% Mizar problem: t39_reloc,reloc,3577,49 fof(t39_reloc,conjecture,( ! [A] : ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & v12_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) => ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k18_ami_1(k1_tarski(k4_numbers),k1_ami_3,A)) = k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k18_ami_1(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(A,B))) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_ami_1,antisymmetry_r2_hidden,cc1_fraenkel,cc1_funct_1,cc1_int_1,cc1_relset_1,cc1_setfam_1,cc2_funct_1,cc2_int_1,cc3_int_1,cc4_int_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,d10_ami_3,d12_ami_3,d15_ami_1,d17_ami_1,d1_ami_3,d22_ami_1,d26_ami_1,d28_ami_1,d3_reloc,d5_ami_1,d5_tarski,d6_reloc,d8_ami_3,d9_ami_3,dt_g1_ami_1,dt_k10_ami_1,dt_k10_ami_3,dt_k10_finseq_1,dt_k11_ami_1,dt_k11_ami_2,dt_k12_ami_1,dt_k12_ami_2,dt_k12_ami_3,dt_k12_finseq_1,dt_k13_ami_1,dt_k13_ami_2,dt_k13_ami_3,dt_k13_finseq_1,dt_k17_ami_1,dt_k17_ami_2,dt_k18_ami_1,dt_k1_ami_3,dt_k1_ami_5,dt_k1_fraenkel,dt_k1_funct_1,dt_k1_funct_2,dt_k1_funct_4,dt_k1_gr_cy_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_reloc,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_ami_1,dt_k2_ami_2,dt_k2_ami_5,dt_k2_cat_3,dt_k2_tarski,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_ami_2,dt_k3_ami_5,dt_k3_cqc_lang,dt_k3_reloc,dt_k3_tarski,dt_k3_xboole_0,dt_k4_ami_2,dt_k4_ami_5,dt_k4_card_3,dt_k4_numbers,dt_k4_reloc,dt_k4_tarski,dt_k5_ami_1,dt_k5_ami_2,dt_k5_finseq_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_reloc,dt_k6_ami_1,dt_k6_ami_5,dt_k6_reloc,dt_k7_ami_1,dt_k7_ami_5,dt_k7_relat_1,dt_k8_ami_1,dt_k8_ami_3,dt_k9_ami_3,dt_l1_ami_1,dt_l1_struct_0,dt_m1_ami_1,dt_m1_ami_3,dt_m1_finseq_1,dt_m1_fraenkel,dt_m1_relset_1,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_ami_1,existence_m1_ami_3,existence_m1_finseq_1,existence_m1_fraenkel,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,existence_m2_subset_1,fc10_ami_1,fc1_ami_3,fc1_ami_5,fc1_fraenkel,fc1_numbers,fc1_ordinal2,fc1_xboole_0,fc2_ami_1,fc2_ami_3,fc2_ami_5,fc2_fraenkel,fc2_setfam_1,fc2_xboole_0,fc3_ami_1,fc3_ami_3,fc3_ami_5,fc3_setfam_1,fc3_xboole_0,fc4_ami_1,fc4_funct_1,fc4_numbers,fc4_setfam_1,fc5_ami_3,fc6_ami_1,free_g1_ami_1,idempotence_k17_ami_1,idempotence_k1_funct_4,idempotence_k2_xboole_0,idempotence_k3_xboole_0,rc12_ami_1,rc1_ami_1,rc1_ami_3,rc1_fraenkel,rc1_funct_1,rc1_int_1,rc1_setfam_1,rc1_xboole_0,rc2_ami_1,rc2_ami_5,rc2_funct_1,rc2_int_1,rc2_xboole_0,rc3_ami_1,rc3_funct_1,rc4_ami_1,rc5_ami_1,rc6_ami_1,rc7_ami_1,rc8_ami_1,rc9_ami_1,redefinition_k11_ami_1,redefinition_k12_finseq_1,redefinition_k13_ami_1,redefinition_k17_ami_1,redefinition_k1_fraenkel,redefinition_k2_cat_3,redefinition_k5_numbers,redefinition_m1_struct_0,redefinition_m2_finseq_1,redefinition_m2_relset_1,redefinition_m2_subset_1,reflexivity_r1_tarski,spc0_boole,spc6_boole,spc6_numerals,spc7_boole,spc7_numerals,spc8_boole,spc8_numerals,spc9_boole,spc9_numerals,t100_relat_1,t1_boole,t1_numerals,t1_subset,t2_boole,t2_subset,t34_reloc,t35_reloc,t37_ami_5,t38_reloc,t39_ami_3,t3_subset,t4_subset,t54_ami_1,t56_ami_1,t5_subset,t6_boole,t7_boole,t82_ami_5,t8_boole,t90_relat_1,t96_ami_5]), [file(reloc,t39_reloc)]). 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_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) ), file(int_1,cc1_int_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_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(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_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_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(d10_ami_3,axiom,( ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m1_ami_3(B) => k10_ami_3(A,B) = k4_tarski(8,k10_finseq_1(A,B)) ) ) ), file(ami_3,d10_ami_3), []). fof(d12_ami_3,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_struct_0(C,B,u2_ami_1(A,B)) => k12_ami_3(A,B,C) = k2_cat_3(u2_ami_1(A,B),k2_ami_1(A,B),C) ) ) ) ), file(ami_3,d12_ami_3), []). 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(d17_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))) => k8_ami_1(A,B,C) = k1_funct_1(C,k6_ami_1(A,B,C)) ) ) ) ), file(ami_1,d17_ami_1), []). fof(d1_ami_3,axiom,( k1_ami_3 = g1_ami_1(k1_tarski(k4_numbers),k5_numbers,0,k3_ami_2,k1_gr_cy_1(9),k4_ami_2,k5_ami_2,k17_ami_2) ), file(ami_3,d1_ami_3), []). fof(d22_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_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))) => ( v9_ami_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => ( D = k12_ami_1(A,B,C) <=> ? [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) & D = k11_ami_1(A,B,k10_ami_1(A,B,C),E) & k8_ami_1(A,B,D) = k5_ami_1(A,B) ) ) ) ) ) ) ) ), file(ami_1,d22_ami_1), []). fof(d26_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( v12_ami_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => ( r1_tarski(C,D) => v9_ami_1(D,A,B) ) ) ) ) ) ) ), file(ami_1,d26_ami_1), []). fof(d28_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ( ( v11_ami_1(C,A,B) & v12_ami_1(C,A,B) & m1_ami_1(C,A,B) ) => ! [D] : ( m1_ami_1(D,A,B) => ( D = k18_ami_1(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_card_3(u5_ami_1(A,B))) => ( r1_tarski(C,E) => D = k7_relat_1(k12_ami_1(A,B,E),k1_relat_1(C)) ) ) ) ) ) ) ) ) ), file(ami_1,d28_ami_1), []). fof(d3_reloc,axiom,( ! [A] : ( m2_subset_1(A,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)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 6 => k3_reloc(A,B) = k8_ami_3(k1_reloc(k3_ami_5(k11_ami_2(k2_ami_5(A))),B)) ) & ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 7 => k3_reloc(A,B) = k9_ami_3(k1_reloc(k3_ami_5(k12_ami_2(k2_ami_5(A))),B),k4_ami_5(k13_ami_2(k2_ami_5(A)))) ) & ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = 8 => k3_reloc(A,B) = k10_ami_3(k1_reloc(k3_ami_5(k12_ami_2(k2_ami_5(A))),B),k4_ami_5(k13_ami_2(k2_ami_5(A)))) ) & ~ ( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != 6 & k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != 7 & k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) != 8 & k3_reloc(A,B) != A ) ) ) ) ), file(reloc,d3_reloc), []). 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(d6_reloc,axiom,( ! [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => k6_reloc(A,B) = k17_ami_1(k1_tarski(k4_numbers),k1_ami_3,k17_ami_1(k1_tarski(k4_numbers),k1_ami_3,k12_ami_3(k1_tarski(k4_numbers),k1_ami_3,k1_reloc(k13_ami_3(k1_tarski(k4_numbers),k1_ami_3,A),B)),k5_reloc(k4_reloc(k6_ami_5(k1_tarski(k4_numbers),k1_ami_3,A),B),B)),k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) ) ) ), file(reloc,d6_reloc), []). fof(d8_ami_3,axiom,( ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => k8_ami_3(A) = k4_tarski(6,k12_finseq_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3),A)) ) ), file(ami_3,d8_ami_3), []). fof(d9_ami_3,axiom,( ! [A] : ( m1_struct_0(A,k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ! [B] : ( m1_ami_3(B) => k9_ami_3(A,B) = k4_tarski(7,k10_finseq_1(A,B)) ) ) ), file(ami_3,d9_ami_3), []). 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_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_ami_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & m1_ami_3(B) ) => m2_subset_1(k10_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,k10_ami_3), []). fof(dt_k10_finseq_1,axiom,( $true ), file(finseq_1,k10_finseq_1), []). 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_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ami_2) => m2_subset_1(k11_ami_2(A),k5_numbers,k3_ami_2) ) ), file(ami_2,k11_ami_2), []). fof(dt_k12_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_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(k12_ami_1(A,B,C),k4_card_3(u5_ami_1(A,B))) ) ), file(ami_1,k12_ami_1), []). fof(dt_k12_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ami_2) => m2_subset_1(k12_ami_2(A),k5_numbers,k3_ami_2) ) ), file(ami_2,k12_ami_2), []). fof(dt_k12_ami_3,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,u2_ami_1(A,B)) ) => m1_ami_1(k12_ami_3(A,B,C),A,B) ) ), file(ami_3,k12_ami_3), []). 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_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_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ami_2) => m2_subset_1(k13_ami_2(A),k5_numbers,k2_ami_2) ) ), file(ami_2,k13_ami_2), []). fof(dt_k13_ami_3,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_ami_1(C,A,B) ) => m1_struct_0(k13_ami_3(A,B,C),B,u2_ami_1(A,B)) ) ), file(ami_3,k13_ami_3), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => m1_ami_1(k17_ami_1(A,B,C,D),A,B) ) ), file(ami_1,k17_ami_1), []). fof(dt_k17_ami_2,axiom, ( v1_funct_1(k17_ami_2) & v1_funct_2(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) & m2_relset_1(k17_ami_2,k4_ami_2,k1_fraenkel(k4_card_3(k5_ami_2),k4_card_3(k5_ami_2))) ), file(ami_2,k17_ami_2), []). fof(dt_k18_ami_1,axiom,( ! [A,B,C] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => m1_ami_1(k18_ami_1(A,B,C),A,B) ) ), file(ami_1,k18_ami_1), []). 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_ami_5,axiom,( ! [A,B,C] : ( ( l1_ami_1(B,A) & m1_subset_1(C,u4_ami_1(A,B)) ) => m1_subset_1(k1_ami_5(A,B,C),u3_ami_1(A,B)) ) ), file(ami_5,k1_ami_5), []). 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_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_funct_4(A,B)) & v1_funct_1(k1_funct_4(A,B)) ) ) ), file(funct_4,k1_funct_4), []). 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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_reloc,axiom,( ! [A,B] : ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & m1_subset_1(B,k5_numbers) ) => m1_struct_0(k1_reloc(A,B),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(reloc,k1_reloc), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_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_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => m1_subset_1(k2_ami_5(A),k4_ami_2) ) ), file(ami_5,k2_ami_5), []). fof(dt_k2_cat_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => ( v1_funct_1(k2_cat_3(A,B,C)) & v1_funct_2(k2_cat_3(A,B,C),k1_tarski(B),A) & m2_relset_1(k2_cat_3(A,B,C),k1_tarski(B),A) ) ) ), file(cat_3,k2_cat_3), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_ami_2,axiom,( m1_subset_1(k3_ami_2,k1_zfmisc_1(k5_numbers)) ), file(ami_2,k3_ami_2), []). fof(dt_k3_ami_5,axiom,( ! [A] : ( m1_subset_1(A,k3_ami_2) => m1_struct_0(k3_ami_5(A),k1_ami_3,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ) ), file(ami_5,k3_ami_5), []). fof(dt_k3_cqc_lang,axiom,( $true ), file(cqc_lang,k3_cqc_lang), []). fof(dt_k3_reloc,axiom,( ! [A,B] : ( ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k3_reloc(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(reloc,k3_reloc), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k4_ami_2,axiom,( m1_subset_1(k4_ami_2,k1_zfmisc_1(k2_zfmisc_1(k1_gr_cy_1(9),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(k4_numbers)),k5_numbers))))) ), file(ami_2,k4_ami_2), []). fof(dt_k4_ami_5,axiom,( ! [A] : ( m1_subset_1(A,k2_ami_2) => m1_ami_3(k4_ami_5(A)) ) ), file(ami_5,k4_ami_5), []). 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_reloc,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & m1_subset_1(B,k5_numbers) ) => ( v1_ami_3(k4_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(k4_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ), file(reloc,k4_reloc), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => m2_subset_1(k5_ami_1(A,B),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,k5_ami_1), []). fof(dt_k5_ami_2,axiom, ( v1_funct_1(k5_ami_2) & v1_funct_2(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) & m2_relset_1(k5_ami_2,k5_numbers,k2_xboole_0(k1_tarski(k4_numbers),k2_tarski(k4_ami_2,k3_ami_2))) ), file(ami_2,k5_ami_2), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_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_reloc,axiom,( ! [A,B] : ( ( v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & m1_subset_1(B,k5_numbers) ) => ( v1_ami_3(k5_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(k5_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ), file(reloc,k5_reloc), []). 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_5,axiom,( ! [A,B,C] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => ( v1_ami_3(k6_ami_5(A,B,C),A,B) & m1_ami_1(k6_ami_5(A,B,C),A,B) ) ) ), file(ami_5,k6_ami_5), []). fof(dt_k6_reloc,axiom,( ! [A,B] : ( ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & m1_subset_1(B,k5_numbers) ) => m1_ami_1(k6_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ), file(reloc,k6_reloc), []). fof(dt_k7_ami_1,axiom,( $true ), file(ami_1,k7_ami_1), []). fof(dt_k7_ami_5,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_ami_1(B,A) & m1_ami_1(C,A,B) ) => m1_ami_1(k7_ami_5(A,B,C),A,B) ) ), file(ami_5,k7_ami_5), []). fof(dt_k7_relat_1,axiom,( ! [A,B] : ( v1_relat_1(A) => v1_relat_1(k7_relat_1(A,B)) ) ), file(relat_1,k7_relat_1), []). fof(dt_k8_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))) ) => m2_subset_1(k8_ami_1(A,B,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)) ) ), file(ami_1,k8_ami_1), []). fof(dt_k8_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => m2_subset_1(k8_ami_3(A),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,k8_ami_3), []). fof(dt_k9_ami_3,axiom,( ! [A,B] : ( ( m1_subset_1(A,u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & m1_ami_3(B) ) => m2_subset_1(k9_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,k9_ami_3), []). 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_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ! [C] : ( m1_ami_1(C,A,B) => m1_subset_1(C,k7_ami_1(u5_ami_1(A,B))) ) ) ), file(ami_1,m1_ami_1), []). 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_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_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_ami_1,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : m1_ami_1(C,A,B) ) ), file(ami_1,m1_ami_1), []). fof(existence_m1_ami_3,axiom,( ? [A] : m1_ami_3(A) ), file(ami_3,m1_ami_3), []). 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_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(fc10_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k7_ami_1(A)) & v1_fraenkel(k7_ami_1(A)) ) ) ), file(ami_1,fc10_ami_1), []). 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_ami_5,axiom, ( ~ v1_xboole_0(k2_ami_2) & ~ v1_finset_1(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_5,fc1_ami_5), []). fof(fc1_fraenkel,axiom,( ! [A,B] : v1_fraenkel(k1_funct_2(A,B)) ), file(fraenkel,fc1_fraenkel), []). 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_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_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_ami_5,axiom, ( ~ v1_xboole_0(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) & ~ v1_finset_1(u2_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ), file(ami_5,fc2_ami_5), []). 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_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_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_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) => ( v4_ordinal2(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) & v1_xreal_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) & v1_int_1(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) & v1_xcmplx_0(k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,A)) ) ) ), file(ami_5,fc3_ami_5), []). 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_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_relat_1(A,B)) & v1_funct_1(k7_relat_1(A,B)) ) ) ), file(funct_1,fc4_funct_1), []). fof(fc4_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_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(fc6_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => v3_ami_1(k5_ami_1(A,B),A,B) ) ), file(ami_1,fc6_ami_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_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => k17_ami_1(A,B,C,C) = C ) ), file(ami_1,k17_ami_1), []). fof(idempotence_k1_funct_4,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) ), file(funct_4,k1_funct_4), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(rc12_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v8_ami_1(B,A) & v10_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v11_ami_1(C,A,B) & v12_ami_1(C,A,B) ) ) ), file(ami_1,rc12_ami_1), []). 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_ami_3,axiom,( ! [A,B] : ( l1_ami_1(B,A) => ? [C] : ( m1_ami_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_ami_3(C,A,B) ) ) ), file(ami_3,rc1_ami_3), []). 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_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_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_ami_5,axiom,( ? [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & v1_relat_1(A) & v1_funct_1(A) & v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & ~ v1_ami_3(A,k1_tarski(k4_numbers),k1_ami_3) ) ), file(ami_5,rc2_ami_5), []). 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_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc4_ami_1,axiom,( ! [A,B] : ( ( v1_setfam_1(A) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & l1_ami_1(B,A) ) => ? [C] : ( m1_subset_1(C,u4_ami_1(A,B)) & v3_ami_1(C,A,B) ) ) ), file(ami_1,rc4_ami_1), []). 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(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(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(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(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_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_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_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_k17_ami_1,axiom,( ! [A,B,C,D] : ( ( l1_ami_1(B,A) & m1_ami_1(C,A,B) & m1_ami_1(D,A,B) ) => k17_ami_1(A,B,C,D) = k1_funct_4(C,D) ) ), file(ami_1,k17_ami_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_cat_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k2_cat_3(A,B,C) = k3_cqc_lang(B,C) ) ), file(cat_3,k2_cat_3), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). 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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). 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(t100_relat_1,axiom,( ! [A,B,C] : ( v1_relat_1(C) => k7_relat_1(k7_relat_1(C,A),B) = k7_relat_1(C,k3_xboole_0(A,B)) ) ), file(relat_1,t100_relat_1), []). 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_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t34_reloc,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B] : ( ( v11_ami_1(B,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(B,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] : ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ! [E] : ( m1_subset_1(E,k4_card_3(u5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) => ( ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(B)) & r1_tarski(B,C) & r1_tarski(k6_reloc(B,A),D) & E = k1_funct_4(C,k7_relat_1(D,k2_ami_2)) ) => ! [F] : ( m2_subset_1(F,k1_numbers,k5_numbers) => ( k1_reloc(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),F)),A) = 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,D),F)) & k3_reloc(k8_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),F)),A) = k8_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,D),F)) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,C),F),k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,B))) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,D),F),k1_relat_1(k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,k6_reloc(B,A)))) & k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),F),k2_ami_2) = k7_relat_1(k11_ami_1(k1_tarski(k4_numbers),k1_ami_3,k10_ami_1(k1_tarski(k4_numbers),k1_ami_3,D),F),k2_ami_2) ) ) ) ) ) ) ) ) ), file(reloc,t34_reloc), []). fof(t35_reloc,axiom,( ! [A] : ( ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) & m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) => ( v12_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) <=> v12_ami_1(k6_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ) ) ), file(reloc,t35_reloc), []). fof(t37_ami_5,axiom,( k1_ami_5(k1_tarski(k4_numbers),k1_ami_3,k5_ami_1(k1_tarski(k4_numbers),k1_ami_3)) = 0 ), file(ami_5,t37_ami_5), []). fof(t38_reloc,axiom,( ! [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) => ( r2_hidden(k2_ami_1(k1_tarski(k4_numbers),k1_ami_3),k1_relat_1(A)) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( v11_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) <=> v11_ami_1(k6_reloc(A,B),k1_tarski(k4_numbers),k1_ami_3) ) ) ) ) ), file(reloc,t38_reloc), []). fof(t39_ami_3,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v2_ami_1(B,A) & l1_ami_1(B,A) ) => ! [C] : ( m1_ami_1(C,A,B) => ? [D] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) & r1_tarski(C,D) ) ) ) ) ), file(ami_3,t39_ami_3), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t54_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v5_ami_1(B,A) & v7_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] : ( m1_struct_0(D,B,u2_ami_1(A,B)) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k13_ami_1(A,B,C,D) = k13_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),E),D) ) ) ) ) ) ), file(ami_1,t54_ami_1), []). fof(t56_ami_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( ~ v3_struct_0(B) & ~ v2_ami_1(B,A) & v4_ami_1(B,A) & v5_ami_1(B,A) & v7_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] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( k13_ami_1(A,B,C,k6_ami_1(A,B,k11_ami_1(A,B,k10_ami_1(A,B,C),D))) = k5_ami_1(A,B) => k12_ami_1(A,B,C) = k11_ami_1(A,B,k10_ami_1(A,B,C),D) ) ) ) ) ) ), file(ami_1,t56_ami_1), []). 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(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t82_ami_5,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] : ( m1_subset_1(D,k4_card_3(u5_ami_1(A,B))) => ! [E] : m1_subset_1(k1_funct_4(C,k7_relat_1(D,E)),k4_card_3(u5_ami_1(A,B))) ) ) ) ) ), file(ami_5,t82_ami_5), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t90_relat_1,axiom,( ! [A,B] : ( v1_relat_1(B) => k1_relat_1(k7_relat_1(B,A)) = k3_xboole_0(k1_relat_1(B),A) ) ), file(relat_1,t90_relat_1), []). fof(t96_ami_5,axiom,( ! [A] : ( m1_ami_1(A,k1_tarski(k4_numbers),k1_ami_3) => k7_ami_5(k1_tarski(k4_numbers),k1_ami_3,A) = k7_relat_1(A,k2_ami_2) ) ), file(ami_5,t96_ami_5), []).