8_real,t8_xreal_1,t9_scm_comp]), [file(scm_comp,t14_scm_comp)]). fof(abstractness_v1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_ami_1(B,A) => B = g1_ami_1(A,u1_struct_0(B),u1_ami_1(A,B),u2_ami_1(A,B),u3_ami_1(A,B),u4_ami_1(A,B),u5_ami_1(A,B),u6_ami_1(A,B)) ) ) ), file(ami_1,v1_ami_1), []). 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(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_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_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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_1), []). 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_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_setfam_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ), file(setfam_1,cc1_setfam_1), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_bintree1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_bintree1(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,k4_dtconstr(A)) => v2_bintree1(B) ) ) ), file(bintree1,cc2_bintree1), []). 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_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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_int_1(A) ) ) ), file(int_1,cc2_int_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_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(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_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(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_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(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_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(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). fof(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(cc7_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_trees_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v4_trees_3(A) ) ) ), file(trees_3,cc7_trees_3), []). fof(cc8_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) ) ) ), file(membered,cc8_membered), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). fof(commutativity_k1_limfunc1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_limfunc1(A,B) = k1_limfunc1(B,A) ) ), file(limfunc1,k1_limfunc1), []). 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_square_1,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => k2_square_1(A,B) = k2_square_1(B,A) ) ), file(square_1,k2_square_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(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(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d10_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ( A = k4_tarski(0,0) => k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,1)))) ) & ( A = k4_tarski(0,1) => k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,1)))) ) & ( A = k4_tarski(0,2) => k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k6_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,1)))) ) & ( A = k4_tarski(0,3) => k14_scm_comp(A,B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,1)))) ) & ( A = k4_tarski(0,4) => k14_scm_comp(A,B) = k4_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,1))),k3_ami_3(k15_ami_3(B),k15_ami_3(k1_nat_1(B,1)))) ) ) ) ) ), file(scm_comp,d10_scm_comp), []). fof(d19_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m2_relset_1(D,k5_numbers,k4_card_3(u5_ami_1(A,B))) ) => ( D = k10_ami_1(A,B,C) <=> ( k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,0) = C & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,k1_nat_1(E,1)) = k9_ami_1(A,B,k8_funct_2(k5_numbers,k4_card_3(u5_ami_1(A,B)),D,E)) ) ) ) ) ) ) ) ), file(ami_1,d19_ami_1), []). fof(d1_scm_1,axiom,( ! [A] : ( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( m1_scm_1(F,A,B,C,D,E) <=> ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,F) = k16_ami_3(C) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(A),G) => k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,F,k16_ami_3(k1_nat_1(D,G))) = k1_funct_1(A,k1_nat_1(G,1)) ) ) & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(B),G) => k2_ami_3(F,k15_ami_3(k1_nat_1(E,G))) = k1_funct_1(B,k1_nat_1(G,1)) ) ) ) ) ) ) ) ) ) ) ), file(scm_1,d1_scm_1), []). fof(d2_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp)) => k4_scm_comp(A) = A ) ), file(scm_comp,d2_scm_comp), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). fof(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(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d7_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k7_finseq_1(A,B) <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ), file(finseq_1,d7_finseq_1), []). fof(d8_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( A = k4_tarski(0,0) => k10_scm_comp(A,B,C) = k2_xcmplx_0(B,C) ) & ( A = k4_tarski(0,1) => k10_scm_comp(A,B,C) = k6_xcmplx_0(B,C) ) & ( A = k4_tarski(0,2) => k10_scm_comp(A,B,C) = k3_xcmplx_0(B,C) ) & ( A = k4_tarski(0,3) => k10_scm_comp(A,B,C) = k5_int_1(B,C) ) & ( A = k4_tarski(0,4) => k10_scm_comp(A,B,C) = k6_int_1(B,C) ) ) ) ) ) ), file(scm_comp,d8_scm_comp), []). fof(dt_g1_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ( v1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) & l1_ami_1(g1_ami_1(A,B,C,D,E,F,G,H),A) ) ) ), file(ami_1,g1_ami_1), []). 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_k10_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => ( v1_funct_1(k10_ami_1(A,B,C)) & v1_funct_2(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) & m2_relset_1(k10_ami_1(A,B,C),k5_numbers,k4_card_3(u5_ami_1(A,B))) ) ) ), file(ami_1,k10_ami_1), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k10_scm_comp,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp)) & v1_int_1(B) & v1_int_1(C) ) => v1_int_1(k10_scm_comp(A,B,C)) ) ), file(scm_comp,k10_scm_comp), []). fof(dt_k10_trees_4,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) & v1_funct_1(D) & v3_trees_2(D) & m3_trees_2(D,A) ) => ( v1_funct_1(k10_trees_4(A,B,C,D)) & v3_trees_2(k10_trees_4(A,B,C,D)) & m3_trees_2(k10_trees_4(A,B,C,D),A) ) ) ), file(trees_4,k10_trees_4), []). fof(dt_k11_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,k5_numbers) ) => m1_subset_1(k11_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k11_ami_1), []). fof(dt_k11_scm_comp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_subset_1(B,k6_dtconstr(k1_scm_comp)) ) => v1_int_1(k11_scm_comp(A,B)) ) ), file(scm_comp,k11_scm_comp), []). fof(dt_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => m2_subset_1(k13_ami_1(A,B,C,D),k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))),u4_ami_1(A,B)) ) ), file(ami_1,k13_ami_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_scm_comp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_subset_1(B,k4_dtconstr(k1_scm_comp)) ) => v1_int_1(k13_scm_comp(A,B)) ) ), file(scm_comp,k13_scm_comp), []). fof(dt_k14_scm_comp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp)) & m1_subset_1(B,k5_numbers) ) => m2_finseq_2(k14_scm_comp(A,B),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_finseq_2(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) ), file(scm_comp,k14_scm_comp), []). fof(dt_k15_ami_3,axiom,( ! [A] : ( v4_ordinal2(A) => m1_ami_3(k15_ami_3(A)) ) ), file(ami_3,k15_ami_3), []). fof(dt_k15_scm_comp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp)) & m1_subset_1(B,k5_numbers) ) => m2_finseq_1(k15_scm_comp(A,B),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(scm_comp,k15_scm_comp), []). fof(dt_k16_ami_3,axiom,( ! [A] : ( v4_ordinal2(A) => m1_struct_0(k16_ami_3(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k16_ami_3), []). fof(dt_k17_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k4_dtconstr(k1_scm_comp)) => m2_subset_1(k17_scm_comp(A),k1_numbers,k5_numbers) ) ), file(scm_comp,k17_scm_comp), []). fof(dt_k1_ami_3,axiom, ( v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & l1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,k1_ami_3), []). fof(dt_k1_bintree1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v3_trees_2(B) & m3_trees_2(B,A) ) => m1_subset_1(k1_bintree1(A,B),A) ) ), file(bintree1,k1_bintree1), []). 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_funct_2,axiom,( $true ), file(funct_2,k1_funct_2), []). fof(dt_k1_limfunc1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_limfunc1(A,B),k1_numbers,k5_numbers) ) ), file(limfunc1,k1_limfunc1), []). 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_scm_comp,axiom, ( ~ v3_struct_0(k1_scm_comp) & v1_lang1(k1_scm_comp) & v3_bintree1(k1_scm_comp) & v1_dtconstr(k1_scm_comp) & v2_dtconstr(k1_scm_comp) & v3_dtconstr(k1_scm_comp) & l1_lang1(k1_scm_comp) ), file(scm_comp,k1_scm_comp), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_trees_4,axiom,( ! [A] : ( v1_relat_1(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) ) ), file(trees_4,k1_trees_4), []). 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_ami_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_ami_3(B) ) => v1_int_1(k2_ami_3(A,B)) ) ), file(ami_3,k2_ami_3), []). 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_lang1,axiom,( ! [A] : ( v1_xboole_0(k2_lang1(A)) & m2_finseq_2(k2_lang1(A),A,k3_finseq_2(A)) ) ), file(lang1,k2_lang1), []). fof(dt_k2_scm_comp,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp)) & m1_subset_1(B,k4_dtconstr(k1_scm_comp)) & m1_subset_1(C,k4_dtconstr(k1_scm_comp)) ) => m1_dtconstr(k2_scm_comp(A,B,C),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ), file(scm_comp,k2_scm_comp), []). fof(dt_k2_square_1,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k2_square_1(A,B)) ) ), file(square_1,k2_square_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_ami_3,axiom,( ! [A,B] : ( ( m1_ami_3(A) & m1_ami_3(B) ) => m2_subset_1(k3_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k3_ami_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_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k3_lang1(A,B),A,k3_finseq_2(A)) ) ), file(lang1,k3_lang1), []). fof(dt_k3_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k6_dtconstr(k1_scm_comp)) => m1_dtconstr(k3_scm_comp(A),u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) ) ), file(scm_comp,k3_scm_comp), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), []). fof(dt_k4_ami_3,axiom,( ! [A,B] : ( ( m1_ami_3(A) & m1_ami_3(B) ) => m2_subset_1(k4_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k4_ami_3), []). 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_lang1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_2(k4_lang1(A,B,C),A,k3_finseq_2(A)) ) ), file(lang1,k4_lang1), []). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), []). fof(dt_k4_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k6_dtconstr(k1_scm_comp)) => m1_ami_3(k4_scm_comp(A)) ) ), file(scm_comp,k4_scm_comp), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_ami_3,axiom,( ! [A,B] : ( ( m1_ami_3(A) & m1_ami_3(B) ) => m2_subset_1(k5_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k5_ami_3), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). fof(dt_k5_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k5_int_1(A,B)) ) ), file(int_1,k5_int_1), []). fof(dt_k5_lang1,axiom,( $true ), file(lang1,k5_lang1), []). 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_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_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_struct_0(k6_ami_1(A,B,C),B,u2_ami_1(A,B)) ) ), file(ami_1,k6_ami_1), []). fof(dt_k6_ami_3,axiom,( ! [A,B] : ( ( m1_ami_3(A) & m1_ami_3(B) ) => m2_subset_1(k6_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k6_ami_3), []). fof(dt_k6_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k6_dtconstr(A)) & m1_subset_1(k6_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(dtconstr,k6_dtconstr), []). fof(dt_k6_finseq_1,axiom,( ! [A] : ( v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A) ) ), file(finseq_1,k6_finseq_1), []). fof(dt_k6_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k6_int_1(A,B)) ) ), file(int_1,k6_int_1), []). fof(dt_k6_lang1,axiom,( $true ), file(lang1,k6_lang1), []). fof(dt_k6_trees_4,axiom,( ! [A,B,C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( v1_relat_1(k6_trees_4(A,B,C)) & v1_funct_1(k6_trees_4(A,B,C)) & v3_trees_2(k6_trees_4(A,B,C)) ) ) ), file(trees_4,k6_trees_4), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_ami_3,axiom,( ! [A,B] : ( ( m1_ami_3(A) & m1_ami_3(B) ) => m2_subset_1(k7_ami_3(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_ami_3),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_ami_3)))),u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_3,k7_ami_3), []). 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_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k8_dtconstr,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k6_dtconstr(A)) ) => m1_dtconstr(k8_dtconstr(A,B),u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ), file(dtconstr,k8_dtconstr), []). fof(dt_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_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_k9_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k9_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k9_ami_1), []). fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) ), file(finseq_1,k9_finseq_1), []). fof(dt_l1_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => l1_struct_0(B) ) ), file(ami_1,l1_ami_1), []). fof(dt_l1_lang1,axiom,( ! [A] : ( l1_lang1(A) => l1_struct_0(A) ) ), file(lang1,l1_lang1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_ami_3,axiom,( ! [A] : ( m1_ami_3(A) => m1_subset_1(A,u1_struct_0(k1_ami_3)) ) ), file(ami_3,m1_ami_3), []). 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_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_scm_1,axiom,( ! [A,B,C,D,E] : ( ( m1_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & m1_finseq_1(B,k4_numbers) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) & m1_subset_1(E,k5_numbers) ) => ! [F] : ( m1_scm_1(F,A,B,C,D,E) => m1_subset_1(F,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ) ) ), file(scm_1,m1_scm_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_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_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_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u1_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,u1_ami_1), []). 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_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => m1_subset_1(u2_ami_1(A,B),k1_zfmisc_1(u1_struct_0(B))) ) ), file(ami_1,u2_ami_1), []). fof(dt_u3_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ~ v1_xboole_0(u3_ami_1(A,B)) ) ), file(ami_1,u3_ami_1), []). fof(dt_u4_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( ~ v1_xboole_0(u4_ami_1(A,B)) & m1_subset_1(u4_ami_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u3_ami_1(A,B),k13_finseq_1(k2_xboole_0(k3_tarski(A),u1_struct_0(B)))))) ) ) ), file(ami_1,u4_ami_1), []). fof(dt_u5_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u5_ami_1(A,B)) & v1_funct_2(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) & m2_relset_1(u5_ami_1(A,B),u1_struct_0(B),k2_xboole_0(A,k2_tarski(u4_ami_1(A,B),u2_ami_1(A,B)))) ) ) ), file(ami_1,u5_ami_1), []). fof(dt_u6_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ( v1_funct_1(u6_ami_1(A,B)) & v1_funct_2(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) & m2_relset_1(u6_ami_1(A,B),u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B)))) ) ) ), file(ami_1,u6_ami_1), []). fof(existence_l1_ami_1,axiom,( ! [A] : ? [B] : l1_ami_1(B,A) ), file(ami_1,l1_ami_1), []). fof(existence_l1_lang1,axiom,( ? [A] : l1_lang1(A) ), file(lang1,l1_lang1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_ami_3,axiom,( ? [A] : m1_ami_3(A) ), file(ami_3,m1_ami_3), []). 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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_scm_1,axiom,( ! [A,B,C,D,E] : ( ( m1_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & m1_finseq_1(B,k4_numbers) & m1_subset_1(C,k5_numbers) & m1_subset_1(D,k5_numbers) & m1_subset_1(E,k5_numbers) ) => ? [F] : m1_scm_1(F,A,B,C,D,E) ) ), file(scm_1,m1_scm_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_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_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_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc10_trees_3), []). 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_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & ~ v1_xboole_0(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v4_trees_3(k10_finseq_1(A,B)) ) ) ), file(trees_3,fc11_trees_3), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). fof(fc13_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) & v5_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc13_trees_3), []). 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_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & ~ v1_xboole_0(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v4_trees_3(k10_finseq_1(A,B)) & v5_trees_3(k10_finseq_1(A,B)) ) ) ), file(trees_3,fc14_trees_3), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). fof(fc16_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v6_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc16_trees_3), []). fof(fc17_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & ~ v1_xboole_0(k10_finseq_1(A,B)) & v1_finset_1(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v6_trees_3(k10_finseq_1(A,B)) ) ) ), file(trees_3,fc17_trees_3), []). fof(fc1_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc1_ami_3), []). 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_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). fof(fc1_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) ), file(funct_2,fc1_funct_2), []). fof(fc1_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v1_int_1(k2_xcmplx_0(A,B)) ) ) ), file(int_1,fc1_int_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(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_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_ami_1,axiom,( ! [A,B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ~ v1_xboole_0(u2_ami_1(A,B)) ) ), file(ami_1,fc2_ami_1), []). fof(fc2_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc2_ami_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_fraenkel,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => ( v1_finset_1(k1_funct_2(A,B)) & v1_fraenkel(k1_funct_2(A,B)) ) ) ), file(fraenkel,fc2_fraenkel), []). fof(fc2_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) ), file(funct_2,fc2_funct_2), []). fof(fc2_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & v1_int_1(k3_xcmplx_0(A,B)) ) ) ), file(int_1,fc2_int_1), []). 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_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_setfam_1(k1_tarski(A)) ) ) ), file(setfam_1,fc2_setfam_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc3_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(ami_1,fc3_ami_1), []). fof(fc3_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc3_ami_3), []). 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_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_setfam_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_setfam_1(k2_tarski(A,B)) ) ) ), file(setfam_1,fc3_setfam_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc4_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( ~ v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)) ) ) ), file(ami_1,fc4_ami_1), []). fof(fc4_int_1,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc4_int_1), []). fof(fc4_membered,axiom, ( ~ v1_xboole_0(k4_numbers) & v1_membered(k4_numbers) & v2_membered(k4_numbers) & v3_membered(k4_numbers) & v4_membered(k4_numbers) ), file(membered,fc4_membered), []). 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_setfam_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) ), file(setfam_1,fc4_setfam_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(fc5_ami_3,axiom, ( ~ v3_struct_0(k1_ami_3) & v1_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v4_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v5_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v6_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v7_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v8_ami_1(k1_ami_3,k1_tarski(k4_numbers)) & v10_ami_1(k1_ami_3,k1_tarski(k4_numbers)) ), file(ami_3,fc5_ami_3), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc6_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v1_int_1(k2_xcmplx_0(B,A)) ) ) ), file(int_1,fc6_int_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_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_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & v1_int_1(k3_xcmplx_0(B,A)) ) ) ), file(int_1,fc7_int_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc7_trees_3), []). fof(fc8_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & v1_int_1(B) ) => ( v1_xcmplx_0(k6_xcmplx_0(B,A)) & v1_xreal_0(k6_xcmplx_0(B,A)) & v1_int_1(k6_xcmplx_0(B,A)) ) ) ), file(int_1,fc8_int_1), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v5_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) & v5_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc8_trees_3), []). fof(fc9_int_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => ( v1_xcmplx_0(k6_xcmplx_0(A,B)) & v1_xreal_0(k6_xcmplx_0(A,B)) & v1_int_1(k6_xcmplx_0(A,B)) ) ) ), file(int_1,fc9_int_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_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v6_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc9_trees_3), []). fof(free_g1_ami_1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,k13_finseq_1(k2_xboole_0(k3_tarski(A),B))))) & v1_funct_1(G) & v1_funct_2(G,B,k2_xboole_0(A,k2_tarski(F,D))) & m1_relset_1(G,B,k2_xboole_0(A,k2_tarski(F,D))) & v1_funct_1(H) & v1_funct_2(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) & m1_relset_1(H,F,k1_funct_2(k4_card_3(G),k4_card_3(G))) ) => ! [I,J,K,L,M,N,O,P] : ( g1_ami_1(A,B,C,D,E,F,G,H) = g1_ami_1(I,J,K,L,M,N,O,P) => ( A = I & B = J & C = K & D = L & E = M & F = N & G = O & H = P ) ) ) ), file(ami_1,g1_ami_1), []). 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(idempotence_k1_limfunc1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_limfunc1(A,A) = A ) ), file(limfunc1,k1_limfunc1), []). fof(idempotence_k2_square_1,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => k2_square_1(A,A) = A ) ), file(square_1,k2_square_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(rc1_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) ) ), file(ami_1,rc1_ami_1), []). 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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). 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_int_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) ), file(int_1,rc1_int_1), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_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_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) ), file(setfam_1,rc1_setfam_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_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc2_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) ) ), file(ami_1,rc2_ami_1), []). fof(rc2_bintree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v2_bintree1(B) ) ) ), file(bintree1,rc2_bintree1), []). 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_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_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_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_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) ), file(trees_3,rc2_trees_3), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc3_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) ) ) ), file(ami_1,rc3_ami_1), []). fof(rc3_bintree1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v2_bintree1(A) ) ), file(bintree1,rc3_bintree1), []). 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_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(rc4_bintree1,axiom,( ? [A] : ( l1_lang1(A) & ~ v3_struct_0(A) & v1_lang1(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_dtconstr(A) & v3_bintree1(A) ) ), file(bintree1,rc4_bintree1), []). 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(rc5_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) ) ), file(ami_1,rc5_ami_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_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc5_trees_3), []). fof(rc6_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) ) ), file(ami_1,rc6_ami_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(rc7_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v7_ami_1(B,A) & v8_ami_1(B,A) ) ) ), file(ami_1,rc7_ami_1), []). fof(rc7_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc7_trees_3), []). fof(rc8_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & v1_ami_1(B,A) & v6_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc8_ami_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(rc9_ami_1,axiom,( ! [A] : ? [B] : ( l1_ami_1(B,A) & ~ v3_struct_0(B) & v1_ami_1(B,A) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v6_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) ) ), file(ami_1,rc9_ami_1), []). fof(redefinition_k10_trees_4,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) & v1_funct_1(D) & v3_trees_2(D) & m3_trees_2(D,A) ) => k10_trees_4(A,B,C,D) = k6_trees_4(B,C,D) ) ), file(trees_4,k10_trees_4), []). fof(redefinition_k11_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_relset_1(C,k5_numbers,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,k5_numbers) ) => k11_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k11_ami_1), []). fof(redefinition_k11_scm_comp,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_subset_1(B,k6_dtconstr(k1_scm_comp)) ) => k11_scm_comp(A,B) = k1_funct_1(A,B) ) ), file(scm_comp,k11_scm_comp), []). fof(redefinition_k13_ami_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) & m1_subset_1(D,u2_ami_1(A,B)) ) => k13_ami_1(A,B,C,D) = k1_funct_1(C,D) ) ), file(ami_1,k13_ami_1), []). fof(redefinition_k1_limfunc1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_limfunc1(A,B) = k2_square_1(A,B) ) ), file(limfunc1,k1_limfunc1), []). 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_ami_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) & m1_ami_3(B) ) => k2_ami_3(A,B) = k1_funct_1(A,B) ) ), file(ami_3,k2_ami_3), []). 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_lang1,axiom,( ! [A] : k2_lang1(A) = k6_finseq_1(A) ), file(lang1,k2_lang1), []). fof(redefinition_k2_scm_comp,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp)) & m1_subset_1(B,k4_dtconstr(k1_scm_comp)) & m1_subset_1(C,k4_dtconstr(k1_scm_comp)) ) => k2_scm_comp(A,B,C) = k6_trees_4(A,B,C) ) ), file(scm_comp,k2_scm_comp), []). 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_k3_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_lang1(A,B) = k5_finseq_1(B) ) ), file(lang1,k3_lang1), []). fof(redefinition_k3_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k6_dtconstr(k1_scm_comp)) => k3_scm_comp(A) = k1_trees_4(A) ) ), file(scm_comp,k3_scm_comp), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_lang1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k4_lang1(A,B,C) = k10_finseq_1(B,C) ) ), file(lang1,k4_lang1), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => k6_dtconstr(A) = k5_lang1(A) ) ), file(dtconstr,k6_dtconstr), []). 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_k8_dtconstr,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k6_dtconstr(A)) ) => k8_dtconstr(A,B) = k1_trees_4(B) ) ), file(dtconstr,k8_dtconstr), []). fof(redefinition_k8_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). fof(redefinition_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_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ), file(finseq_1,k9_finseq_1), []). 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_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(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(s2_bintree1__e3_30__scm_comp,axiom, ( ( ! [A] : ( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_scm_1(E,k15_scm_comp(k8_dtconstr(k1_scm_comp,A),B),k2_lang1(k4_numbers),C,C,D) => ~ ( ~ r1_xreal_0(B,k17_scm_comp(k8_dtconstr(k1_scm_comp,A))) & ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m1_subset_1(G,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ~ ( G = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k1_nat_1(F,1)) & k1_nat_1(F,1) = k3_finseq_1(k15_scm_comp(k8_dtconstr(k1_scm_comp,A),B)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),F)) = k16_ami_3(k1_nat_1(C,F)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,G) = k16_ami_3(k1_nat_1(C,k1_nat_1(F,1))) & k2_ami_3(G,k15_ami_3(B)) = k13_scm_comp(E,k8_dtconstr(k1_scm_comp,A)) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(B,H) => k2_ami_3(E,k15_ami_3(H)) = k2_ami_3(G,k15_ami_3(H)) ) ) ) ) ) ) ) ) ) ) ) & ! [A] : ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ! [I] : ( m1_dtconstr(I,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [J] : ( m1_dtconstr(J,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ( ( r1_lang1(k1_scm_comp,A,k4_lang1(u1_struct_0(k1_scm_comp),k1_bintree1(u1_struct_0(k1_scm_comp),I),k1_bintree1(u1_struct_0(k1_scm_comp),J))) & ! [K] : ( m2_subset_1(K,k1_numbers,k5_numbers) => ! [L] : ( m2_subset_1(L,k1_numbers,k5_numbers) => ! [M] : ( m2_subset_1(M,k1_numbers,k5_numbers) => ! [N] : ( m1_scm_1(N,k15_scm_comp(I,K),k2_lang1(k4_numbers),L,L,M) => ~ ( ~ r1_xreal_0(K,k17_scm_comp(I)) & ! [O] : ( m2_subset_1(O,k1_numbers,k5_numbers) => ! [P] : ( m1_subset_1(P,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ~ ( P = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,N),k1_nat_1(O,1)) & k1_nat_1(O,1) = k3_finseq_1(k15_scm_comp(I,K)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,N),O)) = k16_ami_3(k1_nat_1(L,O)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,P) = k16_ami_3(k1_nat_1(L,k1_nat_1(O,1))) & k2_ami_3(P,k15_ami_3(K)) = k13_scm_comp(N,I) & ! [Q] : ( m2_subset_1(Q,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(K,Q) => k2_ami_3(N,k15_ami_3(Q)) = k2_ami_3(P,k15_ami_3(Q)) ) ) ) ) ) ) ) ) ) ) & ! [R] : ( m2_subset_1(R,k1_numbers,k5_numbers) => ! [S] : ( m2_subset_1(S,k1_numbers,k5_numbers) => ! [T] : ( m2_subset_1(T,k1_numbers,k5_numbers) => ! [U] : ( m1_scm_1(U,k15_scm_comp(J,R),k2_lang1(k4_numbers),S,S,T) => ~ ( ~ r1_xreal_0(R,k17_scm_comp(J)) & ! [V] : ( m2_subset_1(V,k1_numbers,k5_numbers) => ! [W] : ( m1_subset_1(W,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ~ ( W = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,U),k1_nat_1(V,1)) & k1_nat_1(V,1) = k3_finseq_1(k15_scm_comp(J,R)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,U),V)) = k16_ami_3(k1_nat_1(S,V)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,W) = k16_ami_3(k1_nat_1(S,k1_nat_1(V,1))) & k2_ami_3(W,k15_ami_3(R)) = k13_scm_comp(U,J) & ! [X] : ( m2_subset_1(X,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(R,X) => k2_ami_3(U,k15_ami_3(X)) = k2_ami_3(W,k15_ami_3(X)) ) ) ) ) ) ) ) ) ) ) ) => ! [Y] : ( m2_subset_1(Y,k1_numbers,k5_numbers) => ! [Z] : ( m2_subset_1(Z,k1_numbers,k5_numbers) => ! [A1] : ( m2_subset_1(A1,k1_numbers,k5_numbers) => ! [B1] : ( m1_scm_1(B1,k15_scm_comp(k10_trees_4(u1_struct_0(k1_scm_comp),A,I,J),Y),k2_lang1(k4_numbers),Z,Z,A1) => ~ ( ~ r1_xreal_0(Y,k17_scm_comp(k10_trees_4(u1_struct_0(k1_scm_comp),A,I,J))) & ! [C1] : ( m2_subset_1(C1,k1_numbers,k5_numbers) => ! [D1] : ( m1_subset_1(D1,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ~ ( D1 = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B1),k1_nat_1(C1,1)) & k1_nat_1(C1,1) = k3_finseq_1(k15_scm_comp(k10_trees_4(u1_struct_0(k1_scm_comp),A,I,J),Y)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,B1),C1)) = k16_ami_3(k1_nat_1(Z,C1)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,D1) = k16_ami_3(k1_nat_1(Z,k1_nat_1(C1,1))) & k2_ami_3(D1,k15_ami_3(Y)) = k13_scm_comp(B1,k10_trees_4(u1_struct_0(k1_scm_comp),A,I,J)) & ! [E1] : ( m2_subset_1(E1,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(Y,E1) => k2_ami_3(B1,k15_ami_3(E1)) = k2_ami_3(D1,k15_ami_3(E1)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) => ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [F1] : ( m2_subset_1(F1,k1_numbers,k5_numbers) => ! [G1] : ( m2_subset_1(G1,k1_numbers,k5_numbers) => ! [H1] : ( m2_subset_1(H1,k1_numbers,k5_numbers) => ! [I1] : ( m1_scm_1(I1,k15_scm_comp(A,F1),k2_lang1(k4_numbers),G1,G1,H1) => ~ ( ~ r1_xreal_0(F1,k17_scm_comp(A)) & ! [J1] : ( m2_subset_1(J1,k1_numbers,k5_numbers) => ! [K1] : ( m1_subset_1(K1,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ~ ( K1 = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,I1),k1_nat_1(J1,1)) & k1_nat_1(J1,1) = k3_finseq_1(k15_scm_comp(A,F1)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,I1),J1)) = k16_ami_3(k1_nat_1(G1,J1)) & k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,K1) = k16_ami_3(k1_nat_1(G1,k1_nat_1(J1,1))) & k2_ami_3(K1,k15_ami_3(F1)) = k13_scm_comp(I1,A) & ! [L1] : ( m2_subset_1(L1,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(F1,L1) => k2_ami_3(I1,k15_ami_3(L1)) = k2_ami_3(K1,k15_ami_3(L1)) ) ) ) ) ) ) ) ) ) ) ) ), file(scm_comp,s2_bintree1__e3_30__scm_comp), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(spc2_numerals,axiom, ( v2_xreal_0(2) & m1_subset_1(2,k5_numbers) ), file(numerals,spc2_numerals), []). fof(spc3_boole,axiom,( ~ v1_xboole_0(3) ), file(boole,spc3_boole), []). fof(spc3_numerals,axiom, ( v2_xreal_0(3) & m1_subset_1(3,k5_numbers) ), file(numerals,spc3_numerals), []). fof(spc4_boole,axiom,( ~ v1_xboole_0(4) ), file(boole,spc4_boole), []). fof(spc4_numerals,axiom, ( v2_xreal_0(4) & m1_subset_1(4,k5_numbers) ), file(numerals,spc4_numerals), []). fof(t10_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_scm_comp)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_scm_comp)) => ( ( E = k1_bintree1(u1_struct_0(k1_scm_comp),B) & F = k1_bintree1(u1_struct_0(k1_scm_comp),C) & r1_lang1(k1_scm_comp,A,k4_lang1(u1_struct_0(k1_scm_comp),E,F)) ) => k15_scm_comp(k2_scm_comp(A,B,C),D) = k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k15_scm_comp(B,D),k15_scm_comp(C,k1_nat_1(D,1))),k14_scm_comp(A,D)) ) ) ) ) ) ) ) ), file(scm_comp,t10_scm_comp), []). fof(t12_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => k17_scm_comp(k2_scm_comp(A,B,C)) = k1_limfunc1(k17_scm_comp(B),k17_scm_comp(C)) ) ) ) ), file(scm_comp,t12_scm_comp), []). fof(t13_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( m1_subset_1(B,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( r1_xreal_0(D,k17_scm_comp(A)) => k2_ami_3(B,k15_ami_3(D)) = k2_ami_3(C,k15_ami_3(D)) ) ) => k13_scm_comp(B,A) = k13_scm_comp(C,A) ) ) ) ) ), file(scm_comp,t13_scm_comp), []). fof(t18_scm_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [D] : ( m1_ami_3(D) => ! [E] : ( m1_ami_3(E) => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B) & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k3_ami_3(D,E) ) => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1))) = k16_ami_3(k1_nat_1(B,1)) & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),D) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E) & ! [F] : ( m1_ami_3(F) => ( F != D => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ), file(scm_1,t18_scm_1), []). fof(t19_scm_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [D] : ( m1_ami_3(D) => ! [E] : ( m1_ami_3(E) => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B) & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k4_ami_3(D,E) ) => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1))) = k16_ami_3(k1_nat_1(B,1)) & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),D) = k2_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)) & ! [F] : ( m1_ami_3(F) => ( F != D => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ), file(scm_1,t19_scm_1), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_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_scm_comp,axiom,( ! [A] : ( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m2_finseq_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m1_scm_1(G,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A,B),C,D,E,F) => ( m1_scm_1(G,A,C,D,E,F) & m1_scm_1(G,B,C,D,k1_nat_1(E,k3_finseq_1(A)),F) ) ) ) ) ) ) ) ) ), file(scm_comp,t1_scm_comp), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_scm_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [D] : ( m1_ami_3(D) => ! [E] : ( m1_ami_3(E) => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B) & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k5_ami_3(D,E) ) => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1))) = k16_ami_3(k1_nat_1(B,1)) & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),D) = k6_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)) & ! [F] : ( m1_ami_3(F) => ( F != D => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ), file(scm_1,t20_scm_1), []). fof(t21_scm_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [D] : ( m1_ami_3(D) => ! [E] : ( m1_ami_3(E) => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B) & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k6_ami_3(D,E) ) => ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1))) = k16_ami_3(k1_nat_1(B,1)) & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),D) = k3_xcmplx_0(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)) & ! [F] : ( m1_ami_3(F) => ( F != D => k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),F) = k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ), file(scm_1,t21_scm_1), []). fof(t22_scm_1,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [D] : ( m1_ami_3(D) => ! [E] : ( m1_ami_3(E) => ( ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A)) = k16_ami_3(B) & k13_ami_1(k1_tarski(k4_numbers),k1_ami_3,C,k16_ami_3(B)) = k7_ami_3(D,E) ) => ( D = E | ( k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1))) = k16_ami_3(k1_nat_1(B,1)) & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),D) = k5_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)) & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),E) = k6_int_1(k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),D),k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),E)) & ! [F] : ( m1_ami_3(F) => ~ ( F != D & F != E & k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),k1_nat_1(A,1)),F) != k2_ami_3(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),A),F) ) ) ) ) ) ) ) ) ) ) ), file(scm_1,t22_scm_1), []). fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,0) = 0 ) ), file(arithm,t2_arithm), []). 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_scm_comp,axiom,( ! [A] : ( m2_finseq_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m2_finseq_1(B,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ! [H] : ( m1_scm_1(H,k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),A,B),k2_lang1(k4_numbers),C,D,E) => ! [I] : ( m1_subset_1(I,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( ( I = k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,H),F) & k16_ami_3(G) = k6_ami_1(k1_tarski(k4_numbers),k1_ami_3,I) ) => m1_scm_1(I,B,k2_lang1(k4_numbers),G,k1_nat_1(D,k3_finseq_1(A)),E) ) ) ) ) ) ) ) ) ) ) ), file(scm_comp,t2_scm_comp), []). 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_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(B,C) ) => r1_xreal_0(A,C) ) ) ) ) ), file(xreal_1,t2_xreal_1), []). fof(t35_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ), file(finseq_1,t35_finseq_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_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), []). 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_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ~ ( A != k4_tarski(0,0) & A != k4_tarski(0,1) & A != k4_tarski(0,2) & A != k4_tarski(0,3) & A != k4_tarski(0,4) ) ) ), file(scm_comp,t3_scm_comp), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t45_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k7_finseq_1(k7_finseq_1(A,B),C) = k7_finseq_1(A,k7_finseq_1(B,C)) ) ) ) ), file(finseq_1,t45_finseq_1), []). fof(t46_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xreal_0(A,k2_square_1(A,B)) ) ) ), file(square_1,t46_square_1), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_finseq_1,axiom, ( k2_finseq_1(0) = k1_xboole_0 & k2_finseq_1(1) = k1_tarski(1) & k2_finseq_1(2) = k2_tarski(1,2) ), file(finseq_1,t4_finseq_1), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( ( ~ v3_struct_0(C) & ~ v2_ami_1(C,A) & v5_ami_1(C,A) & v8_ami_1(C,A) & l1_ami_1(C,A) ) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,C))) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k11_ami_1(A,C,k10_ami_1(A,C,D),k1_nat_1(B,E)) = k11_ami_1(A,C,k10_ami_1(A,C,k11_ami_1(A,C,k10_ami_1(A,C,D),B)),E) ) ) ) ) ) ), file(ami_1,t51_ami_1), []). fof(t52_ami_3,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( A != B & k15_ami_3(A) = k15_ami_3(B) ) ) ) ), file(ami_3,t52_ami_3), []). fof(t57_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k9_finseq_1(A) <=> ( k3_finseq_1(B) = 1 & k1_funct_1(B,1) = A ) ) ) ), file(finseq_1,t57_finseq_1), []). fof(t59_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A ) ), file(finseq_1,t59_finseq_1), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t61_finseq_1,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k10_finseq_1(A,B) <=> ( k3_finseq_1(C) = 2 & k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) ) ) ), file(finseq_1,t61_finseq_1), []). fof(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(t6_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [B] : ( m1_struct_0(B,k1_scm_comp,k6_dtconstr(k1_scm_comp)) => k13_scm_comp(A,k3_scm_comp(B)) = k11_scm_comp(A,B) ) ) ), file(scm_comp,t6_scm_comp), []). 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(t7_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [B] : ( m1_struct_0(B,k1_scm_comp,k7_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => k13_scm_comp(A,k2_scm_comp(B,C,D)) = k10_scm_comp(B,k13_scm_comp(A,C),k13_scm_comp(A,D)) ) ) ) ) ), file(scm_comp,t7_scm_comp), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t8_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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ), file(xreal_1,t8_xreal_1), []). fof(t9_scm_comp,axiom,( ! [A] : ( m1_struct_0(A,k1_scm_comp,k6_dtconstr(k1_scm_comp)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k15_scm_comp(k3_scm_comp(A),B) = k3_lang1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(B),k4_scm_comp(A))) ) ) ), file(scm_comp,t9_scm_comp), []).