% Mizar problem: t47_waybel21,waybel21,1784,47 fof(t47_waybel21,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( m1_waybel21(C,A,B) => ( v5_pre_topc(C,A,B) <=> v1_waybel21(C,A,B) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v6_waybel_0,antisymmetry_r2_hidden,cc10_waybel_0,cc11_waybel_0,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc1_finset_1,cc1_lattice3,cc1_relat_1,cc1_relset_1,cc1_waybel17,cc1_waybel19,cc1_waybel21,cc1_waybel_2,cc1_yellow_0,cc2_finset_1,cc2_lattice3,cc2_waybel19,cc2_waybel21,cc2_waybel_2,cc2_yellow_0,cc3_waybel_0,cc3_waybel_2,cc3_yellow_0,cc4_waybel_0,cc4_waybel_2,cc4_yellow_0,cc5_waybel19,cc5_waybel_0,cc5_waybel_2,cc5_yellow_0,cc6_waybel_0,cc6_waybel_2,cc7_waybel_2,cc9_waybel_0,commutativity_k2_tarski,d10_xboole_0,d1_funct_2,d1_waybel21,d30_waybel_0,d31_waybel_0,d32_waybel_0,d37_waybel_0,d3_tarski,d4_waybel21,d5_tarski,d6_waybel11,d8_waybel_0,d8_waybel_9,d9_orders_2,dt_g1_orders_2,dt_g1_waybel_0,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_waybel11,dt_k1_waybel_0,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k2_yellow_0,dt_k2_zfmisc_1,dt_k3_waybel_0,dt_k3_yellow_6,dt_k3_yellow_9,dt_k4_pre_topc,dt_k4_relset_1,dt_k4_tarski,dt_k4_waybel17,dt_k5_relat_1,dt_k7_funct_2,dt_k7_waybel_9,dt_k9_relat_1,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_0,dt_l1_waybel_9,dt_m1_relset_1,dt_m1_subset_1,dt_m1_waybel21,dt_m2_relset_1,dt_u1_orders_2,dt_u1_struct_0,dt_u1_waybel_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_0,existence_l1_waybel_9,existence_m1_relset_1,existence_m1_subset_1,existence_m1_waybel21,existence_m2_relset_1,fc10_relat_1,fc12_relat_1,fc13_finset_1,fc14_finset_1,fc15_yellow_6,fc1_finset_1,fc1_struct_0,fc1_subset_1,fc1_waybel_2,fc1_yellow_0,fc27_waybel_9,fc28_waybel_9,fc29_waybel_9,fc2_finset_1,fc2_subset_1,fc2_waybel21,fc30_waybel_9,fc31_waybel_9,fc3_subset_1,fc3_waybel21,fc3_yellow_9,fc4_relat_1,fc4_subset_1,fc5_relat_1,fc5_waybel17,fc5_yellow_9,fc6_waybel17,fc6_waybel_0,fc7_relat_1,fc7_waybel17,fc8_waybel17,fc9_relat_1,fc9_yellow_9,fraenkel_a_0_10_fraenkel,fraenkel_a_0_11_fraenkel,fraenkel_a_0_1_lattice3,fraenkel_a_0_2_lattice3,fraenkel_a_0_4_fraenkel,fraenkel_a_0_5_fraenkel,fraenkel_a_2_0_waybel21,fraenkel_a_2_1_waybel11,fraenkel_a_2_4_waybel21,fraenkel_a_3_0_waybel11,fraenkel_a_3_0_waybel21,fraenkel_a_3_5_waybel21,fraenkel_a_4_4_waybel21,fraenkel_a_4_5_waybel21,fraenkel_a_5_3_waybel21,fraenkel_a_5_4_waybel21,fraenkel_a_5_5_waybel21,fraenkel_a_5_6_waybel21,fraenkel_a_5_7_waybel21,fraenkel_a_5_8_waybel21,fraenkel_a_5_9_waybel21,free_g1_orders_2,free_g1_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_finset_1,rc1_lattice3,rc1_relat_1,rc1_subset_1,rc1_waybel10,rc1_waybel_0,rc1_yellow_0,rc2_lattice3,rc2_partfun1,rc2_relat_1,rc2_subset_1,rc2_waybel21,rc2_waybel_0,rc2_yellow_0,rc3_finset_1,rc3_relat_1,rc3_struct_0,rc3_yellow_9,rc4_finset_1,rc4_waybel_0,rc4_yellow_6,rc5_struct_0,rc5_waybel_0,rc6_waybel_0,redefinition_k1_waybel_0,redefinition_k3_yellow_6,redefinition_k4_pre_topc,redefinition_k4_relset_1,redefinition_k7_funct_2,redefinition_m2_relset_1,reflexivity_r1_tarski,s2_lattice3__e2_58_1_1_1_1__waybel21,s2_lattice3__e7_58_1__waybel21,s3_fraenkel__e6_58_1_1_1_1__waybel21,s3_fraenkel__e8_58_1_1_1_1__waybel21,s6_fraenkel__e4_58_1_1_1_1__waybel21,s6_fraenkel__e5_58_1_1_1_1__waybel21,s6_fraenkel__e9_58_1_1_1_1__waybel21,t10_waybel17,t17_yellow_0,t1_subset,t21_funct_2,t25_waybel20,t25_waybel21,t28_waybel21,t29_waybel21,t2_subset,t2_tarski,t33_waybel21,t3_subset,t46_waybel21,t4_subset,t5_subset,t6_boole,t71_waybel_0,t7_boole,t8_boole]), [file(waybel21,t47_waybel21)]). 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(abstractness_v6_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v6_waybel_0(B,A) => B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) ) ) ), file(waybel_0,v6_waybel_0), []). 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(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_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). 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_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_waybel19,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_pre_topc(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_pre_topc(A) & ~ v1_yellow_3(A) & v1_waybel19(A) ) ) ) ), file(waybel19,cc1_waybel19), []). fof(cc1_waybel21,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(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)) & v19_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) ) ) ), file(waybel21,cc1_waybel21), []). 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_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(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc2_lattice3), []). fof(cc2_waybel19,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_waybel19(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v2_t_0topsp(A) & ~ v1_yellow_3(A) ) ) ) ), file(waybel19,cc2_waybel19), []). fof(cc2_waybel21,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel21(C,A,B) => ( v1_relat_1(C) & v19_waybel_0(C,A,B) ) ) ) ), file(waybel21,cc2_waybel21), []). 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_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(cc3_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & v8_waybel_0(B,A) ) => ( ~ v3_struct_0(B) & v7_waybel_0(B) & v10_waybel_0(B,A) ) ) ) ) ), file(waybel_0,cc3_waybel_0), []). 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_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(cc4_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & v9_waybel_0(B,A) ) => ( ~ v3_struct_0(B) & v7_waybel_0(B) & v11_waybel_0(B,A) ) ) ) ) ), file(waybel_0,cc4_waybel_0), []). 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_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_waybel19,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(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) & v2_pre_topc(A) & ~ v1_yellow_3(A) & v2_compts_1(A) & v1_urysohn1(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(waybel19,cc5_waybel19), []). 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_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_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_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_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(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(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_waybel21,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( ( v2_yellow_0(A) => v2_yellow_0(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)) ) => ( m1_waybel21(C,A,B) <=> ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) ) ) ) ) ) ), file(waybel21,d1_waybel21), []). fof(d30_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)) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r3_waybel_0(A,B,C,D) <=> ( r2_yellow_0(A,D) => ( r2_yellow_0(B,k4_pre_topc(A,B,C,D)) & k2_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k2_yellow_0(A,D)) ) ) ) ) ) ) ) ), file(waybel_0,d30_waybel_0), []). fof(d31_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)) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r4_waybel_0(A,B,C,D) <=> ( r1_yellow_0(A,D) => ( r1_yellow_0(B,k4_pre_topc(A,B,C,D)) & k1_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k1_yellow_0(A,D)) ) ) ) ) ) ) ) ), file(waybel_0,d31_waybel_0), []). fof(d32_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)) ) => ( v17_waybel_0(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r3_waybel_0(A,B,C,D) ) ) ) ) ) ), file(waybel_0,d32_waybel_0), []). fof(d37_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)) ) => ( v22_waybel_0(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel_0(D,A) => ( v1_xboole_0(D) | r4_waybel_0(A,B,C,D) ) ) ) ) ) ) ) ), file(waybel_0,d37_waybel_0), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_waybel21,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)) ) => ( v1_waybel21(C,A,B) <=> ! [D] : ( ( ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => k3_yellow_6(u1_struct_0(A),B,C,k1_waybel11(A,D)) = k1_waybel11(B,k7_waybel_9(A,B,C,D)) ) ) ) ) ) ), file(waybel21,d4_waybel21), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => k1_waybel11(A,B) = k1_yellow_0(A,a_2_1_waybel11(A,B)) ) ) ), file(waybel11,d6_waybel11), []). fof(d8_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_waybel_0(A,B,C) = k1_waybel_0(B,A,u1_waybel_0(A,B),C) ) ) ) ), file(waybel_0,d8_waybel_0), []). fof(d8_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_struct_0(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] : ( l1_waybel_0(D,A) => ! [E] : ( ( v6_waybel_0(E,B) & l1_waybel_0(E,B) ) => ( E = k7_waybel_9(A,B,C,D) <=> ( g1_orders_2(u1_struct_0(E),u1_orders_2(E)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) & u1_waybel_0(B,E) = k7_funct_2(u1_struct_0(D),u1_struct_0(A),u1_struct_0(B),u1_waybel_0(A,D),C) ) ) ) ) ) ) ) ), file(waybel_9,d8_waybel_9), []). fof(d9_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ), file(orders_2,d9_orders_2), []). 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_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( v6_waybel_0(g1_waybel_0(A,B,C,D),A) & l1_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,g1_waybel_0), []). 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_waybel11,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(k1_waybel11(A,B),u1_struct_0(A)) ) ), file(waybel11,k1_waybel11), []). 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_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_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k2_yellow_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_waybel_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)) ) ), file(waybel_0,k3_waybel_0), []). fof(dt_k3_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(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(k3_yellow_6(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_6,k3_yellow_6), []). fof(dt_k3_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) & l1_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(yellow_9,k3_yellow_9), []). fof(dt_k4_pre_topc,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & 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(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ), file(pre_topc,k4_pre_topc), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_waybel17,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v6_waybel_0(k4_waybel17(A,B),A) & l1_waybel_0(k4_waybel17(A,B),A) ) ) ), file(waybel17,k4_waybel17), []). 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_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_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & 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)) & l1_waybel_0(D,A) ) => ( v6_waybel_0(k7_waybel_9(A,B,C,D),B) & l1_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,k7_waybel_9), []). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_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_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => l1_orders_2(B) ) ) ), file(waybel_0,l1_waybel_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_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_waybel21,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel21(C,A,B) => ( 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)) ) ) ) ), file(waybel21,m1_waybel21), []). 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(dt_u1_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(waybel_0,u1_waybel_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_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_waybel_0(B,A) ) ), file(waybel_0,l1_waybel_0), []). fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) ), file(waybel_9,l1_waybel_9), []). 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_waybel21,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ? [C] : m1_waybel21(C,A,B) ) ), file(waybel21,m1_waybel21), []). 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(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(fc13_finset_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => v1_finset_1(k9_relat_1(A,B)) ) ), file(finset_1,fc13_finset_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc15_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ( ~ v1_xboole_0(u1_waybel_0(A,B)) & v1_relat_1(u1_waybel_0(A,B)) & v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(yellow_6,fc15_yellow_6), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_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_waybel_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ~ v1_xboole_0(k9_relat_1(C,D)) ) ), file(waybel_2,fc1_waybel_2), []). 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(fc27_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & 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)) & ~ v3_struct_0(D) & l1_waybel_0(D,A) ) => ( ~ v3_struct_0(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc27_waybel_9), []). fof(fc28_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & 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)) & v2_orders_2(D) & l1_waybel_0(D,A) ) => ( v2_orders_2(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc28_waybel_9), []). fof(fc29_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & 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)) & v4_orders_2(D) & l1_waybel_0(D,A) ) => ( v4_orders_2(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc29_waybel_9), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_waybel21,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) & v9_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(waybel21,fc2_waybel21), []). fof(fc30_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & 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)) & v3_orders_2(D) & l1_waybel_0(D,A) ) => ( v3_orders_2(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc30_waybel_9), []). fof(fc31_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & 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)) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ( v6_waybel_0(k7_waybel_9(A,B,C,D),B) & v7_waybel_0(k7_waybel_9(A,B,C,D)) ) ) ), file(waybel_9,fc31_waybel_9), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_waybel21,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & ~ v3_struct_0(D) & v9_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( ~ v3_struct_0(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) & v9_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel21,fc3_waybel21), []). fof(fc3_yellow_9,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))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v2_orders_2(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(yellow_9,fc3_yellow_9), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc5_waybel17,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k4_waybel17(A,B)) & v2_orders_2(k4_waybel17(A,B)) & v6_waybel_0(k4_waybel17(A,B),A) & v7_waybel_0(k4_waybel17(A,B)) ) ) ), file(waybel17,fc5_waybel17), []). fof(fc5_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v3_orders_2(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(yellow_9,fc5_yellow_9), []). fof(fc6_waybel17,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k4_waybel17(A,B)) & v2_orders_2(k4_waybel17(A,B)) & v3_orders_2(k4_waybel17(A,B)) & v6_waybel_0(k4_waybel17(A,B),A) & v7_waybel_0(k4_waybel17(A,B)) ) ) ), file(waybel17,fc6_waybel17), []). fof(fc6_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & ~ v1_xboole_0(B) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( ~ v3_struct_0(g1_waybel_0(A,B,C,D)) & v6_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,fc6_waybel_0), []). 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_waybel17,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k4_waybel17(A,B)) & v2_orders_2(k4_waybel17(A,B)) & v6_waybel_0(k4_waybel17(A,B),A) & v7_waybel_0(k4_waybel17(A,B)) & v8_waybel_0(k4_waybel17(A,B),A) & v10_waybel_0(k4_waybel17(A,B),A) ) ) ), file(waybel17,fc7_waybel17), []). fof(fc8_waybel17,axiom,( ! [A,B,C,D] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & ~ v3_struct_0(D) & v8_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( ~ v3_struct_0(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) & v8_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel17,fc8_waybel17), []). 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_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v2_orders_2(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) & v7_waybel_0(k3_yellow_9(A,B)) ) ) ), file(yellow_9,fc9_yellow_9), []). fof(fraenkel_a_0_10_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_10_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s6_fraenkel) & A = f2_s6_fraenkel(B) & p1_s6_fraenkel(B) ) ) ), file(fraenkel,a_0_10_fraenkel), []). fof(fraenkel_a_0_11_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_11_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s6_fraenkel) & A = f3_s6_fraenkel(B) & p1_s6_fraenkel(B) ) ) ), file(fraenkel,a_0_11_fraenkel), []). fof(fraenkel_a_0_1_lattice3,axiom,( ! [A] : ( r2_hidden(A,a_0_1_lattice3) <=> ? [B] : ( m1_subset_1(B,f1_s2_lattice3) & A = f3_s2_lattice3(B) & p1_s2_lattice3(B) ) ) ), file(lattice3,a_0_1_lattice3), []). fof(fraenkel_a_0_2_lattice3,axiom,( ! [A] : ( r2_hidden(A,a_0_2_lattice3) <=> ? [B] : ( m1_subset_1(B,f1_s2_lattice3) & A = k1_funct_1(f4_s2_lattice3,f3_s2_lattice3(B)) & p1_s2_lattice3(B) ) ) ), file(lattice3,a_0_2_lattice3), []). fof(fraenkel_a_0_4_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_4_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p1_s3_fraenkel(B) ) ) ), file(fraenkel,a_0_4_fraenkel), []). fof(fraenkel_a_0_5_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_5_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s3_fraenkel) & A = f2_s3_fraenkel(B) & p2_s3_fraenkel(B) ) ) ), file(fraenkel,a_0_5_fraenkel), []). fof(fraenkel_a_2_0_waybel21,axiom,( ! [A,B,C] : ( ( 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(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_0_waybel21(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_0_waybel21(B,C,D)) ) ) ) ), file(waybel21,a_2_0_waybel21), []). fof(fraenkel_a_2_1_waybel11,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_1_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_0_waybel11(B,C,D)) ) ) ) ), file(waybel11,a_2_1_waybel11), []). fof(fraenkel_a_2_4_waybel21,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_4_waybel21(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_5_waybel21(B,C,D)) ) ) ) ), file(waybel21,a_2_4_waybel21), []). fof(fraenkel_a_3_0_waybel11,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k3_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) ), file(waybel11,a_3_0_waybel11), []). fof(fraenkel_a_3_0_waybel21,axiom,( ! [A,B,C,D] : ( ( 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(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k3_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) ), file(waybel21,a_3_0_waybel21), []). fof(fraenkel_a_3_5_waybel21,axiom,( ! [A,B,C,D] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_5_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k3_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) ), file(waybel21,a_3_5_waybel21), []). fof(fraenkel_a_4_4_waybel21,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(A,a_4_4_waybel21(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k7_waybel_9(B,C,D,E))) & A = k2_yellow_0(C,a_5_3_waybel21(B,C,D,E,F)) ) ) ) ), file(waybel21,a_4_4_waybel21), []). fof(fraenkel_a_4_5_waybel21,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(A,a_4_5_waybel21(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(E)) & A = k3_yellow_6(u1_struct_0(B),C,D,k2_yellow_0(B,a_3_5_waybel21(B,E,F))) ) ) ) ), file(waybel21,a_4_5_waybel21), []). fof(fraenkel_a_5_3_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(k7_waybel_9(B,C,D,E))) ) => ( r2_hidden(A,a_5_3_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k7_waybel_9(B,C,D,E))) & A = k3_waybel_0(C,k7_waybel_9(B,C,D,E),G) & r1_orders_2(k7_waybel_9(B,C,D,E),F,G) ) ) ) ), file(waybel21,a_5_3_waybel21), []). fof(fraenkel_a_5_4_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(E)) ) => ( r2_hidden(A,a_5_4_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(E)) & A = k3_yellow_6(u1_struct_0(B),C,D,k3_waybel_0(B,E,G)) & r1_orders_2(E,F,G) ) ) ) ), file(waybel21,a_5_4_waybel21), []). fof(fraenkel_a_5_5_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(E)) ) => ( r2_hidden(A,a_5_5_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(E)) & A = k1_funct_1(D,k1_funct_1(u1_waybel_0(B,E),G)) & r1_orders_2(E,F,G) ) ) ) ), file(waybel21,a_5_5_waybel21), []). fof(fraenkel_a_5_6_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(E)) ) => ( r2_hidden(A,a_5_6_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(E)) & A = k1_funct_1(k7_funct_2(u1_struct_0(E),u1_struct_0(B),u1_struct_0(C),u1_waybel_0(B,E),D),G) & r1_orders_2(E,F,G) ) ) ) ), file(waybel21,a_5_6_waybel21), []). fof(fraenkel_a_5_7_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(k7_waybel_9(B,C,D,E))) ) => ( r2_hidden(A,a_5_7_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(E)) & A = k1_funct_1(k7_funct_2(u1_struct_0(E),u1_struct_0(B),u1_struct_0(C),u1_waybel_0(B,E),D),G) & r2_hidden(k4_tarski(F,G),u1_orders_2(E)) ) ) ) ), file(waybel21,a_5_7_waybel21), []). fof(fraenkel_a_5_8_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(k7_waybel_9(B,C,D,E))) ) => ( r2_hidden(A,a_5_8_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k7_waybel_9(B,C,D,E))) & A = k1_funct_1(k7_funct_2(u1_struct_0(E),u1_struct_0(B),u1_struct_0(C),u1_waybel_0(B,E),D),G) & r2_hidden(k4_tarski(F,G),u1_orders_2(E)) ) ) ) ), file(waybel21,a_5_8_waybel21), []). fof(fraenkel_a_5_9_waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & v2_orders_2(C) & v3_orders_2(C) & v4_orders_2(C) & v2_pre_topc(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v2_waybel19(C) & l1_waybel_9(C) & m1_waybel21(D,B,C) & ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(k7_waybel_9(B,C,D,E))) ) => ( r2_hidden(A,a_5_9_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k7_waybel_9(B,C,D,E))) & A = k1_funct_1(k7_funct_2(u1_struct_0(E),u1_struct_0(B),u1_struct_0(C),u1_waybel_0(B,E),D),G) & r1_orders_2(k7_waybel_9(B,C,D,E),F,G) ) ) ) ), file(waybel21,a_5_9_waybel21), []). 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(free_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ! [E,F,G,H] : ( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(waybel_0,g1_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_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). 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_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_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ), file(waybel_0,rc1_waybel_0), []). 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(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_waybel21,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) & v9_waybel_0(B,A) & v10_waybel_0(B,A) & v11_waybel_0(B,A) ) ) ), file(waybel21,rc2_waybel21), []). fof(rc2_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ), file(waybel_0,rc2_waybel_0), []). 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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). 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_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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) ) ) ), file(waybel_0,rc4_waybel_0), []). fof(rc4_yellow_6,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v7_waybel_0(A) ) ), file(yellow_6,rc4_yellow_6), []). 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_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) ) ) ), file(waybel_0,rc5_waybel_0), []). fof(rc6_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) & v9_waybel_0(B,A) & v10_waybel_0(B,A) & v11_waybel_0(B,A) ) ) ), file(waybel_0,rc6_waybel_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_k3_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(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) ) => k3_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_6,k3_yellow_6), []). fof(redefinition_k4_pre_topc,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & 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)) ) => k4_pre_topc(A,B,C,D) = k9_relat_1(C,D) ) ), file(pre_topc,k4_pre_topc), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_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_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(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(s2_lattice3__e2_58_1_1_1_1__waybel21,axiom,( ! [A,B,C] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) ) => ( r1_tarski(u1_struct_0(A),k1_relat_1(C)) => k9_relat_1(C,a_0_1_lattice3) = a_0_2_lattice3 ) ) ), file(waybel21,s2_lattice3__e2_58_1_1_1_1__waybel21), []). fof(s2_lattice3__e7_58_1__waybel21,axiom,( ! [A,B,C] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) ) => ( r1_tarski(u1_struct_0(A),k1_relat_1(C)) => k9_relat_1(C,a_0_1_lattice3) = a_0_2_lattice3 ) ) ), file(waybel21,s2_lattice3__e7_58_1__waybel21), []). fof(s3_fraenkel__e6_58_1_1_1_1__waybel21,axiom,( ! [A,B,C,D,E,F] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) & m1_subset_1(E,u1_struct_0(D)) & m1_subset_1(F,u1_struct_0(k7_waybel_9(A,B,C,D))) ) => ( ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( r1_orders_2(D,E,G) <=> r2_hidden(k4_tarski(F,G),u1_orders_2(D)) ) ) => a_0_4_fraenkel = a_0_5_fraenkel ) ) ), file(waybel21,s3_fraenkel__e6_58_1_1_1_1__waybel21), []). fof(s3_fraenkel__e8_58_1_1_1_1__waybel21,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) & m1_subset_1(E,u1_struct_0(k7_waybel_9(A,B,C,D))) ) => ( ! [F] : ( m1_subset_1(F,u1_struct_0(k7_waybel_9(A,B,C,D))) => ( r2_hidden(k4_tarski(E,F),u1_orders_2(D)) <=> r1_orders_2(k7_waybel_9(A,B,C,D),E,F) ) ) => a_0_4_fraenkel = a_0_5_fraenkel ) ) ), file(waybel21,s3_fraenkel__e8_58_1_1_1_1__waybel21), []). fof(s6_fraenkel__e4_58_1_1_1_1__waybel21,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) & m1_subset_1(E,u1_struct_0(D)) ) => ( ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( r1_orders_2(D,E,F) => k3_yellow_6(u1_struct_0(A),B,C,k3_waybel_0(A,D,F)) = k1_funct_1(C,k1_funct_1(u1_waybel_0(A,D),F)) ) ) => a_0_10_fraenkel = a_0_11_fraenkel ) ) ), file(waybel21,s6_fraenkel__e4_58_1_1_1_1__waybel21), []). fof(s6_fraenkel__e5_58_1_1_1_1__waybel21,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) & m1_subset_1(E,u1_struct_0(D)) ) => ( ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( r1_orders_2(D,E,F) => k1_funct_1(C,k1_funct_1(u1_waybel_0(A,D),F)) = k1_funct_1(k7_funct_2(u1_struct_0(D),u1_struct_0(A),u1_struct_0(B),u1_waybel_0(A,D),C),F) ) ) => a_0_10_fraenkel = a_0_11_fraenkel ) ) ), file(waybel21,s6_fraenkel__e5_58_1_1_1_1__waybel21), []). fof(s6_fraenkel__e9_58_1_1_1_1__waybel21,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) & m1_waybel21(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) & m1_subset_1(E,u1_struct_0(k7_waybel_9(A,B,C,D))) ) => ( ! [F] : ( m1_subset_1(F,u1_struct_0(k7_waybel_9(A,B,C,D))) => ( r1_orders_2(k7_waybel_9(A,B,C,D),E,F) => k1_funct_1(k7_funct_2(u1_struct_0(D),u1_struct_0(A),u1_struct_0(B),u1_waybel_0(A,D),C),F) = k3_waybel_0(B,k7_waybel_9(A,B,C,D),F) ) ) => a_0_10_fraenkel = a_0_11_fraenkel ) ) ), file(waybel21,s6_fraenkel__e9_58_1_1_1_1__waybel21), []). fof(t10_waybel17,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k1_waybel11(A,k4_waybel17(A,B)) = k1_yellow_0(A,B) ) ) ), file(waybel17,t10_waybel17), []). fof(t17_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( r1_yellow_0(A,B) & r2_yellow_0(A,B) ) ) ), file(yellow_0,t17_yellow_0), []). 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(t25_waybel20,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)) ) => ( v5_orders_3(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel_0(D,A) => v2_waybel_0(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ), file(waybel20,t25_waybel20), []). fof(t25_waybel21,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) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ( ~ v1_xboole_0(a_2_0_waybel21(A,B)) & v1_waybel_0(a_2_0_waybel21(A,B),A) & m1_subset_1(a_2_0_waybel21(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ), file(waybel21,t25_waybel21), []). fof(t28_waybel21,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k1_waybel11(A,k3_yellow_9(A,B)) = k2_yellow_0(A,B) ) ) ), file(waybel21,t28_waybel21), []). fof(t29_waybel21,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v25_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(D,A,B) & m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) ) => k1_waybel11(B,k7_waybel_9(A,B,D,k3_yellow_9(A,C))) = k2_yellow_0(B,k4_pre_topc(A,B,D,C)) ) ) ) ) ), file(waybel21,t29_waybel21), []). 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(t33_waybel21,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k1_waybel11(B,k7_waybel_9(A,B,C,k4_waybel17(A,D))) = k1_yellow_0(B,k4_pre_topc(A,B,C,D)) ) ) ) ) ), file(waybel21,t33_waybel21), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t46_waybel21,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v2_pre_topc(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v2_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( m1_waybel21(C,A,B) => ( v5_pre_topc(C,A,B) <=> ( v17_waybel_0(C,A,B) & v22_waybel_0(C,A,B) ) ) ) ) ) ), file(waybel21,t46_waybel21), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t71_waybel_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(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] : ( ( 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_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) & ! [D] : ( ( ~ v1_xboole_0(D) & v2_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) ) => v17_waybel_0(C,A,B) ) ) ) ) ), file(waybel_0,t71_waybel_0), []). 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), []).