% Mizar problem: t17_waybel27,waybel27,921,42 fof(t17_waybel27,conjecture,( ! [A] : ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k6_yellow_1(A,k3_yellow_1(1)))) & m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k6_yellow_1(A,k3_yellow_1(1)))) & v23_waybel_0(B,k3_yellow_1(A),k6_yellow_1(A,k3_yellow_1(1))) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_funct_1(B,C) = k5_funct_3(C,A) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc10_waybel_0,cc10_waybel_1,cc11_waybel_0,cc12_waybel_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_waybel27,cc1_waybel_2,cc1_waybel_8,cc1_yellow16,cc1_yellow_0,cc1_yellow_1,cc1_yellow_2,cc1_yellow_3,cc2_funct_1,cc2_funct_2,cc2_lattice3,cc2_waybel27,cc2_waybel_2,cc2_waybel_8,cc2_yellow_0,cc2_yellow_3,cc3_funct_2,cc3_waybel_2,cc3_waybel_8,cc3_yellow_0,cc3_yellow_3,cc4_funct_2,cc4_waybel_2,cc4_waybel_8,cc4_yellow_0,cc5_funct_2,cc5_waybel_0,cc5_waybel_1,cc5_waybel_2,cc5_yellow_0,cc6_funct_2,cc6_waybel_1,cc6_waybel_2,cc7_waybel_1,cc7_waybel_2,cc8_waybel_0,cc8_waybel_1,cc9_waybel_0,cc9_waybel_1,commutativity_k2_tarski,d1_tarski,d1_yellow_1,d2_funcop_1,d3_funct_3,d5_yellow_1,dt_g1_orders_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_waybel_0,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_yellow_1,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_tarski,dt_k2_yellow_1,dt_k2_zfmisc_1,dt_k3_yellow_1,dt_k4_funct_3,dt_k5_funct_3,dt_k5_yellow_1,dt_k6_partfun1,dt_k6_relat_1,dt_k6_yellow_1,dt_k7_yellow_2,dt_l1_orders_2,dt_l1_struct_0,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,existence_l1_orders_2,existence_l1_struct_0,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc10_waybel18,fc10_waybel_8,fc10_yellow_1,fc11_waybel18,fc11_waybel24,fc11_waybel_8,fc11_yellow_1,fc12_relat_1,fc12_waybel18,fc12_waybel_8,fc12_yellow_1,fc13_waybel18,fc13_yellow_1,fc13_yellow_3,fc14_waybel18,fc14_waybel_8,fc14_yellow_1,fc15_yellow_1,fc16_yellow_1,fc17_yellow_1,fc18_yellow_1,fc1_funcop_1,fc1_struct_0,fc1_subset_1,fc1_waybel10,fc1_waybel17,fc1_waybel_1,fc1_yellow16,fc1_yellow_0,fc2_funcop_1,fc2_funct_1,fc2_partfun1,fc2_subset_1,fc2_waybel17,fc2_yellow16,fc3_funcop_1,fc3_subset_1,fc3_waybel27,fc4_relat_1,fc4_subset_1,fc4_waybel27,fc4_waybel_8,fc5_relat_1,fc5_waybel_8,fc5_yellow16,fc5_yellow_1,fc6_funct_1,fc6_relat_1,fc6_waybel_8,fc6_yellow_1,fc7_funcop_1,fc7_relat_1,fc7_waybel_8,fc7_yellow_1,fc8_relat_1,fc8_waybel18,fc8_waybel_8,fc8_yellow_1,fc9_funcop_1,fc9_waybel_1,fc9_waybel_8,free_g1_orders_2,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_waybel10,rc1_waybel27,rc1_waybel_2,rc1_waybel_8,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_waybel_2,rc2_yellow_0,rc3_funct_1,rc3_partfun1,rc3_relat_1,rc3_struct_0,rc3_yellow16,rc4_funct_1,rc4_waybel27,rc4_waybel_1,rc5_funct_1,rc5_struct_0,rc5_waybel27,rc5_waybel_1,redefinition_k1_waybel_0,redefinition_k1_yellow_1,redefinition_k2_pre_circ,redefinition_k5_funct_3,redefinition_k6_partfun1,redefinition_k7_yellow_2,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,spc0_boole,spc1_boole,t15_waybel18,t1_subset,t1_zfmisc_1,t27_yellow_1,t2_subset,t35_funct_1,t3_subset,t3_xboole_1,t4_subset,t4_yellow_1,t5_subset,t64_relat_1,t66_waybel_0,t6_boole,t71_relat_1,t7_boole,t8_boole]), [file(waybel27,t17_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_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(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(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_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_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(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_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(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_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(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_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(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_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(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_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(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(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(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(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_yellow_1,axiom,( ! [A] : k2_yellow_1(A) = g1_orders_2(A,k1_yellow_1(A)) ), file(yellow_1,d1_yellow_1), []). 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(d3_funct_3,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k4_funct_3(A,B) <=> ( k1_relat_1(C) = B & ! [D] : ( r2_hidden(D,B) => ( ( r2_hidden(D,A) => k1_funct_1(C,D) = 1 ) & ( ~ r2_hidden(D,A) => k1_funct_1(C,D) = 0 ) ) ) ) ) ) ), file(funct_3,d3_funct_3), []). 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(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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). 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_wellord2,axiom,( ! [A] : v1_relat_1(k1_wellord2(A)) ), file(wellord2,k1_wellord2), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_1,axiom,( ! [A] : ( v1_relat_2(k1_yellow_1(A)) & v4_relat_2(k1_yellow_1(A)) & v8_relat_2(k1_yellow_1(A)) & v1_partfun1(k1_yellow_1(A),A,A) & m2_relset_1(k1_yellow_1(A),A,A) ) ), file(yellow_1,k1_yellow_1), []). 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_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). 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_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). 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_funct_3,axiom,( ! [A,B] : ( v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)) ) ), file(funct_3,k4_funct_3), []). fof(dt_k5_funct_3,axiom,( ! [A,B] : ( v1_funct_1(k5_funct_3(A,B)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(0,1)) & m2_relset_1(k5_funct_3(A,B),B,k2_tarski(0,1)) ) ), file(funct_3,k5_funct_3), []). 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_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_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_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m2_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_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_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). 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_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_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_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_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_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_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_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_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_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(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_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_waybel27,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => v1_fraenkel(u1_struct_0(A)) ) ), file(waybel27,fc3_waybel27), []). 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_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_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_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(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_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc6_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). fof(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_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(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(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_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), []). fof(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_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_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(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(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_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_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_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_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_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_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_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(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_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(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_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_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_k1_yellow_1,axiom,( ! [A] : k1_yellow_1(A) = k1_wellord2(A) ), file(yellow_1,k1_yellow_1), []). 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_k5_funct_3,axiom,( ! [A,B] : k5_funct_3(A,B) = k4_funct_3(A,B) ), file(funct_3,k5_funct_3), []). fof(redefinition_k6_partfun1,axiom,( ! [A] : k6_partfun1(A) = k6_relat_1(A) ), file(partfun1,k6_partfun1), []). 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_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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(t15_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1))))) & m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1))))) & v23_waybel_0(B,k3_yellow_1(A),k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1)))) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_funct_1(B,C) = k5_funct_3(C,A) ) ) ) ), file(waybel18,t15_waybel18), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_zfmisc_1,axiom,( k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) ), file(zfmisc_1,t1_zfmisc_1), []). fof(t27_yellow_1,axiom,( ! [A] : ( l1_orders_2(A) => k6_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) ), file(yellow_1,t27_yellow_1), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t35_funct_1,axiom,( ! [A,B] : ( r2_hidden(B,A) => k1_funct_1(k6_relat_1(A),B) = B ) ), file(funct_1,t35_funct_1), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_xboole_1,axiom,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) ), file(xboole_1,t3_xboole_1), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t4_yellow_1,axiom,( ! [A] : k3_yellow_1(A) = k2_yellow_1(k1_zfmisc_1(A)) ), file(yellow_1,t4_yellow_1), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t64_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ( k1_relat_1(A) = k1_xboole_0 | k2_relat_1(A) = k1_xboole_0 ) => A = k1_xboole_0 ) ) ), file(relat_1,t64_relat_1), []). fof(t66_waybel_0,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)) ) => ( v23_waybel_0(C,A,B) <=> ( v2_funct_1(C) & k2_relat_1(C) = u1_struct_0(B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_orders_2(A,D,E) <=> r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) ) ), file(waybel_0,t66_waybel_0), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t71_relat_1,axiom,( ! [A] : ( k1_relat_1(k6_relat_1(A)) = A & k2_relat_1(k6_relat_1(A)) = A ) ), file(relat_1,t71_relat_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).