% Mizar problem: t26_waybel31,waybel31,1293,39 fof(t26_waybel31,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_pre_topc(B) & v2_waybel19(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v6_waybel23(C,A) & m1_waybel23(C,A) ) => m1_cantor_1(a_2_6_waybel31(A,C),B) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc10_tsp_1,cc10_waybel25,cc10_waybel30,cc10_waybel_0,cc10_yellow13,cc11_waybel_0,cc11_yellow13,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc14_yellow13,cc1_finseq_1,cc1_finset_1,cc1_lattice3,cc1_relset_1,cc1_tsp_1,cc1_waybel19,cc1_waybel25,cc1_waybel30,cc1_waybel31,cc1_waybel_3,cc1_waybel_8,cc1_yellow13,cc1_yellow15,cc1_yellow_0,cc1_yellow_2,cc1_yellow_3,cc1_yellow_9,cc2_finset_1,cc2_lattice3,cc2_tsp_1,cc2_waybel19,cc2_waybel25,cc2_waybel30,cc2_waybel_3,cc2_waybel_8,cc2_yellow13,cc2_yellow15,cc2_yellow_0,cc2_yellow_3,cc2_yellow_9,cc3_tsp_1,cc3_waybel19,cc3_waybel23,cc3_waybel30,cc3_waybel_3,cc3_waybel_8,cc3_yellow13,cc3_yellow_0,cc3_yellow_3,cc3_yellow_9,cc4_tsp_1,cc4_waybel19,cc4_waybel23,cc4_waybel30,cc4_waybel_3,cc4_waybel_4,cc4_waybel_8,cc4_yellow11,cc4_yellow13,cc4_yellow_0,cc4_yellow_9,cc5_tsp_1,cc5_waybel19,cc5_waybel23,cc5_waybel30,cc5_waybel_0,cc5_waybel_3,cc5_yellow11,cc5_yellow13,cc5_yellow_0,cc5_yellow_9,cc6_tsp_1,cc6_waybel19,cc6_waybel25,cc6_waybel30,cc6_waybel_3,cc6_yellow13,cc6_yellow_9,cc7_tsp_1,cc7_waybel23,cc7_waybel25,cc7_waybel30,cc7_waybel_3,cc7_yellow13,cc8_tsp_1,cc8_waybel23,cc8_waybel30,cc8_yellow13,cc9_tsp_1,cc9_waybel30,cc9_waybel_0,cc9_yellow13,commutativity_k3_xboole_0,commutativity_k5_subset_1,d11_yellow_0,d16_waybel_0,d2_waybel31,d3_tarski,d4_tarski,d4_xboole_0,d4_yellow_9,d5_funct_1,d5_pre_topc,d8_waybel23,dt_g1_orders_2,dt_k1_funct_1,dt_k1_relat_1,dt_k1_waybel_3,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_waybel31,dt_k2_waybel_3,dt_k2_zfmisc_1,dt_k3_subset_1,dt_k3_tarski,dt_k3_xboole_0,dt_k3_yellow_0,dt_k4_waybel_0,dt_k4_xboole_0,dt_k5_subset_1,dt_k5_waybel11,dt_k5_waybel_0,dt_k6_subset_1,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_9,dt_m1_cantor_1,dt_m1_relset_1,dt_m1_subset_1,dt_m1_waybel23,dt_m1_yellow_9,dt_m2_relset_1,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_9,existence_m1_cantor_1,existence_m1_relset_1,existence_m1_subset_1,existence_m1_waybel23,existence_m1_yellow_9,existence_m2_relset_1,fc10_finset_1,fc10_waybel_8,fc11_finseq_1,fc11_finset_1,fc11_waybel_0,fc11_waybel_8,fc12_finset_1,fc12_waybel_0,fc12_waybel_8,fc13_yellow_3,fc14_finset_1,fc16_waybel_0,fc17_finseq_1,fc17_waybel_0,fc1_struct_0,fc1_subset_1,fc1_waybel_3,fc1_yellow13,fc2_cantor_1,fc2_finseq_1,fc2_waybel_3,fc2_yellow13,fc3_waybel14,fc3_waybel_3,fc4_subset_1,fc4_waybel_3,fc4_waybel_8,fc5_waybel_3,fc5_waybel_8,fc5_yellow_3,fc6_waybel_3,fc6_waybel_8,fc6_yellow_3,fc7_waybel23,fc7_waybel_0,fc7_waybel_8,fc8_waybel23,fc8_waybel_0,fc8_waybel_8,fc9_waybel23,fc9_waybel_8,fraenkel_a_1_13_waybel19,fraenkel_a_2_5_waybel14,fraenkel_a_2_6_waybel31,fraenkel_a_2_9_waybel31,fraenkel_a_4_2_waybel31,free_g1_orders_2,idempotence_k3_xboole_0,idempotence_k5_subset_1,involutiveness_k3_subset_1,rc10_waybel_0,rc11_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_finseq_1,rc1_finset_1,rc1_lattice3,rc1_subset_1,rc1_waybel31,rc1_waybel_0,rc1_waybel_3,rc1_yellow11,rc1_yellow_0,rc1_yellow_3,rc2_lattice3,rc2_subset_1,rc2_waybel23,rc2_waybel_0,rc2_waybel_3,rc2_yellow13,rc2_yellow_0,rc3_finseq_1,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc4_waybel23,rc4_waybel_3,rc5_struct_0,rc6_finseq_1,rc6_waybel23,rc7_finseq_1,rc7_waybel_0,rc8_finseq_1,rc8_waybel_0,rc9_waybel_0,redefinition_k5_subset_1,redefinition_k6_subset_1,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,s1_zfrefle1__e38_30_3__waybel31,t12_waybel_3,t13_waybel_0,t13_yellow12,t1_subset,t1_waybel_3,t1_xboole_1,t25_waybel31,t26_finset_1,t2_boole,t2_subset,t2_tarski,t2_waybel_3,t31_yellow_9,t32_subset_1,t32_waybel19,t32_yellow_9,t33_waybel14,t33_xboole_1,t35_xboole_1,t38_tops_1,t3_boole,t3_subset,t40_waybel19,t46_waybel23,t47_waybel23,t4_boole,t4_subset,t52_yellow_9,t5_subset,t6_boole,t7_boole,t8_boole,t8_waybel_3,t8_waybel_8]), [file(waybel31,t26_waybel31)]). 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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_tdlat_3(A) & ~ v3_tdlat_3(A) ) ) ) ), file(tsp_1,cc10_tsp_1), []). fof(cc10_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_waybel18(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc10_waybel25), []). fof(cc10_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & v3_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v2_compts_1(A) & v2_waybel19(A) & v1_urysohn1(A) & v1_waybel30(A) & v3_waybel30(A) ) ) ) ), file(waybel30,cc10_waybel30), []). 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_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v3_compts_1(A) ) => ( v2_pre_topc(A) & v1_urysohn1(A) ) ) ) ), file(yellow13,cc10_yellow13), []). fof(cc11_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_yellow_0(A) ) ) ) ), file(waybel_0,cc11_waybel_0), []). fof(cc11_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_urysohn1(A) ) => ( v2_pre_topc(A) & v2_t_0topsp(A) ) ) ) ), file(yellow13,cc11_yellow13), []). 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(cc14_yellow13,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_yellow13(A) ) ) ) ), file(yellow13,cc14_yellow13), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). 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_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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc1_tsp_1), []). 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_waybel25,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) ), file(waybel25,cc1_waybel25), []). fof(cc1_waybel30,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_realset2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( ~ v3_struct_0(B) & v6_group_1(B) & v3_realset2(B) ) ) ) ), file(waybel30,cc1_waybel30), []). fof(cc1_waybel31,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v6_group_1(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(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) & ~ v1_yellow_3(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ) ) ), file(waybel31,cc1_waybel31), []). fof(cc1_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v16_waybel_0(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_3,cc1_waybel_3), []). 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_yellow13,axiom,( ! [A] : ( v1_realset1(A) => v1_finset_1(A) ) ), file(yellow13,cc1_yellow13), []). fof(cc1_yellow15,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => v1_finset_1(B) ) ) ), file(yellow15,cc1_yellow15), []). 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_2,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(yellow_2,cc1_yellow_2), []). fof(cc1_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_struct_0(A) => v1_yellow_3(A) ) ) ), file(yellow_3,cc1_yellow_3), []). fof(cc1_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ~ v3_struct_0(B) ) ) ), file(yellow_9,cc1_yellow_9), []). fof(cc2_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_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & ~ v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) ) ) ) ), file(tsp_1,cc2_tsp_1), []). 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_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & ~ v1_yellow_3(B) & v2_waybel_3(B) & v3_waybel_3(B) & v2_waybel18(B) ) ) ) ) ), file(waybel25,cc2_waybel25), []). fof(cc2_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & ~ v1_yellow_3(A) & v4_waybel11(A) ) ) ) ), file(waybel30,cc2_waybel30), []). fof(cc2_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v16_waybel_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) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_3,cc2_waybel_3), []). 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_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_realset2(A) => v6_group_1(A) ) ) ), file(yellow13,cc2_yellow13), []). fof(cc2_yellow15,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => v1_finset_1(B) ) ) ), file(yellow15,cc2_yellow15), []). fof(cc2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) ) ) ) ), file(yellow_0,cc2_yellow_0), []). fof(cc2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v1_yellow_3(A) => ~ v3_struct_0(A) ) ) ), file(yellow_3,cc2_yellow_3), []). fof(cc2_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v2_orders_2(B) ) ) ), file(yellow_9,cc2_yellow_9), []). fof(cc3_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc3_tsp_1), []). fof(cc3_waybel19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( ~ v3_struct_0(B) & v1_yellow_0(B) ) ) ) ), file(waybel19,cc3_waybel19), []). fof(cc3_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel23(B,A) => v2_waybel_0(B,A) ) ) ) ), file(waybel23,cc3_waybel23), []). fof(cc3_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v2_compts_1(A) & v2_waybel19(A) & v1_urysohn1(A) ) ) ) ), file(waybel30,cc3_waybel30), []). fof(cc3_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) & v2_orders_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc3_waybel_3), []). 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_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v3_realset2(A) => ~ v3_struct_0(A) ) ) ), file(yellow13,cc3_yellow13), []). fof(cc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow_0,cc3_yellow_0), []). fof(cc3_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) ) => ( ~ v3_struct_0(A) & ~ v1_yellow_3(A) ) ) ) ), file(yellow_3,cc3_yellow_3), []). fof(cc3_yellow_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v3_orders_2(B) ) ) ), file(yellow_9,cc3_yellow_9), []). fof(cc4_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) ) ) ) ), file(tsp_1,cc4_tsp_1), []). fof(cc4_waybel19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & v2_waybel_3(B) & v3_waybel_3(B) & ~ v1_yellow_3(B) ) ) ) ), file(waybel19,cc4_waybel19), []). fof(cc4_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel23(B,A) => v1_waybel_0(B,A) ) ) ) ), file(waybel23,cc4_waybel23), []). fof(cc4_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & v3_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & ~ v1_yellow_3(A) & v3_compts_1(A) & v1_urysohn1(A) ) ) ) ), file(waybel30,cc4_waybel30), []). fof(cc4_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc4_waybel_3), []). fof(cc4_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v3_waybel_3(A) & v1_lattice3(A) & v2_lattice3(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_yellow_3(A) & v1_waybel_2(A) & v2_waybel_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(waybel_4,cc4_waybel_4), []). 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_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v6_group_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) ) ) ) ), file(yellow11,cc4_yellow11), []). fof(cc4_yellow13,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v4_pre_topc(B,A) ) ) ) ), file(yellow13,cc4_yellow13), []). fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) ), file(yellow_0,cc4_yellow_0), []). fof(cc4_yellow_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v4_orders_2(B) ) ) ), file(yellow_9,cc4_yellow_9), []). fof(cc5_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & v2_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc5_tsp_1), []). 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_waybel23,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_waybel23(B,A) => ~ v1_xboole_0(B) ) ) ) ), file(waybel23,cc5_waybel23), []). fof(cc5_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_2(A) & v3_compts_1(A) & v2_waybel19(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & 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_waybel_2(A) & v2_waybel_2(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ) ) ), file(waybel30,cc5_waybel30), []). 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_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) ) ) ) ), file(waybel_3,cc5_waybel_3), []). fof(cc5_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v6_group_1(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(yellow11,cc5_yellow11), []). fof(cc5_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & v6_group_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) ) ) ) ), file(yellow13,cc5_yellow13), []). fof(cc5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) ), file(yellow_0,cc5_yellow_0), []). fof(cc5_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( ~ v3_struct_0(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ) ), file(yellow_9,cc5_yellow_9), []). fof(cc6_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & v3_realset2(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc6_tsp_1), []). fof(cc6_waybel19,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v3_waybel_3(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) & v2_waybel_3(A) & v3_waybel_3(A) & ~ v1_yellow_3(A) & v3_compts_1(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) ) ) ), file(waybel19,cc6_waybel19), []). fof(cc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_t_0topsp(A) & v1_waybel25(A) ) ) ) ), file(waybel25,cc6_waybel25), []). fof(cc6_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_waybel30(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_waybel30(A) ) ) ) ), file(waybel30,cc6_waybel30), []). fof(cc6_waybel_3,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) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc6_waybel_3), []). fof(cc6_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v6_group_1(A) ) => ( v2_pre_topc(A) & v2_compts_1(A) ) ) ) ), file(yellow13,cc6_yellow13), []). fof(cc6_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) ) ) ) ) ), file(yellow_9,cc6_yellow_9), []). fof(cc7_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) ) ) ) ), file(tsp_1,cc7_tsp_1), []). fof(cc7_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_waybel23(B,A) => ( v1_waybel_0(B,A) & v2_waybel23(B,A) ) ) ) ), file(waybel23,cc7_waybel23), []). fof(cc7_waybel25,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( ~ v3_struct_0(B) & v2_pre_topc(B) & v2_t_0topsp(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v4_waybel11(B) & v1_waybel25(B) ) ) ) ) ), file(waybel25,cc7_waybel25), []). fof(cc7_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_waybel30(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_waybel30(A) ) ) ) ), file(waybel30,cc7_waybel30), []). fof(cc7_waybel_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v3_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v4_compts_1(A) & v5_compts_1(A) & v6_waybel_3(A) ) ) ) ), file(waybel_3,cc7_waybel_3), []). fof(cc7_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) => ( v2_pre_topc(A) & v1_urysohn1(A) & v3_compts_1(A) & v4_compts_1(A) & v5_compts_1(A) ) ) ) ), file(yellow13,cc7_yellow13), []). fof(cc8_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & v2_t_0topsp(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v3_tdlat_3(A) & v4_tdlat_3(A) & v5_tdlat_3(A) & v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc8_tsp_1), []). fof(cc8_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) & ~ v3_realset2(A) & l1_orders_2(A) ) => ! [B] : ( m1_waybel23(B,A) => ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & v2_waybel23(B,A) ) ) ) ), file(waybel23,cc8_waybel23), []). fof(cc8_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_tdlat_3(A) ) => ( ~ v3_struct_0(A) & v1_waybel30(A) & v3_waybel30(A) ) ) ) ), file(waybel30,cc8_waybel30), []). fof(cc8_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v1_urysohn1(A) & v5_compts_1(A) ) => ( ~ v3_struct_0(A) & v2_pre_topc(A) & v4_compts_1(A) ) ) ) ), file(yellow13,cc8_yellow13), []). fof(cc9_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v3_tdlat_3(A) ) => ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_t_0topsp(A) ) ) ) ), file(tsp_1,cc9_tsp_1), []). fof(cc9_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_waybel30(A) ) ) ) ), file(waybel30,cc9_waybel30), []). 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_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_urysohn1(A) & v4_compts_1(A) ) => ( v2_pre_topc(A) & v3_compts_1(A) ) ) ) ), file(yellow13,cc9_yellow13), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). fof(d11_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => k3_yellow_0(A) = k1_yellow_0(A,k1_xboole_0) ) ), file(yellow_0,d11_yellow_0), []). fof(d16_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k5_waybel_0(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_orders_2(A,E,D) & r2_hidden(E,B) ) ) ) ) ) ) ) ), file(waybel_0,d16_waybel_0), []). fof(d2_waybel31,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))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_waybel31(A,B,C) = k6_subset_1(u1_struct_0(A),k2_waybel_3(A,C),k5_waybel_0(A,B)) ) ) ) ), file(waybel31,d2_waybel31), []). 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_tarski,axiom,( ! [A,B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) ), file(tarski,d4_tarski), []). fof(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). fof(d4_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_waybel_9(B) => ( m1_yellow_9(B,A) <=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ) ), file(yellow_9,d4_yellow_9), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> r2_hidden(B,u1_pre_topc(A)) ) ) ) ), file(pre_topc,d5_pre_topc), []). fof(d8_waybel23,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_waybel23(B,A) <=> r2_hidden(k3_yellow_0(A),B) ) ) ) ), file(waybel23,d8_waybel23), []). 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_waybel_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_3,k1_waybel_3), []). 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_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_waybel31,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_waybel31(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel31,k2_waybel31), []). fof(dt_k2_waybel_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k2_waybel_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_3,k2_waybel_3), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ), file(subset_1,k3_subset_1), []). fof(dt_k3_tarski,axiom,( $true ), file(tarski,k3_tarski), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ), file(yellow_0,k3_yellow_0), []). fof(dt_k4_waybel_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k4_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k4_waybel_0), []). fof(dt_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). fof(dt_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_1), []). fof(dt_k5_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => m1_subset_1(k5_waybel11(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(waybel11,k5_waybel11), []). fof(dt_k5_waybel_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k5_waybel_0), []). fof(dt_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_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_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( l1_pre_topc(A) & l1_orders_2(A) ) ) ), file(waybel_9,l1_waybel_9), []). fof(dt_m1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_cantor_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(cantor_1,m1_cantor_1), []). fof(dt_m1_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_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_waybel23(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(waybel23,m1_waybel23), []). fof(dt_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_9(B,A) => l1_waybel_9(B) ) ) ), file(yellow_9,m1_yellow_9), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pre_topc,u1_pre_topc), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) ), file(waybel_9,l1_waybel_9), []). fof(existence_m1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_cantor_1(B,A) ) ), file(cantor_1,m1_cantor_1), []). fof(existence_m1_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_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ? [B] : m1_waybel23(B,A) ) ), file(waybel23,m1_waybel23), []). fof(existence_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_9(B,A) ) ), file(yellow_9,m1_yellow_9), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). 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(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v12_waybel_0(k4_waybel_0(A,B),A) ) ), file(waybel_0,fc11_waybel_0), []). 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(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). fof(fc12_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v13_waybel_0(k5_waybel_0(A,B),A) ) ), file(waybel_0,fc12_waybel_0), []). fof(fc12_waybel_8,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_waybel_8(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_yellow_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc12_waybel_8), []). fof(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_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(fc16_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_waybel_0(k4_waybel_0(A,B),A) & v12_waybel_0(k4_waybel_0(A,B),A) ) ) ), file(waybel_0,fc16_waybel_0), []). fof(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). fof(fc17_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_waybel_0(k5_waybel_0(A,B),A) & v13_waybel_0(k5_waybel_0(A,B),A) ) ) ), file(waybel_0,fc17_waybel_0), []). fof(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_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v1_xboole_0(k1_waybel_3(A,B)) ) ), file(waybel_3,fc1_waybel_3), []). fof(fc1_yellow13,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) ), file(yellow13,fc1_yellow13), []). fof(fc2_cantor_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(u1_pre_topc(A)) ) ), file(cantor_1,fc2_cantor_1), []). fof(fc2_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_waybel_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v12_waybel_0(k1_waybel_3(A,B),A) ) ), file(waybel_3,fc2_waybel_3), []). fof(fc2_yellow13,axiom,( ! [A] : ( ( v3_realset2(A) & l1_struct_0(A) ) => v1_realset1(u1_struct_0(A)) ) ), file(yellow13,fc2_yellow13), []). fof(fc3_waybel14,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ~ v1_xboole_0(k5_waybel11(A)) ) ), file(waybel14,fc3_waybel14), []). fof(fc3_waybel_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v13_waybel_0(k2_waybel_3(A,B),A) ) ), file(waybel_3,fc3_waybel_3), []). 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_waybel_3,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_waybel_0(k1_waybel_3(A,B),A) & v12_waybel_0(k1_waybel_3(A,B),A) ) ) ), file(waybel_3,fc4_waybel_3), []). 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_waybel_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k1_waybel_3(A,B)) & v1_waybel_0(k1_waybel_3(A,B),A) & v12_waybel_0(k1_waybel_3(A,B),A) ) ) ), file(waybel_3,fc5_waybel_3), []). 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_yellow_3,axiom,( ! [A,B] : ( ( l1_orders_2(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_xboole_0(k4_waybel_0(A,B)) ) ), file(yellow_3,fc5_yellow_3), []). fof(fc6_waybel_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_waybel_3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k1_waybel_3(A,B)) & v1_waybel_0(k1_waybel_3(A,B),A) ) ) ), file(waybel_3,fc6_waybel_3), []). 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_3,axiom,( ! [A,B] : ( ( l1_orders_2(A) & v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_xboole_0(k5_waybel_0(A,B)) ) ), file(yellow_3,fc6_yellow_3), []). fof(fc7_waybel23,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_waybel_0(k1_waybel_3(A,B),A) & v12_waybel_0(k1_waybel_3(A,B),A) & v2_waybel23(k1_waybel_3(A,B),A) ) ) ), file(waybel23,fc7_waybel23), []). fof(fc7_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k4_waybel_0(A,B)) ) ), file(waybel_0,fc7_waybel_0), []). 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(fc8_waybel23,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_waybel_0(k2_waybel_3(A,B),A) & v13_waybel_0(k2_waybel_3(A,B),A) & v2_waybel23(k2_waybel_3(A,B),A) ) ) ), file(waybel23,fc8_waybel23), []). fof(fc8_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k5_waybel_0(A,B)) ) ), file(waybel_0,fc8_waybel_0), []). fof(fc8_waybel_8,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc8_waybel_8), []). fof(fc9_waybel23,axiom,( ! [A,B] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v2_waybel_0(k1_waybel_3(A,B),A) & v12_waybel_0(k1_waybel_3(A,B),A) & v1_waybel23(k1_waybel_3(A,B),A) ) ) ), file(waybel23,fc9_waybel23), []). 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(fraenkel_a_1_13_waybel19,axiom,( ! [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) ) => ( r2_hidden(A,a_1_13_waybel19(B)) <=> ? [C,D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k6_subset_1(u1_struct_0(B),C,k5_waybel_0(B,D)) & r2_hidden(C,k5_waybel11(B)) & v1_finset_1(D) ) ) ) ), file(waybel19,a_1_13_waybel19), []). fof(fraenkel_a_2_5_waybel14,axiom,( ! [A,B,C] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v4_waybel11(B) & l1_waybel_9(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r2_hidden(D,C) ) ) ) ), file(waybel14,a_2_5_waybel14), []). fof(fraenkel_a_2_6_waybel31,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v6_waybel23(C,B) & m1_waybel23(C,B) ) => ( r2_hidden(A,a_2_6_waybel31(B,C)) <=> ? [D,E] : ( m1_subset_1(D,u1_struct_0(B)) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_waybel31(B,E,D) & r2_hidden(D,C) & r1_tarski(E,C) ) ) ) ), file(waybel31,a_2_6_waybel31), []). fof(fraenkel_a_2_9_waybel31,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,B) ) => ( r2_hidden(A,a_2_9_waybel31(B,C)) <=> ? [D,E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k6_subset_1(u1_struct_0(C),D,k5_waybel_0(C,E)) & r2_hidden(D,k5_waybel11(C)) & v1_finset_1(E) ) ) ) ), file(waybel31,a_2_9_waybel31), []). fof(fraenkel_a_4_2_waybel31,axiom,( ! [A,B,C,D,E] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,B) & v4_waybel11(D) & m1_yellow_9(D,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) ) => ( r2_hidden(A,a_4_2_waybel31(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = k2_waybel_3(D,F) & r2_hidden(F,E) ) ) ) ), file(waybel31,a_4_2_waybel31), []). 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(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(involutiveness_k3_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,k3_subset_1(A,B)) = B ) ), file(subset_1,k3_subset_1), []). fof(rc10_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc10_waybel_0), []). fof(rc11_waybel_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc11_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_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). 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_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_waybel31,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v6_group_1(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_waybel_2(A) & v2_waybel_2(A) & v1_waybel_8(A) & v2_waybel_8(A) & v3_waybel_8(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_3(A) & v3_waybel_3(A) & v3_realset2(A) ) ), file(waybel31,rc1_waybel31), []). 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_waybel_3,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) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ), file(waybel_3,rc1_waybel_3), []). fof(rc1_yellow11,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) & v6_group_1(A) ) ), file(yellow11,rc1_yellow11), []). 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_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_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_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_waybel23,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v6_waybel23(B,A) ) ) ), file(waybel23,rc2_waybel23), []). 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_waybel_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_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) & v2_waybel_3(A) & v3_waybel_3(A) ) ), file(waybel_3,rc2_waybel_3), []). fof(rc2_yellow13,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v6_group_1(A) & v3_realset2(A) ) ), file(yellow13,rc2_yellow13), []). 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_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). 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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ? [B] : ( m1_waybel23(B,A) & ~ v1_xboole_0(B) & v6_waybel23(B,A) ) ) ), file(waybel23,rc4_waybel23), []). fof(rc4_waybel_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v2_pre_topc(A) & v2_compts_1(A) & v3_compts_1(A) & v4_compts_1(A) & v5_compts_1(A) & v6_waybel_3(A) ) ), file(waybel_3,rc4_waybel_3), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc6_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc6_waybel23,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) & v24_waybel_0(A) & v25_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) & ~ v3_realset2(A) ) ), file(waybel23,rc6_waybel23), []). fof(rc7_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc7_waybel_0), []). fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(rc8_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc8_waybel_0), []). fof(rc9_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & v12_waybel_0(B,A) ) ) ), file(waybel_0,rc9_waybel_0), []). fof(redefinition_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_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(s1_zfrefle1__e38_30_3__waybel31,axiom,( ! [A,B,C,D] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) & v6_waybel23(B,A) & m1_waybel23(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( ! [E] : ~ ( r2_hidden(E,D) & ! [F] : ~ ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & H = E & G = F & r2_hidden(G,B) & ~ r3_orders_2(A,G,C) & r1_waybel_3(A,G,H) ) ) ) => ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & k1_relat_1(E) = D & ! [F] : ( r2_hidden(F,D) => ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( m1_subset_1(J,u1_struct_0(A)) & J = F & I = k1_funct_1(E,F) & r2_hidden(I,B) & ~ r3_orders_2(A,I,C) & r1_waybel_3(A,I,J) ) ) ) ) ) ) ), file(waybel31,s1_zfrefle1__e38_30_3__waybel31), []). fof(t12_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => ( r1_tarski(k1_waybel_3(A,B),k1_waybel_3(A,C)) & r1_tarski(k2_waybel_3(A,C),k2_waybel_3(A,B)) ) ) ) ) ) ), file(waybel_3,t12_waybel_3), []). fof(t13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( k4_waybel_0(A,C) = k4_waybel_0(B,D) & k5_waybel_0(A,C) = k5_waybel_0(B,D) ) ) ) ) ) ) ) ), file(waybel_0,t13_waybel_0), []). fof(t13_yellow12,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & C = D ) => ( k1_waybel_3(A,C) = k1_waybel_3(B,D) & k2_waybel_3(A,C) = k2_waybel_3(B,D) ) ) ) ) ) ) ), file(yellow12,t13_yellow12), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) => r3_orders_2(A,B,C) ) ) ) ) ), file(waybel_3,t1_waybel_3), []). fof(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t25_waybel31,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v3_pre_topc(k3_subset_1(u1_struct_0(A),k5_waybel_0(A,B)),A) & v3_pre_topc(k3_subset_1(u1_struct_0(A),k4_waybel_0(A,B)),A) ) ) ) ), file(waybel31,t25_waybel31), []). fof(t26_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_finset_1(k1_relat_1(A)) => v1_finset_1(k2_relat_1(A)) ) ) ), file(finset_1,t26_finset_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_orders_2(A,B,C) & r1_waybel_3(A,C,D) & r3_orders_2(A,D,E) ) => r1_waybel_3(A,B,E) ) ) ) ) ) ) ), file(waybel_3,t2_waybel_3), []). fof(t31_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_cantor_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,B) & r2_hidden(D,E) & r1_tarski(E,C) ) ) ) ) ) ) ) ) ), file(yellow_9,t31_yellow_9), []). fof(t32_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k6_subset_1(A,B,C) = k5_subset_1(A,B,k3_subset_1(A,C)) ) ) ), file(subset_1,t32_subset_1), []). fof(t32_waybel19,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) ) => m1_cantor_1(a_1_13_waybel19(A),A) ) ), file(waybel19,t32_waybel19), []). fof(t32_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( r1_tarski(B,u1_pre_topc(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,B) & r2_hidden(D,E) & r1_tarski(E,C) ) ) ) ) ) ) ) => m1_cantor_1(B,A) ) ) ) ), file(yellow_9,t32_yellow_9), []). fof(t33_waybel14,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_waybel_3(A) & r2_hidden(B,k5_waybel11(A)) ) => B = k3_tarski(a_2_5_waybel14(A,B)) ) ) ) ), file(waybel14,t33_waybel14), []). fof(t33_xboole_1,axiom,( ! [A,B,C] : ( r1_tarski(A,B) => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) ), file(xboole_1,t33_xboole_1), []). fof(t35_xboole_1,axiom,( ! [A,B,C,D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)) ) ), file(xboole_1,t35_xboole_1), []). fof(t38_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(B,A) & v3_pre_topc(C,A) ) => v3_pre_topc(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ), file(tops_1,t38_tops_1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t40_waybel19,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v3_waybel_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_pre_topc(k2_waybel_3(A,B),A) & v4_pre_topc(k3_subset_1(u1_struct_0(A),k2_waybel_3(A,B)),A) ) ) ) ), file(waybel19,t40_waybel19), []). fof(t46_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r3_orders_2(A,E,C) & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) ), file(waybel23,t46_waybel23), []). fof(t47_waybel23,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_hidden(k3_yellow_0(A),B) => ( m1_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r3_orders_2(A,C,E) & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) ) ), file(waybel23,t47_waybel23), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). 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(t52_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => k5_waybel11(A) = k5_waybel11(B) ) ) ) ), file(yellow_9,t52_yellow_9), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k2_waybel_3(A,C)) <=> r1_waybel_3(A,C,B) ) ) ) ) ), file(waybel_3,t8_waybel_3), []). fof(t8_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & v24_waybel_0(A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F & r1_waybel_3(A,C,D) ) => r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) ), file(waybel_8,t8_waybel_8), []).