% Mizar problem: t18_osalg_4,osalg_4,2349,31 fof(t18_osalg_4,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) ) => ( r3_msualg_3(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D)),C,k21_osalg_4(A,B,C,D)) & v1_osalg_3(k21_osalg_4(A,B,C,D),A) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc1_finseq_5,cc1_fraenkel,cc1_msualg_1,cc1_msualg_4,cc1_orders_3,cc1_osalg_1,cc1_partfun1,cc1_pboole,cc1_relat_1,cc1_relset_1,cc2_int_1,cc2_msualg_1,cc2_osalg_4,cc2_pboole,cc3_int_1,cc3_osalg_4,cc3_pboole,cc4_int_1,cc4_osalg_4,cc7_osalg_1,commutativity_k2_tarski,d10_msualg_1,d11_msualg_1,d11_msualg_3,d12_osalg_4,d13_osalg_4,d14_osalg_4,d15_osalg_4,d16_osalg_4,d18_osalg_1,d19_msualg_4,d1_funct_2,d1_osalg_3,d20_msualg_4,d20_osalg_4,d21_osalg_4,d22_osalg_4,d25_osalg_4,d26_osalg_4,d27_osalg_4,d3_pboole,d4_finseq_4,d5_funct_1,d5_tarski,d6_msualg_1,d6_osalg_4,d7_msualg_1,d8_funct_1,d8_msualg_3,d8_osalg_4,d9_msualg_1,d9_msualg_3,d9_osalg_4,dt_g3_msualg_1,dt_k10_osalg_4,dt_k13_finseq_1,dt_k14_osalg_4,dt_k15_osalg_4,dt_k16_osalg_4,dt_k17_msualg_4,dt_k18_msualg_4,dt_k19_osalg_4,dt_k1_funct_1,dt_k1_msualg_1,dt_k1_msualg_3,dt_k1_numbers,dt_k1_osalg_1,dt_k1_osalg_4,dt_k1_partfun1,dt_k1_relat_1,dt_k1_tarski,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_osalg_4,dt_k21_osalg_4,dt_k2_msualg_1,dt_k2_msualg_4,dt_k2_osalg_4,dt_k2_relat_1,dt_k2_tarski,dt_k2_zfmisc_1,dt_k3_finseq_2,dt_k3_msualg_1,dt_k3_osalg_4,dt_k3_tarski,dt_k4_card_3,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_msualg_1,dt_k4_osalg_4,dt_k4_relset_1,dt_k4_tarski,dt_k5_msualg_1,dt_k5_msualg_3,dt_k5_msualg_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_osalg_4,dt_k5_relat_1,dt_k5_relset_1,dt_k6_eqrel_1,dt_k6_msualg_3,dt_k6_msualg_4,dt_k6_osalg_4,dt_k6_pboole,dt_k7_eqrel_1,dt_k7_osalg_4,dt_k7_pboole,dt_k8_eqrel_1,dt_k8_funct_2,dt_k8_osalg_4,dt_k8_pboole,dt_k9_osalg_4,dt_l1_msualg_1,dt_l1_orders_2,dt_l1_osalg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l2_osalg_1,dt_l3_msualg_1,dt_l3_osalg_1,dt_m1_eqrel_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_msualg_4,dt_m1_osalg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_msualg_1,existence_l1_orders_2,existence_l1_osalg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l2_osalg_1,existence_l3_msualg_1,existence_l3_osalg_1,existence_m1_eqrel_1,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_msualg_4,existence_m1_osalg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,fc10_relat_1,fc12_relat_1,fc1_filter_1,fc1_msualg_1,fc1_msualg_3,fc1_osalg_1,fc1_osalg_4,fc1_pboole,fc1_pralg_2,fc1_struct_0,fc1_subset_1,fc2_osalg_4,fc2_pboole,fc2_subset_1,fc3_msafree,fc3_osalg_4,fc3_subset_1,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc6_relat_1,fc7_funcop_1,fc7_relat_1,fc8_funcop_1,fc8_relat_1,fc9_relat_1,fraenkel_a_3_0_osalg_4,free_g3_msualg_1,rc10_osalg_1,rc11_osalg_1,rc12_osalg_1,rc1_fraenkel,rc1_funcop_1,rc1_int_1,rc1_msualg_3,rc1_msualg_4,rc1_osalg_4,rc1_partfun1,rc1_pboole,rc1_pralg_2,rc1_relat_1,rc1_subset_1,rc2_int_1,rc2_msualg_4,rc2_partfun1,rc2_pboole,rc2_relat_1,rc2_subset_1,rc3_msualg_4,rc3_osalg_4,rc3_pboole,rc3_relat_1,rc3_struct_0,rc4_osalg_4,rc4_pboole,rc5_msualg_1,rc5_osalg_1,rc5_osalg_4,rc5_struct_0,rc6_msualg_1,rc6_osalg_4,redefinition_k1_msualg_3,redefinition_k1_osalg_1,redefinition_k1_partfun1,redefinition_k2_msualg_4,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_msualg_4,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k6_msualg_3,redefinition_k6_msualg_4,redefinition_k7_pboole,redefinition_k8_eqrel_1,redefinition_k8_funct_2,redefinition_k8_pboole,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t13_osalg_4,t14_osalg_4,t15_osalg_4,t17_osalg_1,t1_msafree,t1_msualg_3,t1_subset,t22_funct_1,t2_subset,t2_tarski,t3_subset,t46_relat_1,t4_subset,t5_subset,t6_boole,t6_msualg_3,t7_boole,t8_boole,t9_funct_1]), [file(osalg_4,t18_osalg_4)]). fof(abstractness_v4_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(B,A) => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ), file(msualg_1,v4_msualg_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_finseq_5,axiom,( ! [A] : ( v1_xboole_0(A) => v1_realset1(A) ) ), file(finseq_5,cc1_finseq_5), []). 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_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc1_msualg_1), []). fof(cc1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => v1_msualg_4(D) ) ) ), file(msualg_4,cc1_msualg_4), []). fof(cc1_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_struct_0(A) => v1_orders_3(A) ) ) ), file(orders_3,cc1_orders_3), []). fof(cc1_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( v4_osalg_1(A) => ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) ) ) ) ), file(osalg_1,cc1_osalg_1), []). fof(cc1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) ), file(partfun1,cc1_partfun1), []). fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_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(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_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc2_msualg_1), []). fof(cc2_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k2_osalg_4(A)) => ~ v1_xboole_0(B) ) ) ), file(osalg_4,cc2_osalg_4), []). fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), []). fof(cc3_int_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), []). fof(cc3_osalg_4,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_orders_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_osalg_4(A) ) ) ) ), file(osalg_4,cc3_osalg_4), []). fof(cc3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => v1_funcop_1(D) ) ) ), file(pboole,cc3_pboole), []). fof(cc4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), []). fof(cc4_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_osalg_4(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k2_osalg_4(A)) => ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) ) ) ) ), file(osalg_4,cc4_osalg_4), []). fof(cc7_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_orders_3(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => v12_osalg_1(B,A) ) ) ), file(osalg_1,cc7_osalg_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(d10_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) ), file(msualg_1,d10_msualg_1), []). fof(d11_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ), file(msualg_1,d11_msualg_1), []). fof(d11_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( r3_msualg_3(A,B,C,D) <=> ( r1_msualg_3(A,B,C,D) & v1_msualg_3(D) ) ) ) ) ) ) ), file(msualg_3,d11_msualg_3), []). fof(d12_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D))))) => ( E = k6_osalg_4(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ? [G] : ( r2_hidden(G,k1_funct_1(u4_msualg_1(A,B),D)) & F = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),G) ) ) ) ) ) ) ) ) ), file(osalg_4,d12_osalg_4), []). fof(d13_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( ( v11_osalg_1(D,A) & m1_pboole(D,u1_struct_0(A)) ) => ( D = k7_osalg_4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = k6_osalg_4(A,B,C,E) ) ) ) ) ) ) ), file(osalg_4,d13_osalg_4), []). fof(d14_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) => k8_osalg_4(A,B,C,D,E) = k6_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D)),E) ) ) ) ) ) ), file(osalg_4,d14_osalg_4), []). fof(d15_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ( m1_subset_1(E,k3_msualg_1(A,B,C)) => ! [F] : ( m1_subset_1(F,k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k7_osalg_4(A,C,D)))) => ( F = k9_osalg_4(A,B,C,D,E) <=> ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ~ ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,B))) & ! [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,C),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G))) => ~ ( H = k1_funct_1(E,G) & k1_funct_1(F,G) = k8_osalg_4(A,C,D,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,B),G),H) ) ) ) ) ) ) ) ) ) ) ) ), file(osalg_4,d15_osalg_4), []). fof(d16_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) & m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) => ( E = k10_osalg_4(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,C),k1_osalg_1(A,B))) => k1_funct_1(E,F) = k8_osalg_4(A,C,D,k1_osalg_1(A,B),F) ) ) ) ) ) ) ) ), file(osalg_4,d16_osalg_4), []). fof(d18_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => ( v11_osalg_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_orders_2(A,C,D) => r1_tarski(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ) ), file(osalg_1,d18_osalg_1), []). fof(d19_msualg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v3_relat_2(F) & v8_relat_2(F) & v1_partfun1(F,k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) & m2_relset_1(F,k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) ) => ( F = k17_msualg_4(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u4_msualg_1(A,B),E)) => ( r2_hidden(k4_tarski(G,H),F) <=> k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),H) ) ) ) ) ) ) ) ) ) ) ), file(msualg_4,d19_msualg_4), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_osalg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funcop_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_osalg_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_orders_2(A,C,D) => ! [E] : ( r2_hidden(E,k1_relat_1(k1_funct_1(B,C))) => ( r2_hidden(E,k1_relat_1(k1_funct_1(B,D))) & k1_funct_1(k1_funct_1(B,C),E) = k1_funct_1(k1_funct_1(B,D),E) ) ) ) ) ) ) ) ) ), file(osalg_3,d1_osalg_3), []). fof(d20_msualg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( r1_msualg_3(A,B,C,D) => ! [E] : ( ( v3_msualg_4(E,A,B) & v4_msualg_4(E,A,B) & m1_msualg_4(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) => ( E = k18_msualg_4(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k2_msualg_4(A,B,E,F) = k17_msualg_4(A,B,C,D,F) ) ) ) ) ) ) ) ) ), file(msualg_4,d20_msualg_4), []). fof(d20_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) & m2_relset_1(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) => ( E = k14_osalg_4(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k3_msualg_1(A,B,C)) => ( r2_hidden(k9_osalg_4(A,B,C,D,F),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,C,D))),B)) => k1_funct_1(E,k9_osalg_4(A,B,C,D,F)) = k1_funct_1(k1_partfun1(k3_msualg_1(A,B,C),k4_msualg_1(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B),k5_msualg_1(A,B,C),k10_osalg_4(A,B,C,D)),F) ) ) ) ) ) ) ) ) ), file(osalg_4,d20_osalg_4), []). fof(d21_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m3_pboole(D,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C))) => ( D = k15_osalg_4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_msualg_1(A)) => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C)),D,E) = k14_osalg_4(A,E,B,C) ) ) ) ) ) ) ), file(osalg_4,d21_osalg_4), []). fof(d22_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => k16_osalg_4(A,B,C) = g3_msualg_1(A,k7_osalg_4(A,B,C),k15_osalg_4(A,B,C)) ) ) ) ), file(osalg_4,d22_osalg_4), []). fof(d25_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) ) => k19_osalg_4(A,B,C,D) = k18_msualg_4(A,B,C,D) ) ) ) ) ) ), file(osalg_4,d25_osalg_4), []). fof(d26_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) & m2_relset_1(F,k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) ) => ( F = k20_osalg_4(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E)) => k1_funct_1(F,k8_osalg_4(A,B,k19_osalg_4(A,B,C,D),E,G)) = k8_funct_2(k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,C),E),k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,E),G) ) ) ) ) ) ) ) ) ) ), file(osalg_4,d26_osalg_4), []). fof(d27_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C)) => ( E = k21_osalg_4(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C),E,F) = k20_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ) ), file(osalg_4,d27_osalg_4), []). fof(d3_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), []). fof(d4_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B) ) ) ), file(msualg_1,d6_msualg_1), []). fof(d6_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => k2_osalg_4(A) = k8_eqrel_1(u1_struct_0(A),k1_osalg_4(A)) ) ), file(osalg_4,d6_osalg_4), []). fof(d7_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) ), file(msualg_1,d7_msualg_1), []). fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B,C] : ( ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ), file(funct_1,d8_funct_1), []). fof(d8_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v5_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,D,C)) => ( G = k6_msualg_3(A,B,C,D,E,F) <=> ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k1_relat_1(F)) => k1_funct_1(G,H) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),E,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,D),H)),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) ), file(msualg_3,d8_msualg_3), []). fof(d8_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_osalg_4(A,B) = k6_eqrel_1(u1_struct_0(A),k1_osalg_4(A),B) ) ) ), file(osalg_4,d8_osalg_4), []). fof(d9_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k3_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,C))),B) ) ) ) ), file(msualg_1,d9_msualg_1), []). fof(d9_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) => ( r1_msualg_3(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_msualg_1(A)) => ( k3_msualg_1(A,E,B) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,B)) => k1_funct_1(k1_msualg_3(u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,B),F)) = k1_funct_1(k5_msualg_1(A,E,C),k5_msualg_3(A,B,C,E,D,F)) ) ) ) ) ) ) ) ) ), file(msualg_3,d9_msualg_3), []). fof(d9_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) => k4_osalg_4(A,B,C) = k3_tarski(a_3_0_osalg_4(A,B,C)) ) ) ) ), file(osalg_4,d9_osalg_4), []). fof(dt_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ( v4_msualg_1(g3_msualg_1(A,B,C),A) & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ), file(msualg_1,g3_msualg_1), []). fof(dt_k10_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ( v1_funct_1(k10_osalg_4(A,B,C,D)) & v1_funct_2(k10_osalg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) & m2_relset_1(k10_osalg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) ) ), file(osalg_4,k10_osalg_4), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k14_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ( v1_funct_1(k14_osalg_4(A,B,C,D)) & v1_funct_2(k14_osalg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) & m2_relset_1(k14_osalg_4(A,B,C,D),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,C,D))),B),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,C,D)),B)) ) ) ), file(osalg_4,k14_osalg_4), []). fof(dt_k15_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => m3_pboole(k15_osalg_4(A,B,C),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,B,C))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k7_osalg_4(A,B,C))) ) ), file(osalg_4,k15_osalg_4), []). fof(dt_k16_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v12_osalg_1(k16_osalg_4(A,B,C),A) & l3_msualg_1(k16_osalg_4(A,B,C),A) ) ) ), file(osalg_4,k16_osalg_4), []). fof(dt_k17_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(E,u1_struct_0(A)) ) => ( v3_relat_2(k17_msualg_4(A,B,C,D,E)) & v8_relat_2(k17_msualg_4(A,B,C,D,E)) & v1_partfun1(k17_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) & m2_relset_1(k17_msualg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),E),k1_funct_1(u4_msualg_1(A,B),E)) ) ) ), file(msualg_4,k17_msualg_4), []). fof(dt_k18_msualg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) => ( v3_msualg_4(k18_msualg_4(A,B,C,D),A,B) & v4_msualg_4(k18_msualg_4(A,B,C,D),A,B) & m1_msualg_4(k18_msualg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ), file(msualg_4,k18_msualg_4), []). fof(dt_k19_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) => ( v3_msualg_4(k19_osalg_4(A,B,C,D),A,B) & v4_msualg_4(k19_osalg_4(A,B,C,D),A,B) & m1_osalg_4(k19_osalg_4(A,B,C,D),A,B) ) ) ), file(osalg_4,k19_osalg_4), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(msualg_1,k1_msualg_1), []). fof(dt_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => ( v1_funct_1(k1_msualg_3(A,B,C,D,E)) & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ), file(msualg_3,k1_msualg_3), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_osalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m1_subset_1(k1_osalg_1(A,B),u1_struct_0(A)) ) ), file(osalg_1,k1_osalg_1), []). fof(dt_k1_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_partfun1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(k1_osalg_4(A)) & v8_relat_2(k1_osalg_4(A)) & m2_relset_1(k1_osalg_4(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(osalg_4,k1_osalg_4), []). fof(dt_k1_partfun1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) ) => ( v1_funct_1(k1_partfun1(A,B,C,D,E,F)) & m2_relset_1(k1_partfun1(A,B,C,D,E,F),A,D) ) ) ), file(partfun1,k1_partfun1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k20_osalg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(E,u1_struct_0(A)) ) => ( v1_funct_1(k20_osalg_4(A,B,C,D,E)) & v1_funct_2(k20_osalg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) & m2_relset_1(k20_osalg_4(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),E),k1_funct_1(u4_msualg_1(A,C),E)) ) ) ), file(osalg_4,k20_osalg_4), []). fof(dt_k21_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & m3_pboole(D,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) ) => m3_pboole(k21_osalg_4(A,B,C,D),u1_struct_0(A),u4_msualg_1(A,k16_osalg_4(A,B,k19_osalg_4(A,B,C,D))),u4_msualg_1(A,C)) ) ), file(osalg_4,k21_osalg_4), []). fof(dt_k2_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,k2_msualg_1), []). fof(dt_k2_msualg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) ) => ( v3_relat_2(k2_msualg_4(A,B,C,D)) & v8_relat_2(k2_msualg_4(A,B,C,D)) & v1_partfun1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D)) & m2_relset_1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ), file(msualg_4,k2_msualg_4), []). fof(dt_k2_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_osalg_4(A)) & m1_subset_1(k2_osalg_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(osalg_4,k2_osalg_4), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) ), file(msualg_1,k3_msualg_1), []). fof(dt_k3_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m2_subset_1(k3_osalg_4(A,B),k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) ) ), file(osalg_4,k3_osalg_4), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) ), file(msualg_1,k4_msualg_1), []). fof(dt_k4_osalg_4,axiom,( $true ), file(osalg_4,k4_osalg_4), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => ( v1_funct_1(k5_msualg_1(A,B,C)) & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) ), file(msualg_1,k5_msualg_1), []). fof(dt_k5_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & l3_msualg_1(C,A) & m1_subset_1(D,u1_msualg_1(A)) & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(F,k3_msualg_1(A,D,B)) ) => m1_subset_1(k5_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ), file(msualg_3,k5_msualg_3), []). fof(dt_k5_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_msualg_1(A)) & m1_pboole(C,u1_msualg_1(A)) & m3_pboole(D,u1_msualg_1(A),B,C) & m1_subset_1(E,u1_msualg_1(A)) ) => ( v1_funct_1(k5_msualg_4(A,B,C,D,E)) & v1_funct_2(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ), file(msualg_4,k5_msualg_4), []). 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_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,k2_osalg_4(A)) ) => ( v1_partfun1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) & v3_relat_2(k5_osalg_4(A,B,C,D)) & v8_relat_2(k5_osalg_4(A,B,C,D)) & m2_relset_1(k5_osalg_4(A,B,C,D),k4_osalg_4(A,u4_msualg_1(A,B),D),k4_osalg_4(A,u4_msualg_1(A,B),D)) ) ) ), file(osalg_4,k5_osalg_4), []). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). fof(dt_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_1), []). fof(dt_k6_eqrel_1,axiom,( ! [A,B,C] : ( ( v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_subset_1(k6_eqrel_1(A,B,C),k1_zfmisc_1(A)) ) ), file(eqrel_1,k6_eqrel_1), []). fof(dt_k6_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & m1_subset_1(D,u1_msualg_1(A)) & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(F,k3_msualg_1(A,D,B)) ) => m1_subset_1(k6_msualg_3(A,B,C,D,E,F),k3_msualg_1(A,D,C)) ) ), file(msualg_3,k6_msualg_3), []). fof(dt_k6_msualg_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v2_relat_1(C) & m1_pboole(C,A) ) => ( v2_relat_1(k6_msualg_4(A,B,C)) & m1_pboole(k6_msualg_4(A,B,C),k4_finseq_1(B)) ) ) ), file(msualg_4,k6_msualg_4), []). fof(dt_k6_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k6_osalg_4(A,B,C,D),k1_zfmisc_1(k8_eqrel_1(k4_osalg_4(A,u4_msualg_1(A,B),k3_osalg_4(A,D)),k5_osalg_4(A,B,C,k3_osalg_4(A,D))))) ) ), file(osalg_4,k6_osalg_4), []). fof(dt_k6_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ), file(pboole,k6_pboole), []). fof(dt_k7_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_subset_1(k7_eqrel_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,k7_eqrel_1), []). fof(dt_k7_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v11_osalg_1(k7_osalg_4(A,B,C),A) & m1_pboole(k7_osalg_4(A,B,C),u1_struct_0(A)) ) ) ), file(osalg_4,k7_osalg_4), []). fof(dt_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => m1_pboole(k7_pboole(A,B,C,D),A) ) ), file(pboole,k7_pboole), []). fof(dt_k8_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => m1_eqrel_1(k8_eqrel_1(A,B),A) ) ), file(eqrel_1,k8_eqrel_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_osalg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) ) => m1_subset_1(k8_osalg_4(A,B,C,D,E),k6_osalg_4(A,B,C,D)) ) ), file(osalg_4,k8_osalg_4), []). fof(dt_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => ( v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ), file(pboole,k8_pboole), []). fof(dt_k9_osalg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) & v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) & m1_subset_1(E,k3_msualg_1(A,B,C)) ) => m1_subset_1(k9_osalg_4(A,B,C,D,E),k4_card_3(k6_msualg_4(u1_struct_0(A),k1_msualg_1(A,B),k7_osalg_4(A,C,D)))) ) ), file(osalg_4,k9_osalg_4), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_osalg_1,axiom,( ! [A] : ( l1_osalg_1(A) => l1_msualg_1(A) ) ), file(osalg_1,l1_osalg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l2_osalg_1,axiom,( ! [A] : ( l2_osalg_1(A) => ( l1_msualg_1(A) & l1_orders_2(A) ) ) ), file(osalg_1,l2_osalg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_l3_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( l1_osalg_1(A) & l2_osalg_1(A) ) ) ), file(osalg_1,l3_osalg_1), []). fof(dt_m1_eqrel_1,axiom,( ! [A,B] : ( m1_eqrel_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(eqrel_1,m1_eqrel_1), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => m1_pboole(D,A) ) ) ), file(msualg_4,m1_msualg_4), []). fof(dt_m1_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osalg_4(C,A,B) => m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ), file(osalg_4,m1_osalg_4), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). fof(dt_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => m1_pboole(D,A) ) ) ), file(pboole,m3_pboole), []). fof(dt_u1_msualg_1,axiom,( $true ), file(msualg_1,u1_msualg_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u2_msualg_1(A)) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ), file(msualg_1,u2_msualg_1), []). fof(dt_u3_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u3_msualg_1(A)) & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ), file(msualg_1,u3_msualg_1), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(dt_u5_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ), file(msualg_1,u5_msualg_1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_osalg_1,axiom,( ? [A] : l1_osalg_1(A) ), file(osalg_1,l1_osalg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l2_osalg_1,axiom,( ? [A] : l2_osalg_1(A) ), file(osalg_1,l2_osalg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_l3_osalg_1,axiom,( ? [A] : l3_osalg_1(A) ), file(osalg_1,l3_osalg_1), []). fof(existence_m1_eqrel_1,axiom,( ! [A] : ? [B] : m1_eqrel_1(B,A) ), file(eqrel_1,m1_eqrel_1), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m1_msualg_4(D,A,B,C) ) ), file(msualg_4,m1_msualg_4), []). fof(existence_m1_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : m1_osalg_4(C,A,B) ) ), file(osalg_4,m1_osalg_4), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). fof(existence_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m3_pboole(D,A,B,C) ) ), file(pboole,m3_pboole), []). fof(fc10_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc1_filter_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => ~ v1_xboole_0(k7_eqrel_1(A,B)) ) ), file(filter_1,fc1_filter_1), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_1), []). fof(fc1_msualg_3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_msualg_1(A)) ) => ( ~ v1_xboole_0(k3_msualg_1(A,C,B)) & v1_fraenkel(k3_msualg_1(A,C,B)) ) ) ), file(msualg_3,fc1_msualg_3), []). fof(fc1_osalg_1,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_finseq_1(C,A) ) => ( v1_relat_1(k5_relat_1(C,B)) & v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) ) ) ), file(osalg_1,fc1_osalg_1), []). fof(fc1_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) & m1_subset_1(D,u1_struct_0(A)) ) => ~ v1_xboole_0(k6_osalg_4(A,B,C,D)) ) ), file(osalg_4,fc1_osalg_4), []). fof(fc1_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & ~ v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) ) ) ), file(pboole,fc1_pboole), []). fof(fc1_pralg_2,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( ~ v1_xboole_0(k4_card_3(B)) & v1_fraenkel(k4_card_3(B)) & v1_pralg_2(k4_card_3(B)) ) ) ), file(pralg_2,fc1_pralg_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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc2_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v1_relat_1(k7_osalg_4(A,B,C)) & v2_relat_1(k7_osalg_4(A,B,C)) & ~ v3_relat_1(k7_osalg_4(A,B,C)) & v1_funct_1(k7_osalg_4(A,B,C)) & v11_osalg_1(k7_osalg_4(A,B,C),A) ) ) ), file(osalg_4,fc2_osalg_4), []). fof(fc2_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc3_msafree,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(u1_msualg_1(A)) ) ), file(msafree,fc3_msafree), []). fof(fc3_osalg_4,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v4_msualg_1(k16_osalg_4(A,B,C),A) & v5_msualg_1(k16_osalg_4(A,B,C),A) & v12_osalg_1(k16_osalg_4(A,B,C),A) ) ) ), file(osalg_4,fc3_osalg_4), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc8_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) ) ) ), file(funcop_1,fc8_funcop_1), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(fc9_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fraenkel_a_3_0_osalg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_pboole(C,u1_struct_0(B)) & m2_subset_1(D,k1_zfmisc_1(u1_struct_0(B)),k2_osalg_4(B)) ) => ( r2_hidden(A,a_3_0_osalg_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_funct_1(C,E) & r2_hidden(E,D) ) ) ) ), file(osalg_4,a_3_0_osalg_4), []). fof(free_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ! [D,E,F] : ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(msualg_1,g3_msualg_1), []). fof(rc10_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) ) ) ), file(osalg_1,rc10_osalg_1), []). fof(rc11_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) ) ) ), file(osalg_1,rc11_osalg_1), []). fof(rc12_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) ) ) ), file(osalg_1,rc12_osalg_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_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_msualg_3,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_msualg_3(B) ) ), file(msualg_3,rc1_msualg_3), []). fof(rc1_msualg_4,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_msualg_4(B) ) ), file(msualg_4,rc1_msualg_4), []). fof(rc1_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) & v1_msualg_4(B) ) ) ), file(osalg_4,rc1_osalg_4), []). fof(rc1_partfun1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_xboole_0(A) ) ), file(partfun1,rc1_partfun1), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_pralg_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) & v1_pralg_2(A) ) ), file(pralg_2,rc1_pralg_2), []). fof(rc1_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), []). fof(rc2_msualg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) ) ) ), file(msualg_4,rc2_msualg_4), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). fof(rc2_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), []). fof(rc2_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc3_msualg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) ) ) ), file(msualg_4,rc3_msualg_4), []). fof(rc3_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) ) ) ), file(osalg_4,rc3_osalg_4), []). fof(rc3_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc4_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) & v4_msualg_4(C,A,B) ) ) ), file(osalg_4,rc4_osalg_4), []). fof(rc4_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ), file(pboole,rc4_pboole), []). fof(rc5_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) ), file(msualg_1,rc5_msualg_1), []). fof(rc5_osalg_1,axiom,( ? [A] : ( l1_osalg_1(A) & ~ v3_struct_0(A) & ~ v2_msualg_1(A) ) ), file(osalg_1,rc5_osalg_1), []). fof(rc5_osalg_4,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_osalg_4(A) ) ), file(osalg_4,rc5_osalg_4), []). 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_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) ) ) ), file(msualg_1,rc6_msualg_1), []). fof(rc6_osalg_4,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) ) ), file(osalg_4,rc6_osalg_4), []). fof(redefinition_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_3,k1_msualg_3), []). fof(redefinition_k1_osalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => k1_osalg_1(A,B) = k2_msualg_1(A,B) ) ), file(osalg_1,k1_osalg_1), []). fof(redefinition_k1_partfun1,axiom,( ! [A,B,C,D,E,F] : ( ( v1_funct_1(E) & m1_relset_1(E,A,B) & v1_funct_1(F) & m1_relset_1(F,C,D) ) => k1_partfun1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ), file(partfun1,k1_partfun1), []). fof(redefinition_k2_msualg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) ) => k2_msualg_4(A,B,C,D) = k1_funct_1(C,D) ) ), file(msualg_4,k2_msualg_4), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k5_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_msualg_1(A)) & m1_pboole(C,u1_msualg_1(A)) & m3_pboole(D,u1_msualg_1(A),B,C) & m1_subset_1(E,u1_msualg_1(A)) ) => k5_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_4,k5_msualg_4), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), []). fof(redefinition_k6_msualg_3,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & v5_msualg_1(C,A) & l3_msualg_1(C,A) & m1_subset_1(D,u1_msualg_1(A)) & m3_pboole(E,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,C)) & m1_subset_1(F,k3_msualg_1(A,D,B)) ) => k6_msualg_3(A,B,C,D,E,F) = k5_msualg_3(A,B,C,D,E,F) ) ), file(msualg_3,k6_msualg_3), []). fof(redefinition_k6_msualg_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v2_relat_1(C) & m1_pboole(C,A) ) => k6_msualg_4(A,B,C) = k5_relat_1(B,C) ) ), file(msualg_4,k6_msualg_4), []). fof(redefinition_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k7_pboole), []). fof(redefinition_k8_eqrel_1,axiom,( ! [A,B] : ( ( v3_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) & m1_relset_1(B,A,A) ) => k8_eqrel_1(A,B) = k7_eqrel_1(A,B) ) ), file(eqrel_1,k8_eqrel_1), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k8_pboole), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r3_orders_2(A,B,C) <=> r1_orders_2(A,B,C) ) ) ), file(orders_2,r3_orders_2), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r3_orders_2(A,B,B) ) ), file(orders_2,r3_orders_2), []). fof(t13_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,B),D)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D)) => ( k8_osalg_4(A,B,C,D,E) = k8_osalg_4(A,B,C,D,F) <=> r2_hidden(k4_tarski(E,F),k2_msualg_4(A,B,C,D)) ) ) ) ) ) ) ) ), file(osalg_4,t13_osalg_4), []). fof(t14_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,B),D)) => ( r3_orders_2(A,D,E) => ! [G] : ( m1_subset_1(G,k1_funct_1(u4_msualg_1(A,B),E)) => ( G = F => k8_osalg_4(A,B,C,D,F) = k8_osalg_4(A,B,C,E,G) ) ) ) ) ) ) ) ) ) ), file(osalg_4,t14_osalg_4), []). fof(t15_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( ( v5_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v3_msualg_4(D,A,C) & v4_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ~ ( r2_hidden(E,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k7_osalg_4(A,C,D))),B)) & ! [F] : ( m1_subset_1(F,k3_msualg_1(A,B,C)) => E != k9_osalg_4(A,B,C,D,F) ) ) ) ) ) ) ), file(osalg_4,t15_osalg_4), []). fof(t17_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v12_osalg_1(B,A) <=> ( v11_osalg_1(u4_msualg_1(A,B),A) & m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ) ) ) ), file(osalg_1,t17_osalg_1), []). fof(t1_msafree,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k3_finseq_2(B)) & m2_relset_1(C,A,k3_finseq_2(B)) ) => ! [D] : ( m1_pboole(D,B) => ! [E] : ( m2_finseq_2(E,B,k3_finseq_2(B)) => ! [F] : ( ( r2_hidden(F,A) & E = k1_funct_1(C,F) ) => k1_funct_1(k7_pboole(A,k3_finseq_2(B),C,k6_pboole(B,D)),F) = k4_card_3(k5_relat_1(E,D)) ) ) ) ) ) ), file(msafree,t1_msafree), []). fof(t1_msualg_3,axiom,( ! [A,B] : ( ( v1_funcop_1(B) & m1_pboole(B,A) ) => ( v1_msualg_3(B) <=> ! [C] : ( r2_hidden(C,A) => v2_funct_1(k1_funct_1(B,C)) ) ) ) ), file(msualg_3,t1_msualg_3), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t22_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ), file(funct_1,t22_funct_1), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t46_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_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_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,B,C)) => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B)) & ! [E] : ( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)))) => r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) ), file(msualg_3,t6_msualg_3), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []).