% Mizar problem: t57_scmpds_2,scmpds_2,1112,45 fof(t57_scmpds_2,conjecture,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_scmpds_2(C) => ( k1_funct_1(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),k2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) = k18_scmpds_2(k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A)) & k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),C) = B & ! [D] : ( m1_scmpds_2(D) => ( D != C => k2_scmpds_2(k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,k6_scmpds_2(C,B),A),D) = k2_scmpds_2(A,D) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc1_fraenkel,cc1_int_1,cc1_nat_1,cc1_relset_1,cc1_setfam_1,cc2_int_1,cc2_nat_1,cc3_int_1,cc3_nat_1,cc4_int_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,connectedness_r1_xreal_0,d15_ami_1,d1_scmpds_2,d24_scmpds_1,d2_scmpds_2,d5_ami_1,d5_tarski,d7_ami_1,d7_scmpds_2,dt_g1_ami_1,dt_k10_finseq_1,dt_k10_scmpds_1,dt_k11_finseq_1,dt_k11_scmpds_1,dt_k12_finseq_1,dt_k12_scmpds_1,dt_k13_finseq_1,dt_k13_scmpds_1,dt_k14_ami_2,dt_k14_scmpds_1,dt_k15_ami_2,dt_k15_scmpds_1,dt_k16_scmpds_1,dt_k17_scmpds_1,dt_k18_scmpds_1,dt_k18_scmpds_2,dt_k19_scmpds_1,dt_k1_cqc_lang,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_gr_cy_1,dt_k1_numbers,dt_k1_scmpds_1,dt_k1_scmpds_2,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_scmpds_1,dt_k21_scmpds_1,dt_k22_scmpds_1,dt_k23_scmpds_1,dt_k24_scmpds_1,dt_k25_scmpds_1,dt_k26_scmpds_1,dt_k27_scmpds_1,dt_k28_scmpds_1,dt_k29_scmpds_1,dt_k2_ami_1,dt_k2_ami_2,dt_k2_cqc_lang,dt_k2_scmpds_2,dt_k2_tarski,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_ami_2,dt_k3_tarski,dt_k3_xcmplx_0,dt_k4_ami_1,dt_k4_card_3,dt_k4_numbers,dt_k4_tarski,dt_k5_finseq_1,dt_k5_int_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_scmpds_1,dt_k6_ami_1,dt_k6_int_1,dt_k6_scmpds_1,dt_k6_scmpds_2,dt_k6_xcmplx_0,dt_k7_scmpds_1,dt_k8_funct_2,dt_k8_scmpds_1,dt_k9_finseq_1,dt_k9_scmpds_1,dt_l1_ami_1,dt_l1_struct_0,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_relset_1,dt_m1_scmpds_2,dt_m1_struct_0,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,dt_m2_subset_1,dt_u1_ami_1,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_struct_0,existence_m1_finseq_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_scmpds_2,existence_m1_struct_0,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc1_ami_2,fc1_fraenkel,fc1_int_1,fc1_nat_1,fc1_numbers,fc1_ordinal2,fc1_scmpds_1,fc1_scmpds_2,fc1_struct_0,fc1_xboole_0,fc2_ami_1,fc2_ami_2,fc2_fraenkel,fc2_int_1,fc2_nat_1,fc2_scmpds_2,fc2_setfam_1,fc2_xboole_0,fc3_ami_1,fc3_nat_1,fc3_scmpds_1,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc4_int_1,fc4_nat_1,fc4_numbers,fc4_setfam_1,fc5_scmpds_1,fc6_int_1,fc6_scmpds_1,fc7_int_1,fc8_int_1,fc9_int_1,free_g1_ami_1,idempotence_k2_xboole_0,rc1_ami_1,rc1_fraenkel,rc1_int_1,rc1_nat_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_int_1,rc2_nat_1,rc2_xboole_0,rc3_nat_1,rc3_struct_0,rc5_ami_1,rc5_struct_0,rc6_ami_1,redefinition_k10_scmpds_1,redefinition_k12_finseq_1,redefinition_k13_scmpds_1,redefinition_k1_fraenkel,redefinition_k2_cqc_lang,redefinition_k2_scmpds_2,redefinition_k5_numbers,redefinition_k8_funct_2,redefinition_k9_finseq_1,redefinition_m1_struct_0,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc10_boole,spc10_numerals,spc11_boole,spc11_numerals,spc12_boole,spc12_numerals,spc13_boole,spc13_numerals,spc14_boole,spc14_numerals,spc1_boole,spc1_numerals,spc2_boole,spc2_numerals,spc3_boole,spc3_numerals,spc4_boole,spc4_numerals,spc5_boole,spc5_numerals,spc6_boole,spc6_numerals,spc7_boole,spc7_numerals,spc8_boole,spc8_numerals,spc9_boole,spc9_numerals,t10_gr_cy_1,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t26_scmpds_1,t27_scmpds_1,t2_arithm,t2_real,t2_subset,t30_scmpds_1,t31_scmpds_1,t35_scmpds_1,t3_arithm,t3_real,t3_subset,t4_arithm,t4_real,t4_subset,t55_scmpds_2,t56_scmpds_2,t5_real,t5_subset,t6_boole,t6_real,t7_boole,t7_real,t7_scmpds_2,t8_boole,t8_real]), [file(scmpds_2,t57_scmpds_2)]). 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(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). 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_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_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_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(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_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_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(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(d15_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u5_ami_1(A,B))) => k6_ami_1(A,B,C) = k1_funct_1(C,k2_ami_1(A,B)) ) ) ) ), file(ami_1,d15_ami_1), []). fof(d1_scmpds_2,axiom,( k1_scmpds_2 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,0,k3_ami_2,k1_gr_cy_1(14),k5_scmpds_1,k6_scmpds_1,k29_scmpds_1) ), file(scmpds_2,d1_scmpds_2), []). fof(d24_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => ! [B] : ( m1_subset_1(B,k4_card_3(k6_scmpds_1)) => ( ( ? [C] : ( v1_int_1(C) & A = k4_tarski(0,k9_finseq_1(C)) ) => k28_scmpds_1(A,B) = k8_scmpds_1(B,k12_scmpds_1(B,k15_scmpds_1(A))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & A = k4_tarski(2,k13_scmpds_1(C,D)) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k16_scmpds_1(A),k17_scmpds_1(A)),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & A = k4_tarski(3,k13_scmpds_1(C,D)) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k16_scmpds_1(A),k17_scmpds_1(A)),k7_scmpds_1(B)),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & A = k4_tarski(1,k12_finseq_1(k2_ami_2,C)) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k14_scmpds_1(A),k10_scmpds_1(B,k11_scmpds_1(B,k14_scmpds_1(A),k26_scmpds_1))),k25_scmpds_1(B,k11_scmpds_1(B,k14_scmpds_1(A),k27_scmpds_1))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & A = k4_tarski(4,k11_finseq_1(C,D,E)) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(B,k2_cqc_lang(k3_ami_2,k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),0,k15_ami_2(k7_scmpds_1(B)),k12_scmpds_1(B,k20_scmpds_1(A)))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & A = k4_tarski(5,k11_finseq_1(C,D,E)) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(B,k14_ami_2(k3_ami_2,k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),0,k15_ami_2(k7_scmpds_1(B)),k12_scmpds_1(B,k20_scmpds_1(A)))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & A = k4_tarski(6,k11_finseq_1(C,D,E)) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(B,k14_ami_2(k3_ami_2,0,k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),k15_ami_2(k7_scmpds_1(B)),k12_scmpds_1(B,k20_scmpds_1(A)))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & A = k4_tarski(7,k11_finseq_1(C,D,E)) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A)),k20_scmpds_1(A)),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & A = k4_tarski(8,k11_finseq_1(C,D,E)) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A)),k2_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k18_scmpds_1(A),k19_scmpds_1(A))),k20_scmpds_1(A))),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) & ? [E] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & A = k4_tarski(9,k1_scmpds_1(C,D,E,F)) ) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k2_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) & ? [E] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & A = k4_tarski(10,k1_scmpds_1(C,D,E,F)) ) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k6_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) & ? [E] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & A = k4_tarski(11,k1_scmpds_1(C,D,E,F)) ) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k3_xcmplx_0(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) & ? [E] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & A = k4_tarski(13,k1_scmpds_1(C,D,E,F)) ) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A)))),k15_ami_2(k7_scmpds_1(B))) ) & ( ? [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) & ? [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) & ? [E] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & A = k4_tarski(12,k1_scmpds_1(C,D,E,F)) ) ) ) ) => k28_scmpds_1(A,B) = k8_scmpds_1(k9_scmpds_1(k9_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A)),k5_int_1(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A)),k6_int_1(k10_scmpds_1(B,k11_scmpds_1(B,k21_scmpds_1(A),k23_scmpds_1(A))),k10_scmpds_1(B,k11_scmpds_1(B,k22_scmpds_1(A),k24_scmpds_1(A))))),k15_ami_2(k7_scmpds_1(B))) ) & ( ( ! [C] : ( v1_int_1(C) => A != k4_tarski(0,k9_finseq_1(C)) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => A != k4_tarski(2,k13_scmpds_1(C,D)) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => A != k4_tarski(3,k13_scmpds_1(C,D)) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => A != k4_tarski(1,k12_finseq_1(k2_ami_2,C)) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k4_tarski(4,k11_finseq_1(C,D,E)) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k4_tarski(5,k11_finseq_1(C,D,E)) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k4_tarski(6,k11_finseq_1(C,D,E)) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k4_tarski(7,k11_finseq_1(C,D,E)) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k4_tarski(8,k11_finseq_1(C,D,E)) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => A != k4_tarski(9,k1_scmpds_1(C,D,E,F)) ) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => A != k4_tarski(10,k1_scmpds_1(C,D,E,F)) ) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => A != k4_tarski(11,k1_scmpds_1(C,D,E,F)) ) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => A != k4_tarski(13,k1_scmpds_1(C,D,E,F)) ) ) ) ) & ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => A != k4_tarski(12,k1_scmpds_1(C,D,E,F)) ) ) ) ) ) => k28_scmpds_1(A,B) = B ) ) ) ) ), file(scmpds_1,d24_scmpds_1), []). fof(d2_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_scmpds_2)) => ( m1_scmpds_2(A) <=> r2_hidden(A,k2_ami_2) ) ) ), file(scmpds_2,d2_scmpds_2), []). fof(d5_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => k2_ami_1(A,B) = u1_ami_1(A,B) ) ), file(ami_1,d5_ami_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_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m2_subset_1(C,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)) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => k4_ami_1(A,B,C,D) = k1_funct_1(k8_funct_2(u4_ami_1(A,B),k1_funct_2(k4_card_3(u5_ami_1(A,B)),k4_card_3(u5_ami_1(A,B))),u6_ami_1(A,B),C),D) ) ) ) ) ), file(ami_1,d7_ami_1), []). fof(d7_scmpds_2,axiom,( ! [A] : ( m1_scmpds_2(A) => ! [B] : ( v1_int_1(B) => k6_scmpds_2(A,B) = k4_tarski(2,k10_finseq_1(A,B)) ) ) ), file(scmpds_2,d7_scmpds_2), []). 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_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). fof(dt_k10_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & m1_subset_1(B,k2_ami_2) ) => v1_int_1(k10_scmpds_1(A,B)) ) ), file(scmpds_1,k10_scmpds_1), []). fof(dt_k11_finseq_1,axiom,( $true ), file(finseq_1,k11_finseq_1), []). fof(dt_k11_scmpds_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & m1_subset_1(B,k2_ami_2) & v1_int_1(C) ) => m2_subset_1(k11_scmpds_1(A,B,C),k5_numbers,k2_ami_2) ) ), file(scmpds_1,k11_scmpds_1), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k12_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & v1_int_1(B) ) => m2_subset_1(k12_scmpds_1(A,B),k5_numbers,k3_ami_2) ) ), file(scmpds_1,k12_scmpds_1), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_ami_2) & v1_int_1(B) ) => m2_finseq_1(k13_scmpds_1(A,B),k2_xboole_0(k2_ami_2,k4_numbers)) ) ), file(scmpds_1,k13_scmpds_1), []). fof(dt_k14_ami_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => m1_subset_1(k14_ami_2(A,B,C,D,E),A) ) ), file(ami_2,k14_ami_2), []). fof(dt_k14_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => m2_subset_1(k14_scmpds_1(A),k5_numbers,k2_ami_2) ) ), file(scmpds_1,k14_scmpds_1), []). fof(dt_k15_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k3_ami_2) => m2_subset_1(k15_ami_2(A),k5_numbers,k3_ami_2) ) ), file(ami_2,k15_ami_2), []). fof(dt_k15_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => v1_int_1(k15_scmpds_1(A)) ) ), file(scmpds_1,k15_scmpds_1), []). fof(dt_k16_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => m2_subset_1(k16_scmpds_1(A),k5_numbers,k2_ami_2) ) ), file(scmpds_1,k16_scmpds_1), []). fof(dt_k17_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => v1_int_1(k17_scmpds_1(A)) ) ), file(scmpds_1,k17_scmpds_1), []). fof(dt_k18_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => m2_subset_1(k18_scmpds_1(A),k5_numbers,k2_ami_2) ) ), file(scmpds_1,k18_scmpds_1), []). fof(dt_k18_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => m1_struct_0(k18_scmpds_2(A),k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ), file(scmpds_2,k18_scmpds_2), []). fof(dt_k19_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => v1_int_1(k19_scmpds_1(A)) ) ), file(scmpds_1,k19_scmpds_1), []). fof(dt_k1_cqc_lang,axiom,( $true ), file(cqc_lang,k1_cqc_lang), []). fof(dt_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => m1_fraenkel(k1_fraenkel(A,B),A,B) ) ), file(fraenkel,k1_fraenkel), []). 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_gr_cy_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( ~ v1_xboole_0(k1_gr_cy_1(A)) & m1_subset_1(k1_gr_cy_1(A),k1_zfmisc_1(k5_numbers)) ) ) ), file(gr_cy_1,k1_gr_cy_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_scmpds_1,axiom,( $true ), file(scmpds_1,k1_scmpds_1), []). fof(dt_k1_scmpds_2,axiom, ( v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & l1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,k1_scmpds_2), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k20_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => v1_int_1(k20_scmpds_1(A)) ) ), file(scmpds_1,k20_scmpds_1), []). fof(dt_k21_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => m2_subset_1(k21_scmpds_1(A),k5_numbers,k2_ami_2) ) ), file(scmpds_1,k21_scmpds_1), []). fof(dt_k22_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => m2_subset_1(k22_scmpds_1(A),k5_numbers,k2_ami_2) ) ), file(scmpds_1,k22_scmpds_1), []). fof(dt_k23_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => v1_int_1(k23_scmpds_1(A)) ) ), file(scmpds_1,k23_scmpds_1), []). fof(dt_k24_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k5_scmpds_1) => v1_int_1(k24_scmpds_1(A)) ) ), file(scmpds_1,k24_scmpds_1), []). fof(dt_k25_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & m1_subset_1(B,k2_ami_2) ) => m2_subset_1(k25_scmpds_1(A,B),k5_numbers,k3_ami_2) ) ), file(scmpds_1,k25_scmpds_1), []). fof(dt_k26_scmpds_1,axiom,( m2_subset_1(k26_scmpds_1,k1_numbers,k5_numbers) ), file(scmpds_1,k26_scmpds_1), []). fof(dt_k27_scmpds_1,axiom,( m2_subset_1(k27_scmpds_1,k1_numbers,k5_numbers) ), file(scmpds_1,k27_scmpds_1), []). fof(dt_k28_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_scmpds_1) & m1_subset_1(B,k4_card_3(k6_scmpds_1)) ) => m1_subset_1(k28_scmpds_1(A,B),k4_card_3(k6_scmpds_1)) ) ), file(scmpds_1,k28_scmpds_1), []). fof(dt_k29_scmpds_1,axiom, ( v1_funct_1(k29_scmpds_1) & v1_funct_2(k29_scmpds_1,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1))) & m2_relset_1(k29_scmpds_1,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1))) ), file(scmpds_1,k29_scmpds_1), []). fof(dt_k2_ami_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) ) => m1_subset_1(k2_ami_1(A,B),u1_struct_0(B)) ) ), file(ami_1,k2_ami_1), []). fof(dt_k2_ami_2,axiom,( m1_subset_1(k2_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k2_ami_2), []). fof(dt_k2_cqc_lang,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => m1_subset_1(k2_cqc_lang(A,B,C,D,E),A) ) ), file(cqc_lang,k2_cqc_lang), []). fof(dt_k2_scmpds_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) & m1_scmpds_2(B) ) => v1_int_1(k2_scmpds_2(A,B)) ) ), file(scmpds_2,k2_scmpds_2), []). 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_2,axiom,( m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k3_ami_2), []). 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_1,axiom,( ! [A,B,C,D] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) & m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) ) => m1_subset_1(k4_ami_1(A,B,C,D),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k4_ami_1), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_numbers,axiom,( $true ), file(numbers,k4_numbers), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). 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_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_scmpds_1,axiom,( m1_subset_1(k5_scmpds_1,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(14),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ), file(scmpds_1,k5_scmpds_1), []). 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_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_scmpds_1,axiom, ( v1_funct_1(k6_scmpds_1) & v1_funct_2(k6_scmpds_1,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2))) & m2_relset_1(k6_scmpds_1,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k5_scmpds_1,k3_ami_2))) ), file(scmpds_1,k6_scmpds_1), []). fof(dt_k6_scmpds_2,axiom,( ! [A,B] : ( ( m1_scmpds_2(A) & v1_int_1(B) ) => m2_subset_1(k6_scmpds_2(A,B),k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) ) ), file(scmpds_2,k6_scmpds_2), []). fof(dt_k6_xcmplx_0,axiom,( $true ), file(xcmplx_0,k6_xcmplx_0), []). fof(dt_k7_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) => m2_subset_1(k7_scmpds_1(A),k5_numbers,k3_ami_2) ) ), file(scmpds_1,k7_scmpds_1), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & m1_subset_1(B,k3_ami_2) ) => m1_subset_1(k8_scmpds_1(A,B),k4_card_3(k6_scmpds_1)) ) ), file(scmpds_1,k8_scmpds_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_k9_scmpds_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & m1_subset_1(B,k2_ami_2) & v1_int_1(C) ) => m1_subset_1(k9_scmpds_1(A,B,C),k4_card_3(k6_scmpds_1)) ) ), file(scmpds_1,k9_scmpds_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_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_fraenkel,axiom,( ! [A,B,C] : ( m1_fraenkel(C,A,B) => ( ~ v1_xboole_0(C) & v1_fraenkel(C) ) ) ), file(fraenkel,m1_fraenkel), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_scmpds_2,axiom,( ! [A] : ( m1_scmpds_2(A) => m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) ), file(scmpds_2,m1_scmpds_2), []). 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_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_u1_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_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_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_fraenkel,axiom,( ! [A,B] : ? [C] : m1_fraenkel(C,A,B) ), file(fraenkel,m1_fraenkel), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_scmpds_2,axiom,( ? [A] : m1_scmpds_2(A) ), file(scmpds_2,m1_scmpds_2), []). 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_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(fc1_ami_2,axiom, ( ~ v1_xboole_0(k2_ami_2) & v1_membered(k2_ami_2) & v2_membered(k2_ami_2) & v3_membered(k2_ami_2) & v4_membered(k2_ami_2) & v5_membered(k2_ami_2) ), file(ami_2,fc1_ami_2), []). fof(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). 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_numbers,axiom,( ~ v1_xboole_0(k1_numbers) ), file(numbers,fc1_numbers), []). 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_scmpds_1,axiom,( ! [A,B,C,D] : ( v1_relat_1(k1_scmpds_1(A,B,C,D)) & v1_funct_1(k1_scmpds_1(A,B,C,D)) ) ), file(scmpds_1,fc1_scmpds_1), []). fof(fc1_scmpds_2,axiom, ( ~ v3_struct_0(k1_scmpds_2) & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,fc1_scmpds_2), []). 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_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). 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_2,axiom, ( ~ v1_xboole_0(k3_ami_2) & v1_membered(k3_ami_2) & v2_membered(k3_ami_2) & v3_membered(k3_ami_2) & v4_membered(k3_ami_2) & v5_membered(k3_ami_2) ), file(ami_2,fc2_ami_2), []). 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_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_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_scmpds_2,axiom, ( ~ v3_struct_0(k1_scmpds_2) & v1_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & ~ v2_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v5_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v6_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) & v8_ami_1(k1_scmpds_2,k1_tarski(k4_numbers)) ), file(scmpds_2,fc2_scmpds_2), []). 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_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_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_scmpds_1,axiom,( ! [A,B,C,D] : ( v1_relat_1(k1_scmpds_1(A,B,C,D)) & v1_funct_1(k1_scmpds_1(A,B,C,D)) & v1_finset_1(k1_scmpds_1(A,B,C,D)) & v1_finseq_1(k1_scmpds_1(A,B,C,D)) ) ), file(scmpds_1,fc3_scmpds_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_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_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_numbers,axiom,( ~ v1_xboole_0(k4_numbers) ), file(numbers,fc4_numbers), []). 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(fc5_scmpds_1,axiom, ( ~ v1_xboole_0(k5_scmpds_1) & v1_relat_1(k5_scmpds_1) ), file(scmpds_1,fc5_scmpds_1), []). 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_scmpds_1,axiom,( ! [A,B] : ( ( v1_funct_1(A) & v1_funct_2(A,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1))) & m1_relset_1(A,k5_scmpds_1,k1_fraenkel(k4_card_3(k6_scmpds_1),k4_card_3(k6_scmpds_1))) & m1_subset_1(B,k5_scmpds_1) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(scmpds_1,fc6_scmpds_1), []). 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(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(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(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(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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). 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_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_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_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_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). 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(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(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(redefinition_k10_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) & m1_subset_1(B,k2_ami_2) ) => k10_scmpds_1(A,B) = k1_funct_1(A,B) ) ), file(scmpds_1,k10_scmpds_1), []). fof(redefinition_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k13_scmpds_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k2_ami_2) & v1_int_1(B) ) => k13_scmpds_1(A,B) = k10_finseq_1(A,B) ) ), file(scmpds_1,k13_scmpds_1), []). fof(redefinition_k1_fraenkel,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => k1_fraenkel(A,B) = k1_funct_2(A,B) ) ), file(fraenkel,k1_fraenkel), []). fof(redefinition_k2_cqc_lang,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => k2_cqc_lang(A,B,C,D,E) = k1_cqc_lang(B,C,D,E) ) ), file(cqc_lang,k2_cqc_lang), []). fof(redefinition_k2_scmpds_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) & m1_scmpds_2(B) ) => k2_scmpds_2(A,B) = k1_funct_1(A,B) ) ), file(scmpds_2,k2_scmpds_2), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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_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_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc10_boole,axiom,( ~ v1_xboole_0(10) ), file(boole,spc10_boole), []). fof(spc10_numerals,axiom, ( v2_xreal_0(10) & m1_subset_1(10,k5_numbers) ), file(numerals,spc10_numerals), []). fof(spc11_boole,axiom,( ~ v1_xboole_0(11) ), file(boole,spc11_boole), []). fof(spc11_numerals,axiom, ( v2_xreal_0(11) & m1_subset_1(11,k5_numbers) ), file(numerals,spc11_numerals), []). fof(spc12_boole,axiom,( ~ v1_xboole_0(12) ), file(boole,spc12_boole), []). fof(spc12_numerals,axiom, ( v2_xreal_0(12) & m1_subset_1(12,k5_numbers) ), file(numerals,spc12_numerals), []). fof(spc13_boole,axiom,( ~ v1_xboole_0(13) ), file(boole,spc13_boole), []). fof(spc13_numerals,axiom, ( v2_xreal_0(13) & m1_subset_1(13,k5_numbers) ), file(numerals,spc13_numerals), []). fof(spc14_boole,axiom,( ~ v1_xboole_0(14) ), file(boole,spc14_boole), []). fof(spc14_numerals,axiom, ( v2_xreal_0(14) & m1_subset_1(14,k5_numbers) ), file(numerals,spc14_numerals), []). 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(spc5_boole,axiom,( ~ v1_xboole_0(5) ), file(boole,spc5_boole), []). fof(spc5_numerals,axiom, ( v2_xreal_0(5) & m1_subset_1(5,k5_numbers) ), file(numerals,spc5_numerals), []). fof(spc6_boole,axiom,( ~ v1_xboole_0(6) ), file(boole,spc6_boole), []). fof(spc6_numerals,axiom, ( v2_xreal_0(6) & m1_subset_1(6,k5_numbers) ), file(numerals,spc6_numerals), []). fof(spc7_boole,axiom,( ~ v1_xboole_0(7) ), file(boole,spc7_boole), []). fof(spc7_numerals,axiom, ( v2_xreal_0(7) & m1_subset_1(7,k5_numbers) ), file(numerals,spc7_numerals), []). fof(spc8_boole,axiom,( ~ v1_xboole_0(8) ), file(boole,spc8_boole), []). fof(spc8_numerals,axiom, ( v2_xreal_0(8) & m1_subset_1(8,k5_numbers) ), file(numerals,spc8_numerals), []). fof(spc9_boole,axiom,( ~ v1_xboole_0(9) ), file(boole,spc9_boole), []). fof(spc9_numerals,axiom, ( v2_xreal_0(9) & m1_subset_1(9,k5_numbers) ), file(numerals,spc9_numerals), []). fof(t10_gr_cy_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(A,0) => ( r2_hidden(B,k1_gr_cy_1(A)) <=> ~ r1_xreal_0(A,B) ) ) ) ) ), file(gr_cy_1,t10_gr_cy_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_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t26_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) => ! [B] : ( m2_subset_1(B,k5_numbers,k3_ami_2) => k1_funct_1(k8_scmpds_1(A,B),0) = B ) ) ), file(scmpds_1,t26_scmpds_1), []). fof(t27_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) => ! [B] : ( m2_subset_1(B,k5_numbers,k3_ami_2) => ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => k1_funct_1(k8_scmpds_1(A,B),C) = k1_funct_1(A,C) ) ) ) ), file(scmpds_1,t27_scmpds_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_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t30_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) => ! [B] : ( m2_subset_1(B,k5_numbers,k2_ami_2) => ! [C] : ( v1_int_1(C) => k1_funct_1(k9_scmpds_1(A,B,C),B) = C ) ) ) ), file(scmpds_1,t30_scmpds_1), []). fof(t31_scmpds_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k6_scmpds_1)) => ! [B] : ( m2_subset_1(B,k5_numbers,k2_ami_2) => ! [C] : ( v1_int_1(C) => ! [D] : ( m2_subset_1(D,k5_numbers,k2_ami_2) => ( D != B => k1_funct_1(k9_scmpds_1(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ) ), file(scmpds_1,t31_scmpds_1), []). fof(t35_scmpds_1,axiom,( ! [A] : ( m2_subset_1(A,k5_numbers,k1_gr_cy_1(14)) => ! [B] : ( m1_subset_1(B,k5_scmpds_1) => ! [C] : ( m2_subset_1(C,k5_numbers,k2_ami_2) => ! [D] : ( v1_int_1(D) => ( B = k4_tarski(A,k13_scmpds_1(C,D)) => ( k16_scmpds_1(B) = C & k17_scmpds_1(B) = D ) ) ) ) ) ) ), file(scmpds_1,t35_scmpds_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_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,0) = A ) ), file(arithm,t4_arithm), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t55_scmpds_2,axiom,( ! [A] : ( m1_struct_0(A,k1_scmpds_2,u2_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ! [B] : ( m2_subset_1(B,k5_numbers,k3_ami_2) => ( B = A => k15_ami_2(B) = k18_scmpds_2(A) ) ) ) ), file(scmpds_2,t55_scmpds_2), []). fof(t56_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(k4_numbers),k1_scmpds_2),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),u1_struct_0(k1_scmpds_2)))),u4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2)) => ! [C] : ( m1_subset_1(C,k5_scmpds_1) => ( C = B => ! [D] : ( m1_subset_1(D,k4_card_3(k6_scmpds_1)) => ( D = A => k4_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,B,A) = k28_scmpds_1(C,D) ) ) ) ) ) ) ), file(scmpds_2,t56_scmpds_2), []). 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(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(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_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_scmpds_2))) => ! [B] : ( m1_subset_1(B,k4_card_3(k6_scmpds_1)) => ( B = A => k6_ami_1(k1_tarski(k4_numbers),k1_scmpds_2,A) = k7_scmpds_1(B) ) ) ) ), file(scmpds_2,t7_scmpds_2), []). 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), []).