% Mizar problem: t44_waybel27,waybel27,2078,29 fof(t44_waybel27,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_waybel_8(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_waybel_8(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => v2_waybel_8(k2_waybel27(A,B)) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc10_waybel25,cc10_waybel_0,cc10_waybel_1,cc11_waybel_0,cc11_yellow_0,cc12_waybel_0,cc12_yellow_0,cc13_waybel_0,cc14_waybel_0,cc1_fraenkel,cc1_funct_1,cc1_funct_2,cc1_lattice3,cc1_monoid_0,cc1_partfun1,cc1_relat_1,cc1_relset_1,cc1_tops_1,cc1_waybel10,cc1_waybel17,cc1_waybel18,cc1_waybel25,cc1_waybel27,cc1_waybel_0,cc1_waybel_2,cc1_waybel_8,cc1_yellow16,cc1_yellow_0,cc1_yellow_1,cc1_yellow_2,cc1_yellow_3,cc1_yellow_9,cc2_funct_1,cc2_funct_2,cc2_lattice3,cc2_tops_1,cc2_waybel10,cc2_waybel17,cc2_waybel25,cc2_waybel27,cc2_waybel_2,cc2_waybel_8,cc2_yellow_0,cc2_yellow_3,cc2_yellow_9,cc3_funct_2,cc3_tops_1,cc3_waybel17,cc3_waybel27,cc3_waybel_1,cc3_waybel_2,cc3_waybel_8,cc3_yellow_0,cc3_yellow_3,cc3_yellow_9,cc4_funct_2,cc4_tops_1,cc4_waybel17,cc4_waybel_1,cc4_waybel_2,cc4_waybel_8,cc4_yellow_0,cc4_yellow_9,cc5_funct_2,cc5_tops_1,cc5_waybel_0,cc5_waybel_1,cc5_waybel_2,cc5_yellow_0,cc5_yellow_9,cc6_funct_2,cc6_tops_1,cc6_waybel25,cc6_waybel_0,cc6_waybel_1,cc6_waybel_2,cc6_yellow_0,cc6_yellow_9,cc7_waybel25,cc7_waybel_0,cc7_waybel_1,cc7_waybel_2,cc7_yellow_0,cc8_waybel_0,cc8_waybel_1,cc8_yellow_0,cc9_waybel_0,cc9_waybel_1,cc9_yellow_0,d11_grcat_1,d13_waybel_1,d14_waybel_1,d18_waybel_0,d2_funcop_1,d4_waybel27,d4_yellow_9,d5_waybel27,d5_yellow_1,d9_quantal1,dt_g1_orders_2,dt_k1_funct_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_waybel_0,dt_k1_waybel_8,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_waybel27,dt_k2_yellow16,dt_k2_yellow_1,dt_k2_yellow_2,dt_k2_zfmisc_1,dt_k3_waybel27,dt_k3_yellow_1,dt_k4_waybel27,dt_k5_relat_1,dt_k5_waybel11,dt_k5_waybel_0,dt_k5_yellow_1,dt_k6_partfun1,dt_k6_relat_1,dt_k6_waybel_3,dt_k6_yellow_1,dt_k7_funct_2,dt_k7_grcat_1,dt_k7_relset_1,dt_k7_waybel_0,dt_k7_yellow_2,dt_k8_funct_2,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_9,dt_m1_cantor_1,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m1_yellow_9,dt_m2_relset_1,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_9,existence_m1_cantor_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m1_yellow_9,existence_m2_relset_1,fc10_relat_1,fc10_waybel10,fc10_waybel18,fc10_waybel_0,fc10_waybel_8,fc10_yellow_1,fc11_waybel18,fc11_waybel24,fc11_waybel_8,fc11_yellow_1,fc12_relat_1,fc12_waybel18,fc12_waybel_0,fc12_waybel_8,fc12_yellow_1,fc13_waybel18,fc13_yellow_1,fc13_yellow_3,fc14_waybel18,fc14_waybel_0,fc14_waybel_8,fc14_yellow_1,fc15_waybel10,fc15_yellow_1,fc16_yellow_1,fc17_waybel_0,fc17_yellow_1,fc18_yellow_1,fc1_funcop_1,fc1_funct_1,fc1_struct_0,fc1_subset_1,fc1_waybel10,fc1_waybel17,fc1_waybel_1,fc1_waybel_8,fc1_yellow16,fc1_yellow_0,fc2_funcop_1,fc2_funct_1,fc2_partfun1,fc2_subset_1,fc2_waybel14,fc2_waybel17,fc2_waybel_1,fc2_yellow16,fc2_yellow_2,fc3_funcop_1,fc3_waybel10,fc3_waybel14,fc3_waybel27,fc3_waybel_1,fc3_waybel_8,fc4_relat_1,fc4_subset_1,fc4_waybel10,fc4_waybel27,fc4_waybel_1,fc4_waybel_8,fc5_waybel27,fc5_waybel_1,fc5_waybel_8,fc5_yellow16,fc5_yellow_1,fc6_waybel27,fc6_waybel_8,fc6_yellow16,fc6_yellow_1,fc6_yellow_3,fc7_funcop_1,fc7_waybel27,fc7_waybel_8,fc7_yellow_1,fc8_funcop_1,fc8_waybel18,fc8_waybel_0,fc8_waybel_8,fc8_yellow_1,fc9_funcop_1,fc9_relat_1,fc9_waybel18,fc9_waybel_1,fc9_waybel_8,fc9_yellow_1,fraenkel_a_1_0_waybel14,fraenkel_a_2_0_waybel27,free_g1_orders_2,rc10_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_funct_2,rc1_lattice3,rc1_monoid_0,rc1_partfun1,rc1_relat_1,rc1_subset_1,rc1_tops_1,rc1_waybel10,rc1_waybel18,rc1_waybel27,rc1_waybel_1,rc1_waybel_2,rc1_waybel_8,rc1_yellow16,rc1_yellow_0,rc1_yellow_1,rc1_yellow_3,rc2_funct_1,rc2_funct_2,rc2_lattice3,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_tops_1,rc2_waybel10,rc2_waybel18,rc2_waybel_1,rc2_waybel_2,rc2_yellow16,rc2_yellow_0,rc3_funct_1,rc3_partfun1,rc3_relat_1,rc3_struct_0,rc3_tops_1,rc3_waybel_1,rc3_yellow16,rc3_yellow_0,rc3_yellow_9,rc4_funct_1,rc4_tops_1,rc4_waybel27,rc4_waybel_1,rc4_yellow_0,rc4_yellow_9,rc5_funct_1,rc5_struct_0,rc5_tops_1,rc5_waybel27,rc5_waybel_1,redefinition_k1_struct_0,redefinition_k1_waybel_0,redefinition_k2_pre_circ,redefinition_k2_yellow16,redefinition_k3_waybel27,redefinition_k6_partfun1,redefinition_k6_waybel_3,redefinition_k7_funct_2,redefinition_k7_relset_1,redefinition_k7_yellow_2,redefinition_k8_funct_2,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,reflexivity_r5_waybel_1,spc1_boole,t10_yellow_2,t11_grcat_1,t13_funcop_1,t18_waybel20,t18_waybel27,t1_subset,t21_funct_2,t23_funct_2,t23_waybel27,t25_waybel13,t26_waybel13,t26_waybel_8,t28_waybel27,t2_subset,t2_tarski,t30_waybel27,t32_waybel13,t32_yellow_2,t34_waybel27,t35_waybel13,t36_waybel27,t37_waybel27,t3_subset,t42_waybel14,t42_waybel27,t43_waybel14,t4_subset,t51_yellow_9,t52_yellow_9,t5_subset,t6_boole,t7_boole,t7_waybel_1,t8_boole,t8_waybel_1]), [file(waybel27,t44_waybel27)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc10_waybel25), []). fof(cc10_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_0,cc10_waybel_0), []). fof(cc10_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v11_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ) ) ), file(waybel_1,cc10_waybel_1), []). fof(cc11_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_yellow_0(A) ) ) ) ), file(waybel_0,cc11_waybel_0), []). fof(cc11_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc11_yellow_0), []). fof(cc12_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(waybel_0,cc12_waybel_0), []). fof(cc12_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc12_yellow_0), []). fof(cc13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) ) ) ) ), file(waybel_0,cc13_waybel_0), []). fof(cc14_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc14_waybel_0), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_partfun1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) ) ) ) ), file(funct_2,cc1_funct_2), []). fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). fof(cc1_monoid_0,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(monoid_0,cc1_monoid_0), []). 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_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(cc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => ( v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ) ) ), file(tops_1,cc1_tops_1), []). fof(cc1_waybel10,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) ) => ( v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(B) & v5_orders_3(B,A,A) ) ) ) ) ), file(waybel10,cc1_waybel10), []). fof(cc1_waybel17,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(C,A,B) ) => ( ~ v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(waybel17,cc1_waybel17), []). fof(cc1_waybel18,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel18(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) ), file(waybel18,cc1_waybel18), []). fof(cc1_waybel25,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel25,cc1_waybel25), []). fof(cc1_waybel27,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel27(A) & v2_waybel27(A) & v3_waybel27(A) ) ) ), file(waybel27,cc1_waybel27), []). fof(cc1_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) => v3_waybel_0(B,A) ) ) ) ), file(waybel_0,cc1_waybel_0), []). fof(cc1_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel_2,cc1_waybel_2), []). fof(cc1_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ) ) ), file(waybel_8,cc1_waybel_8), []). fof(cc1_yellow16,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_yellow16(A) ) => ( v1_relat_1(A) & v1_yellow_1(A) & v5_waybel_3(A) ) ) ), file(yellow16,cc1_yellow16), []). fof(cc1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(yellow_0,cc1_yellow_0), []). fof(cc1_yellow_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_yellow_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) ), file(yellow_1,cc1_yellow_1), []). fof(cc1_yellow_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(yellow_2,cc1_yellow_2), []). fof(cc1_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_struct_0(A) => v1_yellow_3(A) ) ) ), file(yellow_3,cc1_yellow_3), []). fof(cc1_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ~ v3_struct_0(B) ) ) ), file(yellow_9,cc1_yellow_9), []). 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_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) ) ) ), file(funct_2,cc2_funct_2), []). fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc2_lattice3), []). fof(cc2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_tops_1(B,A) ) ) ) ), file(tops_1,cc2_tops_1), []). fof(cc2_waybel10,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) => ~ v3_struct_0(B) ) ) ) ), file(waybel10,cc2_waybel10), []). fof(cc2_waybel17,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & l1_waybel_9(A) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & l1_waybel_9(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) ) => ( ~ v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(waybel17,cc2_waybel17), []). fof(cc2_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & ~ v1_yellow_3(B) & v2_waybel_3(B) & v3_waybel_3(B) & v2_waybel18(B) ) ) ) ) ), file(waybel25,cc2_waybel25), []). fof(cc2_waybel27,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & v1_fraenkel(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v1_funcop_1(C) & v1_partfun1(C,A,B) ) ) ) ) ), file(waybel27,cc2_waybel27), []). fof(cc2_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ), file(waybel_2,cc2_waybel_2), []). fof(cc2_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_8(A) ) ) ) ), file(waybel_8,cc2_waybel_8), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(cc2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v1_yellow_3(A) => ~ v3_struct_0(A) ) ) ), file(yellow_3,cc2_yellow_3), []). fof(cc2_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v2_orders_2(B) ) ) ), file(yellow_9,cc2_yellow_9), []). fof(cc3_funct_2,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,A,B) & v2_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_funct_2(C,A,B) ) ) ) ), file(funct_2,cc3_funct_2), []). fof(cc3_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_tops_1(B,A) ) ) ) ), file(tops_1,cc3_tops_1), []). fof(cc3_waybel17,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_waybel_9(A) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_waybel_9(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) ) => ( ~ v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(C,A,B) ) ) ) ) ), file(waybel17,cc3_waybel17), []). fof(cc3_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_monoid_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ~ v3_struct_0(B) => ( ~ v3_struct_0(B) & v1_monoid_0(B) ) ) ) ) ), file(waybel27,cc3_waybel27), []). fof(cc3_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v7_waybel_1(B,A) ) => ( v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) ) ) ) ) ), file(waybel_1,cc3_waybel_1), []). fof(cc3_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc3_waybel_2), []). fof(cc3_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & v1_waybel_8(A) & v2_waybel_8(A) ) ) ) ), file(waybel_8,cc3_waybel_8), []). fof(cc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow_0,cc3_yellow_0), []). fof(cc3_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) ) => ( ~ v3_struct_0(A) & ~ v1_yellow_3(A) ) ) ) ), file(yellow_3,cc3_yellow_3), []). fof(cc3_yellow_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v3_orders_2(B) ) ) ), file(yellow_9,cc3_yellow_9), []). fof(cc4_funct_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( ( v1_funct_1(B) & v1_partfun1(B,A,A) & v1_relat_2(B) & v1_funct_2(B,A,A) ) => ( v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ) ) ), file(funct_2,cc4_funct_2), []). fof(cc4_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) => v2_tops_1(B,A) ) ) ) ), file(tops_1,cc4_tops_1), []). fof(cc4_waybel17,axiom,( ! [A,B] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v4_waybel11(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_waybel_9(A) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_waybel_9(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(C,A,B) ) => ( ~ v1_xboole_0(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(C,A,B) & v5_orders_3(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ), file(waybel17,cc4_waybel17), []). fof(cc4_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) => ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v8_waybel_1(B,A) ) => ( v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) ) ) ) ) ), file(waybel_1,cc4_waybel_1), []). fof(cc4_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v1_waybel_2(A) ) ) ) ), file(waybel_2,cc4_waybel_2), []). fof(cc4_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) ) ) ) ), file(waybel_8,cc4_waybel_8), []). fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(cc4_yellow_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v4_orders_2(B) ) ) ), file(yellow_9,cc4_yellow_9), []). fof(cc5_funct_2,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc5_funct_2), []). fof(cc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_pre_topc(B,A) & v2_tops_1(B,A) ) => ( v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ) ) ), file(tops_1,cc5_tops_1), []). fof(cc5_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) ) ) ), file(waybel_0,cc5_waybel_0), []). fof(cc5_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel_1,cc5_waybel_1), []). fof(cc5_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc5_waybel_2), []). fof(cc5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) ), file(yellow_0,cc5_yellow_0), []). fof(cc5_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( ~ v3_struct_0(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ) ), file(yellow_9,cc5_yellow_9), []). fof(cc6_funct_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A,B) & v1_funct_2(C,A,B) ) ) ) ) ), file(funct_2,cc6_funct_2), []). fof(cc6_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(B,A) & v3_tops_1(B,A) ) => ( v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ) ) ), file(tops_1,cc6_tops_1), []). fof(cc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc6_waybel25), []). fof(cc6_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B) ) ) ) ) ), file(waybel_0,cc6_waybel_0), []). fof(cc6_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_waybel_1(A) ) ) ) ), file(waybel_1,cc6_waybel_1), []). fof(cc6_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v1_waybel_2(A) & v2_waybel_2(A) ) ) ) ), file(waybel_2,cc6_waybel_2), []). fof(cc6_yellow_0,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v2_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc6_yellow_0), []). fof(cc6_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ) ) ), file(yellow_9,cc6_yellow_9), []). fof(cc7_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v4_waybel11(B) & v1_waybel25(B) ) ) ) ) ), file(waybel25,cc7_waybel25), []). fof(cc7_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) ) ) ) ) ), file(waybel_0,cc7_waybel_0), []). fof(cc7_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v9_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_yellow_0(A) ) ) ) ), file(waybel_1,cc7_waybel_1), []). fof(cc7_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v2_waybel_1(A) & v2_waybel_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ) ) ), file(waybel_2,cc7_waybel_2), []). fof(cc7_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v3_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc7_yellow_0), []). fof(cc8_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) ) ) ), file(waybel_0,cc8_waybel_0), []). fof(cc8_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v11_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ), file(waybel_1,cc8_waybel_1), []). fof(cc8_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) ), file(yellow_0,cc8_yellow_0), []). fof(cc9_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v1_lattice3(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc9_waybel_0), []). fof(cc9_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) ) ) ) ), file(waybel_1,cc9_waybel_1), []). fof(cc9_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) => v5_yellow_0(B,A) ) ) ) ), file(yellow_0,cc9_yellow_0), []). fof(d11_grcat_1,axiom,( ! [A] : ( l1_struct_0(A) => k7_grcat_1(A) = k6_partfun1(u1_struct_0(A)) ) ), file(grcat_1,d11_grcat_1), []). fof(d13_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( v6_waybel_1(B,A) <=> ( v11_quantal1(B) & v5_orders_3(B,A,A) ) ) ) ) ), file(waybel_1,d13_waybel_1), []). fof(d14_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( v7_waybel_1(B,A) <=> ( v6_waybel_1(B,A) & r1_yellow_2(u1_struct_0(A),A,k7_grcat_1(A),B) ) ) ) ) ), file(waybel_1,d14_waybel_1), []). fof(d18_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_0(A,B) = k5_waybel_0(A,k1_struct_0(A,B)) ) ) ), file(waybel_0,d18_waybel_0), []). fof(d2_funcop_1,axiom,( ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ), file(funcop_1,d2_funcop_1), []). fof(d4_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k2_waybel27(A,B) <=> ( v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B)) & ! [D] : ( r2_hidden(D,u1_struct_0(C)) <=> ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) ) ) ), file(waybel27,d4_waybel27), []). fof(d4_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_waybel_9(B) => ( m1_yellow_9(B,A) <=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ) ), file(yellow_9,d4_yellow_9), []). fof(d5_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v2_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v3_struct_0(D) & v2_orders_2(D) & v4_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) ) => ( v22_waybel_0(E,A,B) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) ) => ( v22_waybel_0(F,C,D) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) & m2_relset_1(G,u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) ) => ( G = k4_waybel27(A,B,C,D,E,F) <=> ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(B),u1_struct_0(C)) & v22_waybel_0(H,B,C) & m2_relset_1(H,u1_struct_0(B),u1_struct_0(C)) ) => k1_funct_1(G,H) = k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(D),E,k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),H,F)) ) ) ) ) ) ) ) ) ) ) ) ), file(waybel27,d5_waybel27), []). fof(d5_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)) ) ), file(yellow_1,d5_yellow_1), []). fof(d9_quantal1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v11_quantal1(A) <=> k5_relat_1(A,A) = A ) ) ), file(quantal1,d9_quantal1), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ), file(waybel_0,k1_waybel_0), []). fof(dt_k1_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) & m1_yellow_0(k1_waybel_8(A),A) ) ) ), file(waybel_8,k1_waybel_8), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k1_yellow_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). fof(dt_k2_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k2_waybel27(A,B)) & l1_orders_2(k2_waybel27(A,B)) ) ) ), file(waybel27,k2_waybel27), []). fof(dt_k2_yellow16,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_yellow16(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k2_yellow16(A,B,C)) & v2_orders_2(k2_yellow16(A,B,C)) & v3_orders_2(k2_yellow16(A,B,C)) & v4_orders_2(k2_yellow16(A,B,C)) & l1_orders_2(k2_yellow16(A,B,C)) ) ) ), file(yellow16,k2_yellow16), []). fof(dt_k2_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & l1_orders_2(k2_yellow_1(A)) ) ), file(yellow_1,k2_yellow_1), []). fof(dt_k2_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v1_orders_2(k2_yellow_2(A,B,C)) & v4_yellow_0(k2_yellow_2(A,B,C),B) & m1_yellow_0(k2_yellow_2(A,B,C),B) ) ) ), file(yellow_2,k2_yellow_2), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_waybel27,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(k2_waybel27(A,B))) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k3_waybel27(A,B,C,D),u1_struct_0(B)) ) ), file(waybel27,k3_waybel27), []). fof(dt_k3_yellow_1,axiom,( ! [A] : ( v1_orders_2(k3_yellow_1(A)) & l1_orders_2(k3_yellow_1(A)) ) ), file(yellow_1,k3_yellow_1), []). fof(dt_k4_waybel27,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & ~ v3_struct_0(C) & v2_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) & ~ v3_struct_0(D) & v2_orders_2(D) & v4_orders_2(D) & l1_orders_2(D) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(E,u1_struct_0(A),u1_struct_0(B)) & v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & m1_relset_1(F,u1_struct_0(C),u1_struct_0(D)) ) => ( v1_funct_1(k4_waybel27(A,B,C,D,E,F)) & v1_funct_2(k4_waybel27(A,B,C,D,E,F),u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) & m2_relset_1(k4_waybel27(A,B,C,D,E,F),u1_struct_0(k2_waybel27(B,C)),u1_struct_0(k2_waybel27(A,D))) ) ) ), file(waybel27,k4_waybel27), []). 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_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => m1_subset_1(k5_waybel11(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(waybel11,k5_waybel11), []). fof(dt_k5_waybel_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k5_waybel_0), []). fof(dt_k5_yellow_1,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & m1_pboole(B,A) ) => ( v1_orders_2(k5_yellow_1(A,B)) & l1_orders_2(k5_yellow_1(A,B)) ) ) ), file(yellow_1,k5_yellow_1), []). fof(dt_k6_partfun1,axiom,( ! [A] : ( v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A) ) ), file(partfun1,k6_partfun1), []). fof(dt_k6_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), []). fof(dt_k6_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k6_waybel_3(A,B,C)) & v2_orders_2(k6_waybel_3(A,B,C)) & l1_orders_2(k6_waybel_3(A,B,C)) ) ) ), file(waybel_3,k6_waybel_3), []). fof(dt_k6_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_orders_2(k6_yellow_1(A,B)) & l1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,k6_yellow_1), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_grcat_1,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(grcat_1,k7_grcat_1), []). fof(dt_k7_relset_1,axiom,( ! [A,B,C,D,E,F] : ( ( m1_relset_1(E,A,B) & m1_relset_1(F,C,D) ) => m2_relset_1(k7_relset_1(A,B,C,D,E,F),A,D) ) ), file(relset_1,k7_relset_1), []). fof(dt_k7_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k7_waybel_0), []). fof(dt_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => m1_subset_1(k7_yellow_2(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_2,k7_yellow_2), []). 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_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( l1_pre_topc(A) & l1_orders_2(A) ) ) ), file(waybel_9,l1_waybel_9), []). fof(dt_m1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_cantor_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(cantor_1,m1_cantor_1), []). 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_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) ), file(yellow_0,m1_yellow_0), []). fof(dt_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_9(B,A) => l1_waybel_9(B) ) ) ), file(yellow_9,m1_yellow_9), []). 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_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pre_topc,u1_pre_topc), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) ), file(waybel_9,l1_waybel_9), []). fof(existence_m1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_cantor_1(B,A) ) ), file(cantor_1,m1_cantor_1), []). 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_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) ), file(yellow_0,m1_yellow_0), []). fof(existence_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_9(B,A) ) ), file(yellow_9,m1_yellow_9), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). 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(fc10_waybel10,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v7_waybel_1(B,A) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_yellow_2(A,A,B)) & v1_orders_2(k2_yellow_2(A,A,B)) & v2_orders_2(k2_yellow_2(A,A,B)) & v3_orders_2(k2_yellow_2(A,A,B)) & v4_orders_2(k2_yellow_2(A,A,B)) & v4_yellow_0(k2_yellow_2(A,A,B),A) & v5_yellow_0(k2_yellow_2(A,A,B),A) & v7_yellow_0(k2_yellow_2(A,A,B),A) & v3_waybel_0(k2_yellow_2(A,A,B),A) ) ) ), file(waybel10,fc10_waybel10), []). fof(fc10_waybel18,axiom,( ! [A,B] : ( ( v2_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc10_waybel18), []). fof(fc10_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k7_waybel_0(A,B)) & v2_waybel_0(k7_waybel_0(A,B),A) ) ) ), file(waybel_0,fc10_waybel_0), []). fof(fc10_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc10_waybel_8), []). fof(fc10_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) ) ) ), file(yellow_1,fc10_yellow_1), []). fof(fc11_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc11_waybel18), []). fof(fc11_waybel24,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v1_monoid_0(k6_yellow_1(A,B)) ) ) ), file(waybel24,fc11_waybel24), []). fof(fc11_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc11_waybel_8), []). fof(fc11_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc11_yellow_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(fc12_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc12_waybel18), []). fof(fc12_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v13_waybel_0(k5_waybel_0(A,B),A) ) ), file(waybel_0,fc12_waybel_0), []). fof(fc12_waybel_8,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc12_waybel_8), []). fof(fc12_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v2_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc12_yellow_1), []). fof(fc13_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc13_waybel18), []). fof(fc13_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ), file(yellow_1,fc13_yellow_1), []). fof(fc13_yellow_3,axiom,( ! [A] : ( ( ~ v1_yellow_3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(u1_orders_2(A)) & v1_relat_1(u1_orders_2(A)) ) ) ), file(yellow_3,fc13_yellow_3), []). fof(fc14_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v2_waybel_8(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc14_waybel18), []). fof(fc14_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v13_waybel_0(k7_waybel_0(A,B),A) ) ), file(waybel_0,fc14_waybel_0), []). fof(fc14_waybel_8,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v9_waybel_1(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) & v11_waybel_1(k3_yellow_1(A)) & v2_waybel_3(k3_yellow_1(A)) & v3_waybel_3(k3_yellow_1(A)) & v1_waybel_8(k3_yellow_1(A)) & v2_waybel_8(k3_yellow_1(A)) ) ), file(waybel_8,fc14_waybel_8), []). fof(fc14_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k6_yellow_1(k1_xboole_0,A)) & v1_orders_2(k6_yellow_1(k1_xboole_0,A)) & v2_orders_2(k6_yellow_1(k1_xboole_0,A)) & v3_orders_2(k6_yellow_1(k1_xboole_0,A)) & v4_orders_2(k6_yellow_1(k1_xboole_0,A)) & v1_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v2_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v3_yellow_0(k6_yellow_1(k1_xboole_0,A)) & v1_lattice3(k6_yellow_1(k1_xboole_0,A)) & v2_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_lattice3(k6_yellow_1(k1_xboole_0,A)) & v3_realset2(k6_yellow_1(k1_xboole_0,A)) ) ) ), file(yellow_1,fc14_yellow_1), []). fof(fc15_waybel10,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v22_waybel_0(B,A,A) & v7_waybel_1(B,A) & m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_yellow_2(A,A,B)) & v1_orders_2(k2_yellow_2(A,A,B)) & v2_orders_2(k2_yellow_2(A,A,B)) & v3_orders_2(k2_yellow_2(A,A,B)) & v4_orders_2(k2_yellow_2(A,A,B)) & v2_lattice3(k2_yellow_2(A,A,B)) & v4_yellow_0(k2_yellow_2(A,A,B),A) & v5_yellow_0(k2_yellow_2(A,A,B),A) & v7_yellow_0(k2_yellow_2(A,A,B),A) & v3_waybel_0(k2_yellow_2(A,A,B),A) & v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) ), file(waybel10,fc15_waybel10), []). fof(fc15_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v3_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc15_yellow_1), []). fof(fc16_yellow_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc16_yellow_1), []). fof(fc17_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_waybel_0(k5_waybel_0(A,B),A) & v13_waybel_0(k5_waybel_0(A,B),A) ) ) ), file(waybel_0,fc17_waybel_0), []). fof(fc17_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v2_lattice3(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc17_yellow_1), []). fof(fc18_yellow_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_orders_2(k6_yellow_1(A,B)) & v1_lattice3(k6_yellow_1(A,B)) ) ) ), file(yellow_1,fc18_yellow_1), []). fof(fc1_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc1_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_waybel10,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v4_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(waybel10,fc1_waybel10), []). fof(fc1_waybel17,axiom,( ! [A,B] : ( ( v2_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) ) ) ), file(waybel17,fc1_waybel17), []). fof(fc1_waybel_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) ) ), file(waybel_1,fc1_waybel_1), []). fof(fc1_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k1_waybel_8(A)) & v1_orders_2(k1_waybel_8(A)) & v2_orders_2(k1_waybel_8(A)) & v4_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) ) ) ), file(waybel_8,fc1_waybel_8), []). fof(fc1_yellow16,axiom,( ! [A,B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow16(k2_funcop_1(A,B)) ) ) ), file(yellow16,fc1_yellow16), []). fof(fc1_yellow_0,axiom,( ! [A,B] : ( m1_relset_1(B,k1_tarski(A),k1_tarski(A)) => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ), file(yellow_0,fc1_yellow_0), []). fof(fc2_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_1), []). fof(fc2_funct_1,axiom,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) ) ), file(funct_1,fc2_funct_1), []). fof(fc2_partfun1,axiom,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) & v1_relat_2(k6_relat_1(A)) & v3_relat_2(k6_relat_1(A)) & v4_relat_2(k6_relat_1(A)) & v8_relat_2(k6_relat_1(A)) ) ), file(partfun1,fc2_partfun1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_waybel14,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A))) & v1_orders_2(k2_yellow_1(u1_pre_topc(A))) & v2_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_orders_2(k2_yellow_1(u1_pre_topc(A))) & v4_orders_2(k2_yellow_1(u1_pre_topc(A))) & v1_lattice3(k2_yellow_1(u1_pre_topc(A))) & v2_lattice3(k2_yellow_1(u1_pre_topc(A))) & v3_lattice3(k2_yellow_1(u1_pre_topc(A))) & v1_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v2_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v3_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v24_waybel_0(k2_yellow_1(u1_pre_topc(A))) & v25_waybel_0(k2_yellow_1(u1_pre_topc(A))) & v2_waybel_1(k2_yellow_1(u1_pre_topc(A))) & ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) ), file(waybel14,fc2_waybel14), []). fof(fc2_waybel17,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( v1_orders_2(k6_yellow_1(A,B)) & v3_lattice3(k6_yellow_1(A,B)) ) ) ), file(waybel17,fc2_waybel17), []). fof(fc2_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v23_waybel_0(k7_grcat_1(A),A,A) ) ) ), file(waybel_1,fc2_waybel_1), []). fof(fc2_yellow16,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_yellow16(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v2_orders_2(k5_yellow_1(A,B)) & v3_orders_2(k5_yellow_1(A,B)) & v4_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(yellow16,fc2_yellow16), []). fof(fc2_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( ~ v3_struct_0(k2_yellow_2(A,B,C)) & v1_orders_2(k2_yellow_2(A,B,C)) & v4_yellow_0(k2_yellow_2(A,B,C),B) ) ) ), file(yellow_2,fc2_yellow_2), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_waybel10,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(waybel10,fc3_waybel10), []). fof(fc3_waybel14,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ~ v1_xboole_0(k5_waybel11(A)) ) ), file(waybel14,fc3_waybel14), []). fof(fc3_waybel27,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => v1_fraenkel(u1_struct_0(A)) ) ), file(waybel27,fc3_waybel27), []). fof(fc3_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & ~ v1_xboole_0(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v5_orders_3(k7_grcat_1(A),A,A) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) ) ) ), file(waybel_1,fc3_waybel_1), []). fof(fc3_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_waybel_8(A)) & v2_orders_2(k1_waybel_8(A)) & v3_orders_2(k1_waybel_8(A)) & v4_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) & v6_yellow_0(k1_waybel_8(A),A) ) ) ), file(waybel_8,fc3_waybel_8), []). 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(fc4_waybel10,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & ~ v1_xboole_0(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(k7_grcat_1(A)) & v5_orders_3(k7_grcat_1(A),A,A) & v17_waybel_0(k7_grcat_1(A),A,A) & v18_waybel_0(k7_grcat_1(A),A,A) & v19_waybel_0(k7_grcat_1(A),A,A) & v20_waybel_0(k7_grcat_1(A),A,A) & v21_waybel_0(k7_grcat_1(A),A,A) & v22_waybel_0(k7_grcat_1(A),A,A) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) & v8_waybel_1(k7_grcat_1(A),A) ) ) ), file(waybel10,fc4_waybel10), []). fof(fc4_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v1_monoid_0(k6_yellow_1(A,B)) ) ) ), file(waybel27,fc4_waybel27), []). fof(fc4_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & ~ v1_xboole_0(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v5_orders_3(k7_grcat_1(A),A,A) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) ) ) ), file(waybel_1,fc4_waybel_1), []). fof(fc4_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc4_waybel_8), []). fof(fc5_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k2_waybel27(A,B)) & v1_orders_2(k2_waybel27(A,B)) & v2_orders_2(k2_waybel27(A,B)) & v4_orders_2(k2_waybel27(A,B)) & ~ v1_yellow_3(k2_waybel27(A,B)) & v1_monoid_0(k2_waybel27(A,B)) ) ) ), file(waybel27,fc5_waybel27), []). fof(fc5_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v1_relat_1(k7_grcat_1(A)) & v1_funct_1(k7_grcat_1(A)) & v2_funct_1(k7_grcat_1(A)) & ~ v1_xboole_0(k7_grcat_1(A)) & v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) & v5_orders_3(k7_grcat_1(A),A,A) & v23_waybel_0(k7_grcat_1(A),A,A) & v6_waybel_1(k7_grcat_1(A),A) & v7_waybel_1(k7_grcat_1(A),A) & v8_waybel_1(k7_grcat_1(A),A) ) ) ), file(waybel_1,fc5_waybel_1), []). fof(fc5_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc5_waybel_8), []). fof(fc5_yellow16,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) ) => ( ~ v3_struct_0(k6_yellow_1(B,A)) & v1_orders_2(k6_yellow_1(B,A)) & v2_orders_2(k6_yellow_1(B,A)) & v3_orders_2(k6_yellow_1(B,A)) & v4_orders_2(k6_yellow_1(B,A)) & v24_waybel_0(k6_yellow_1(B,A)) ) ) ), file(yellow16,fc5_yellow16), []). fof(fc5_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) ) ), file(yellow_1,fc5_yellow_1), []). fof(fc6_waybel27,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k2_waybel27(A,B)) & v1_orders_2(k2_waybel27(A,B)) & v2_orders_2(k2_waybel27(A,B)) & v3_orders_2(k2_waybel27(A,B)) & v4_orders_2(k2_waybel27(A,B)) & ~ v1_yellow_3(k2_waybel27(A,B)) & v1_monoid_0(k2_waybel27(A,B)) ) ) ), file(waybel27,fc6_waybel27), []). fof(fc6_waybel_8,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc6_waybel_8), []). fof(fc6_yellow16,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(u1_pre_topc(A)) ) ), file(yellow16,fc6_yellow16), []). fof(fc6_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v3_struct_0(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) ) ) ), file(yellow_1,fc6_yellow_1), []). fof(fc6_yellow_3,axiom,( ! [A,B] : ( ( l1_orders_2(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_xboole_0(k5_waybel_0(A,B)) ) ), file(yellow_3,fc6_yellow_3), []). 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_waybel27,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k2_waybel27(A,B)) & v1_orders_2(k2_waybel27(A,B)) & v2_orders_2(k2_waybel27(A,B)) & v3_orders_2(k2_waybel27(A,B)) & v4_orders_2(k2_waybel27(A,B)) & v1_yellow_0(k2_waybel27(A,B)) & v2_yellow_0(k2_waybel27(A,B)) & v3_yellow_0(k2_waybel27(A,B)) & v24_waybel_0(k2_waybel27(A,B)) & v25_waybel_0(k2_waybel27(A,B)) & ~ v1_yellow_3(k2_waybel27(A,B)) & v1_lattice3(k2_waybel27(A,B)) & v2_lattice3(k2_waybel27(A,B)) & v3_lattice3(k2_waybel27(A,B)) & v1_monoid_0(k2_waybel27(A,B)) ) ) ), file(waybel27,fc7_waybel27), []). fof(fc7_waybel_8,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc7_waybel_8), []). fof(fc7_yellow_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) ) ), file(yellow_1,fc7_yellow_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_waybel18,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v4_waybel_3(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc8_waybel18), []). fof(fc8_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k5_waybel_0(A,B)) ) ), file(waybel_0,fc8_waybel_0), []). fof(fc8_waybel_8,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc8_waybel_8), []). fof(fc8_yellow_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(yellow_1,fc8_yellow_1), []). fof(fc9_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_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(fc9_waybel18,axiom,( ! [A,B] : ( l1_pre_topc(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_waybel18(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc9_waybel18), []). fof(fc9_waybel_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) ) ), file(waybel_1,fc9_waybel_1), []). fof(fc9_waybel_8,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc9_waybel_8), []). fof(fc9_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A))) & v1_orders_2(k2_yellow_1(u1_pre_topc(A))) & v2_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_orders_2(k2_yellow_1(u1_pre_topc(A))) & v4_orders_2(k2_yellow_1(u1_pre_topc(A))) & v1_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v2_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v3_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v1_lattice3(k2_yellow_1(u1_pre_topc(A))) & v2_lattice3(k2_yellow_1(u1_pre_topc(A))) & v3_lattice3(k2_yellow_1(u1_pre_topc(A))) & ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) ), file(yellow_1,fc9_yellow_1), []). fof(fraenkel_a_1_0_waybel14,axiom,( ! [A,B] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v4_waybel11(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_0_waybel14(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k7_waybel_0(B,C) & r2_hidden(C,u1_struct_0(k1_waybel_8(B))) ) ) ) ), file(waybel14,a_1_0_waybel14), []). fof(fraenkel_a_2_0_waybel27,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_waybel_8(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & v4_waybel11(C) & m1_yellow_9(C,B) ) => ( r2_hidden(A,a_2_0_waybel27(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k7_waybel_0(C,D) & r2_hidden(D,u1_struct_0(k1_waybel_8(C))) ) ) ) ), file(waybel27,a_2_0_waybel27), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(rc10_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc10_waybel_0), []). fof(rc12_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) ) ), file(waybel_0,rc12_waybel_0), []). fof(rc13_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ), file(waybel_0,rc13_waybel_0), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_funct_2,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ), file(funct_2,rc1_funct_2), []). fof(rc1_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ), file(lattice3,rc1_lattice3), []). fof(rc1_monoid_0,axiom,( ? [A] : ( l1_struct_0(A) & v1_monoid_0(A) ) ), file(monoid_0,rc1_monoid_0), []). 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_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(rc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) ) ) ), file(tops_1,rc1_tops_1), []). fof(rc1_waybel10,axiom,( ! [A,B] : ( ( l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) ), file(waybel10,rc1_waybel10), []). fof(rc1_waybel18,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_waybel18(B) ) ), file(waybel18,rc1_waybel18), []). fof(rc1_waybel27,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel27(A) & v2_waybel27(A) & v3_waybel27(A) ) ), file(waybel27,rc1_waybel27), []). fof(rc1_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) ) ) ), file(waybel_1,rc1_waybel_1), []). fof(rc1_waybel_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v3_realset2(A) ) ), file(waybel_2,rc1_waybel_2), []). fof(rc1_waybel_8,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v2_waybel_3(A) & v3_waybel_3(A) & v3_realset2(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) ) ), file(waybel_8,rc1_waybel_8), []). fof(rc1_yellow16,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v22_waybel_0(C,A,B) ) ) ), file(yellow16,rc1_yellow16), []). fof(rc1_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) ), file(yellow_0,rc1_yellow_0), []). fof(rc1_yellow_1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_yellow_1(B) ) ), file(yellow_1,rc1_yellow_1), []). fof(rc1_yellow_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v1_yellow_3(A) ) ), file(yellow_3,rc1_yellow_3), []). 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_funct_2,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,A) & v2_funct_2(B,A,A) & v3_funct_2(B,A,A) ) ), file(funct_2,rc2_funct_2), []). fof(rc2_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ), file(lattice3,rc2_lattice3), []). 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_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(rc2_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc2_tops_1), []). fof(rc2_waybel10,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(B) & v5_orders_3(B,A,A) & v17_waybel_0(B,A,A) & v18_waybel_0(B,A,A) & v19_waybel_0(B,A,A) & v20_waybel_0(B,A,A) & v21_waybel_0(B,A,A) & v22_waybel_0(B,A,A) & v6_waybel_1(B,A) & v7_waybel_1(B,A) & v8_waybel_1(B,A) ) ) ), file(waybel10,rc2_waybel10), []). fof(rc2_waybel18,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v4_waybel_3(B) & v2_pralg_1(B) & v1_waybel18(B) ) ), file(waybel18,rc2_waybel18), []). fof(rc2_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & v7_waybel_1(B,A) ) ) ), file(waybel_1,rc2_waybel_1), []). fof(rc2_waybel_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v3_realset2(A) & v1_waybel_2(A) & v2_waybel_2(A) ) ), file(waybel_2,rc2_waybel_2), []). fof(rc2_yellow16,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(B) ) ) ), file(yellow16,rc2_yellow16), []). fof(rc2_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ), file(yellow_0,rc2_yellow_0), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_partfun1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,A,A) & v1_relat_1(B) & v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A,A) ) ), file(partfun1,rc3_partfun1), []). 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(rc3_tops_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ), file(tops_1,rc3_tops_1), []). fof(rc3_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) & v8_waybel_1(B,A) ) ) ), file(waybel_1,rc3_waybel_1), []). fof(rc3_yellow16,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & v2_pralg_1(B) & v1_yellow16(B) ) ), file(yellow16,rc3_yellow16), []). fof(rc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc3_yellow_0), []). fof(rc3_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) & v19_waybel_0(C,A,B) & v21_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ), file(yellow_9,rc3_yellow_9), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) ) ) ), file(tops_1,rc4_tops_1), []). fof(rc4_waybel27,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_monoid_0(A) ) ), file(waybel27,rc4_waybel27), []). fof(rc4_waybel_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) ) ), file(waybel_1,rc4_waybel_1), []). fof(rc4_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v3_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) ), file(yellow_0,rc4_yellow_0), []). fof(rc4_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v1_relat_1(C) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) & v20_waybel_0(C,A,B) & v22_waybel_0(C,A,B) & v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ), file(yellow_9,rc4_yellow_9), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) & v2_tops_1(B,A) & v3_tops_1(B,A) ) ) ), file(tops_1,rc5_tops_1), []). fof(rc5_waybel27,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) & v1_monoid_0(A) ) ), file(waybel27,rc5_waybel27), []). fof(rc5_waybel_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v2_waybel_1(A) & v9_waybel_1(A) ) ), file(waybel_1,rc5_waybel_1), []). fof(redefinition_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). fof(redefinition_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_0,k1_waybel_0), []). fof(redefinition_k2_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). fof(redefinition_k2_yellow16,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v4_waybel_3(B) & v1_yellow16(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k2_yellow16(A,B,C) = k1_funct_1(B,C) ) ), file(yellow16,k2_yellow16), []). fof(redefinition_k3_waybel27,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(k2_waybel27(A,B))) & m1_subset_1(D,u1_struct_0(A)) ) => k3_waybel27(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel27,k3_waybel27), []). fof(redefinition_k6_partfun1,axiom,( ! [A] : k6_partfun1(A) = k6_relat_1(A) ), file(partfun1,k6_partfun1), []). fof(redefinition_k6_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k6_waybel_3(A,B,C) = k1_funct_1(B,C) ) ), file(waybel_3,k6_waybel_3), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), []). fof(redefinition_k7_relset_1,axiom,( ! [A,B,C,D,E,F] : ( ( m1_relset_1(E,A,B) & m1_relset_1(F,C,D) ) => k7_relset_1(A,B,C,D,E,F) = k5_relat_1(E,F) ) ), file(relset_1,k7_relset_1), []). fof(redefinition_k7_yellow_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) & m1_subset_1(D,A) ) => k7_yellow_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_2,k7_yellow_2), []). 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_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_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(reflexivity_r5_waybel_1,axiom,( ! [A,B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => r5_waybel_1(A,A) ) ), file(waybel_1,r5_waybel_1), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(t10_yellow_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => ( r1_yellow_2(u1_struct_0(A),B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_orders_2(B,k1_waybel_0(A,B,C,E),k1_waybel_0(A,B,D,E)) ) ) ) ) ) ) ), file(yellow_2,t10_yellow_2), []). fof(t11_grcat_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_funct_2(u1_struct_0(A),u1_struct_0(A),k7_grcat_1(A),B) = B ) ) ), file(grcat_1,t11_grcat_1), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t18_waybel20,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v3_lattice3(A) ) => v3_lattice3(B) ) ) ) ), file(waybel20,t18_waybel20), []). fof(t18_waybel27,axiom,( ! [A] : r5_waybel_1(k3_yellow_1(A),k6_yellow_1(A,k3_yellow_1(1))) ), file(waybel27,t18_waybel27), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t21_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | k1_funct_1(k5_relat_1(D,E),C) = k1_funct_1(E,k1_funct_1(D,C)) ) ) ) ) ), file(funct_2,t21_funct_2), []). fof(t23_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( k7_relset_1(A,A,A,B,k6_partfun1(A),C) = C & k7_relset_1(A,B,B,B,C,k6_partfun1(B)) = C ) ) ), file(funct_2,t23_funct_2), []). fof(t23_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_waybel27(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_waybel27(A,B))) => ( r3_orders_2(k2_waybel27(A,B),C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r3_orders_2(B,k3_waybel27(A,B,C,E),k3_waybel27(A,B,D,E)) ) ) ) ) ) ) ), file(waybel27,t23_waybel27), []). fof(t25_waybel13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) ) => ( ! [C] : ( m1_subset_1(C,A) => ( v2_orders_2(k6_waybel_3(A,B,C)) & v3_orders_2(k6_waybel_3(A,B,C)) & v4_orders_2(k6_waybel_3(A,B,C)) & v1_lattice3(k6_waybel_3(A,B,C)) & v2_lattice3(k6_waybel_3(A,B,C)) & v1_yellow_0(k6_waybel_3(A,B,C)) & v2_waybel_8(k6_waybel_3(A,B,C)) & l1_orders_2(k6_waybel_3(A,B,C)) ) ) => ( v2_orders_2(k5_yellow_1(A,B)) & v3_orders_2(k5_yellow_1(A,B)) & v4_orders_2(k5_yellow_1(A,B)) & v1_lattice3(k5_yellow_1(A,B)) & v2_lattice3(k5_yellow_1(A,B)) & v1_yellow_0(k5_yellow_1(A,B)) & v2_waybel_8(k5_yellow_1(A,B)) & l1_orders_2(k5_yellow_1(A,B)) ) ) ) ) ), file(waybel13,t25_waybel13), []). fof(t26_waybel13,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => r5_waybel_1(A,B) ) ) ) ), file(waybel13,t26_waybel13), []). fof(t26_waybel_8,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v2_waybel_8(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v7_waybel_1(B,A) & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) => ( v22_waybel_0(B,A,A) => ( v2_orders_2(k2_yellow_2(A,A,B)) & v3_orders_2(k2_yellow_2(A,A,B)) & v4_orders_2(k2_yellow_2(A,A,B)) & v1_lattice3(k2_yellow_2(A,A,B)) & v2_lattice3(k2_yellow_2(A,A,B)) & v2_waybel_8(k2_yellow_2(A,A,B)) & l1_orders_2(k2_yellow_2(A,A,B)) ) ) ) ) ), file(waybel_8,t26_waybel_8), []). fof(t28_waybel27,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v3_struct_0(D) & v2_orders_2(D) & v3_orders_2(D) & v4_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( ~ v3_struct_0(E) & v2_orders_2(E) & v3_orders_2(E) & v4_orders_2(E) & l1_orders_2(E) ) => ! [F] : ( ( ~ v3_struct_0(F) & v2_orders_2(F) & v3_orders_2(F) & v4_orders_2(F) & l1_orders_2(F) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(B),u1_struct_0(C)) & v22_waybel_0(G,B,C) & m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(H,A,B) & m2_relset_1(H,u1_struct_0(A),u1_struct_0(B)) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,u1_struct_0(D),u1_struct_0(E)) & v22_waybel_0(I,D,E) & m2_relset_1(I,u1_struct_0(D),u1_struct_0(E)) ) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,u1_struct_0(E),u1_struct_0(F)) & v22_waybel_0(J,E,F) & m2_relset_1(J,u1_struct_0(E),u1_struct_0(F)) ) => k7_funct_2(u1_struct_0(k2_waybel27(C,D)),u1_struct_0(k2_waybel27(B,E)),u1_struct_0(k2_waybel27(A,F)),k4_waybel27(B,C,D,E,G,I),k4_waybel27(A,B,E,F,H,J)) = k4_waybel27(A,C,D,F,k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),H,G),k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),I,J)) ) ) ) ) ) ) ) ) ) ) ), file(waybel27,t28_waybel27), []). 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(t30_waybel27,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( v2_orders_2(D) & v3_orders_2(D) & v4_orders_2(D) & v1_lattice3(D) & v2_lattice3(D) & v3_lattice3(D) & l1_orders_2(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B)) & v22_waybel_0(E,A,B) & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D)) & v22_waybel_0(F,C,D) & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) ) => v22_waybel_0(k4_waybel27(A,B,C,D,E,F),k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ) ), file(waybel27,t30_waybel27), []). fof(t32_waybel13,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v1_yellow_0(A) & v2_waybel_8(A) ) => v2_waybel_8(B) ) ) ) ), file(waybel13,t32_waybel13), []). fof(t32_yellow_2,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v4_yellow_0(B,A) & v7_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) ) ) ), file(yellow_2,t32_yellow_2), []). fof(t34_waybel27,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => r5_waybel_1(k2_waybel27(A,k3_yellow_1(1)),k2_yellow_1(k5_waybel11(A))) ) ), file(waybel27,t34_waybel27), []). fof(t35_waybel13,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( ~ ( v2_waybel_8(A) & ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) & v7_waybel_1(C,k3_yellow_1(B)) & m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) ) => ~ ( v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B)) & r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) ) ) ) ) & ( ? [B,C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) & v7_waybel_1(C,k3_yellow_1(B)) & m2_relset_1(C,u1_struct_0(k3_yellow_1(B)),u1_struct_0(k3_yellow_1(B))) & v22_waybel_0(C,k3_yellow_1(B),k3_yellow_1(B)) & r5_waybel_1(A,k2_yellow_2(k3_yellow_1(B),k3_yellow_1(B),C)) ) => v2_waybel_8(A) ) ) ) ), file(waybel13,t35_waybel13), []). fof(t36_waybel27,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( v2_orders_2(D) & v3_orders_2(D) & v4_orders_2(D) & v1_lattice3(D) & v2_lattice3(D) & v3_lattice3(D) & l1_orders_2(D) ) => ( ( r5_waybel_1(A,B) & r5_waybel_1(C,D) ) => r5_waybel_1(k2_waybel27(B,C),k2_waybel27(A,D)) ) ) ) ) ) ), file(waybel27,t36_waybel27), []). fof(t37_waybel27,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v22_waybel_0(C,B,B) & v6_waybel_1(C,B) & m2_relset_1(C,u1_struct_0(B),u1_struct_0(B)) ) => k2_yellow_2(k2_waybel27(A,B),k2_waybel27(A,B),k4_waybel27(A,A,B,B,k7_grcat_1(A),C)) = k2_waybel27(A,k2_yellow_2(B,B,C)) ) ) ) ), file(waybel27,t37_waybel27), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t42_waybel14,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ~ ( v2_waybel_8(A) & ! [B] : ( m1_cantor_1(B,A) => B != a_1_0_waybel14(A) ) ) ) ), file(waybel14,t42_waybel14), []). fof(t42_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v3_struct_0(C) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & l1_orders_2(C) ) => r5_waybel_1(k2_waybel27(B,k6_yellow_1(A,C)),k6_yellow_1(A,k2_waybel27(B,C))) ) ) ) ), file(waybel27,t42_waybel27), []). fof(t43_waybel14,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ( ? [B] : ( m1_cantor_1(B,A) & B = a_1_0_waybel14(A) ) => ( v2_waybel_8(k2_yellow_1(k5_waybel11(A))) & ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(k5_waybel11(A)))) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A))))) & B = k1_yellow_0(k2_yellow_1(k5_waybel11(A)),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k2_yellow_1(k5_waybel11(A)))) => ( r2_hidden(D,C) => v6_waybel_6(D,k2_yellow_1(k5_waybel11(A))) ) ) ) ) ) ) ) ), file(waybel14,t43_waybel14), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => u1_pre_topc(B) = k5_waybel11(A) ) ) ), file(yellow_9,t51_yellow_9), []). fof(t52_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => k5_waybel11(A) = k5_waybel11(B) ) ) ) ), file(yellow_9,t52_yellow_9), []). 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(t7_waybel_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ( r5_waybel_1(A,B) => r5_waybel_1(B,A) ) ) ) ), file(waybel_1,t7_waybel_1), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( l1_orders_2(C) => ( ( r5_waybel_1(A,B) & r5_waybel_1(B,C) ) => r5_waybel_1(A,C) ) ) ) ) ), file(waybel_1,t8_waybel_1), []).