% Mizar problem: t37_waybel14,waybel14,1279,48 fof(t37_waybel14,conjecture,( ! [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,u1_struct_0(A)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_yellow_8(D,A,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(E,D) => ( v3_pre_topc(E,A) & v2_waybel_0(E,A) ) ) ) ) ) & v3_waybel_3(k2_yellow_1(k5_waybel11(A))) ) => B = k1_yellow_0(A,a_2_9_waybel14(A,B)) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,antisymmetry_r2_hidden,cc10_membered,cc10_waybel_0,cc11_membered,cc11_waybel_0,cc12_membered,cc12_waybel_0,cc13_membered,cc13_waybel_0,cc14_membered,cc14_waybel_0,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finset_1,cc1_lattice3,cc1_membered,cc1_relset_1,cc1_waybel_3,cc1_waybel_8,cc20_membered,cc2_finset_1,cc2_lattice3,cc2_membered,cc2_waybel11,cc2_waybel_3,cc2_waybel_8,cc3_membered,cc3_waybel_3,cc3_waybel_8,cc4_membered,cc4_waybel11,cc4_waybel_3,cc4_waybel_8,cc5_waybel_0,cc5_waybel_3,cc6_waybel_3,cc9_waybel_0,d17_waybel_0,d2_yellow_8,d3_tarski,d3_waybel_3,d4_tarski,d5_pre_topc,d5_waybel_3,d6_waybel_3,d8_lattice3,d8_setfam_1,d9_lattice3,dt_g1_orders_2,dt_k1_setfam_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_waybel_3,dt_k1_wellord2,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_yellow_1,dt_k1_zfmisc_1,dt_k2_yellow_0,dt_k2_yellow_1,dt_k2_zfmisc_1,dt_k3_subset_1,dt_k3_tarski,dt_k4_waybel_0,dt_k5_setfam_1,dt_k5_waybel11,dt_k6_setfam_1,dt_k6_waybel_0,dt_k7_setfam_1,dt_k8_setfam_1,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_9,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_8,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_relset_1,existence_m1_subset_1,existence_m1_yellow_8,existence_m2_relset_1,fc10_membered,fc10_waybel_8,fc11_membered,fc11_waybel_0,fc11_waybel_8,fc12_waybel_8,fc13_waybel_0,fc14_finset_1,fc16_waybel_0,fc1_finset_1,fc1_struct_0,fc1_subset_1,fc1_waybel_3,fc2_cantor_1,fc2_subset_1,fc2_waybel14,fc2_waybel_3,fc3_waybel11,fc3_waybel14,fc4_subset_1,fc4_waybel_3,fc4_waybel_8,fc5_waybel11,fc5_waybel_3,fc5_waybel_8,fc5_yellow_1,fc6_membered,fc6_waybel11,fc6_waybel_3,fc6_waybel_8,fc6_yellow_1,fc6_yellow_6,fc7_membered,fc7_waybel_0,fc7_waybel_8,fc7_yellow_6,fc8_membered,fc8_waybel_8,fc9_membered,fc9_waybel_0,fc9_waybel_8,fc9_yellow_1,fraenkel_a_2_0_waybel14,fraenkel_a_2_0_waybel_3,fraenkel_a_2_10_waybel14,fraenkel_a_2_2_waybel14,fraenkel_a_2_9_waybel14,free_g1_orders_2,involutiveness_k3_subset_1,involutiveness_k7_setfam_1,l26_waybel14,rc10_waybel_0,rc11_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_finset_1,rc1_lattice3,rc1_membered,rc1_subset_1,rc1_waybel11,rc1_waybel_0,rc1_waybel_3,rc1_waybel_6,rc2_lattice3,rc2_subset_1,rc2_waybel_0,rc2_waybel_3,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc4_waybel11,rc5_struct_0,rc6_waybel11,rc7_waybel_0,rc8_waybel_0,rc9_waybel_0,redefinition_k1_struct_0,redefinition_k1_yellow_1,redefinition_k5_setfam_1,redefinition_k6_setfam_1,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t10_yellow_6,t12_tops_2,t12_waybel11,t14_yellow_8,t15_waybel14,t17_waybel_0,t1_subset,t1_waybel_3,t1_yellow_1,t21_waybel_0,t21_yellow_8,t22_yellow_1,t23_waybel14,t24_waybel14,t25_orders_2,t2_subset,t2_tarski,t31_subset_1,t32_yellow_0,t33_yellow_0,t3_subset,t3_yellow_1,t4_subset,t54_waybel_4,t5_subset,t6_boole,t7_boole,t7_waybel_3,t8_boole]), [file(waybel14,t37_waybel14)]). 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_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). 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_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). 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_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). 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_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). 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(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). 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_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). 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_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(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). 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_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_realset2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v13_waybel_0(B,A) ) ) ), file(waybel11,cc2_waybel11), []). 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(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). 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(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_waybel11,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) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) => v3_waybel11(B,A) ) ) ) ), file(waybel11,cc4_waybel11), []). 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_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(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(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(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(d17_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_waybel_0(A,B) = k4_waybel_0(A,k1_struct_0(A,B)) ) ) ), file(waybel_0,d17_waybel_0), []). fof(d2_yellow_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m1_yellow_8(C,A,B) <=> ( r1_tarski(C,u1_pre_topc(A)) & r2_hidden(B,k8_setfam_1(u1_struct_0(A),C)) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(D,A) & r2_hidden(B,D) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) ) ) ) ) ), file(yellow_8,d2_yellow_8), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_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)) => k1_waybel_3(A,B) = a_2_0_waybel_3(A,B) ) ) ), file(waybel_3,d3_waybel_3), []). 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(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(d5_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v2_waybel_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_yellow_0(A,k1_waybel_3(A,B)) ) ) ) ), file(waybel_3,d5_waybel_3), []). fof(d6_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v3_waybel_3(A) <=> ( ! [B] : ( 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) ) ) & v24_waybel_0(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,d6_waybel_3), []). fof(d8_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B,C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r1_orders_2(A,C,D) ) ) ) ) ) ), file(lattice3,d8_lattice3), []). fof(d8_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k7_setfam_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> r2_hidden(k3_subset_1(A,D),B) ) ) ) ) ) ), file(setfam_1,d8_setfam_1), []). fof(d9_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B,C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r1_orders_2(A,D,C) ) ) ) ) ) ), file(lattice3,d9_lattice3), []). 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_setfam_1,axiom,( $true ), file(setfam_1,k1_setfam_1), []). fof(dt_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel_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_wellord2,axiom,( ! [A] : v1_relat_1(k1_wellord2(A)) ), file(wellord2,k1_wellord2), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_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_yellow_1,axiom,( ! [A] : ( v1_relat_2(k1_yellow_1(A)) & v4_relat_2(k1_yellow_1(A)) & v8_relat_2(k1_yellow_1(A)) & v1_partfun1(k1_yellow_1(A),A,A) & m2_relset_1(k1_yellow_1(A),A,A) ) ), file(yellow_1,k1_yellow_1), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_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_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & l1_orders_2(k2_yellow_1(A)) ) ), file(yellow_1,k2_yellow_1), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_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_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_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k5_setfam_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_k6_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k6_setfam_1), []). fof(dt_k6_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k6_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k6_waybel_0), []). fof(dt_k7_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k7_setfam_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(setfam_1,k7_setfam_1), []). fof(dt_k8_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) ), file(setfam_1,k8_setfam_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_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_yellow_8,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_yellow_8(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(yellow_8,m1_yellow_8), []). 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_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_yellow_8,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : m1_yellow_8(C,A,B) ) ), file(yellow_8,m1_yellow_8), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). 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_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). 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_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_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v12_waybel_0(k6_waybel_0(A,B),A) ) ), file(waybel_0,fc13_waybel_0), []). 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(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_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(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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_waybel14,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A))) & v1_orders_2(k2_yellow_1(u1_pre_topc(A))) & v2_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_orders_2(k2_yellow_1(u1_pre_topc(A))) & v4_orders_2(k2_yellow_1(u1_pre_topc(A))) & v1_lattice3(k2_yellow_1(u1_pre_topc(A))) & v2_lattice3(k2_yellow_1(u1_pre_topc(A))) & v3_lattice3(k2_yellow_1(u1_pre_topc(A))) & v1_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v2_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v3_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v24_waybel_0(k2_yellow_1(u1_pre_topc(A))) & v25_waybel_0(k2_yellow_1(u1_pre_topc(A))) & v2_waybel_1(k2_yellow_1(u1_pre_topc(A))) & ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) ), file(waybel14,fc2_waybel14), []). fof(fc2_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(fc3_waybel11,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v3_waybel11(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v2_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) ), file(waybel11,fc3_waybel11), []). 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(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_waybel11,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v1_waybel11(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v2_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) ), file(waybel11,fc5_waybel11), []). 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_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) ) ), file(yellow_1,fc5_yellow_1), []). fof(fc6_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_waybel11,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v2_waybel11(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_waybel11(k3_subset_1(u1_struct_0(A),B),A) ) ), file(waybel11,fc6_waybel11), []). 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_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v3_struct_0(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)) & v2_orders_2(k2_yellow_1(A)) & v3_orders_2(k2_yellow_1(A)) & v4_orders_2(k2_yellow_1(A)) ) ) ), file(yellow_1,fc6_yellow_1), []). fof(fc6_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v13_waybel_0(k3_subset_1(u1_struct_0(A),B),A) ) ), file(yellow_6,fc6_yellow_6), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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(fc7_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v12_waybel_0(k3_subset_1(u1_struct_0(A),B),A) ) ), file(yellow_6,fc7_yellow_6), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). 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_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k6_waybel_0(A,B)) & v1_waybel_0(k6_waybel_0(A,B),A) ) ) ), file(waybel_0,fc9_waybel_0), []). fof(fc9_waybel_8,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc9_waybel_8), []). fof(fc9_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(k2_yellow_1(u1_pre_topc(A))) & v1_orders_2(k2_yellow_1(u1_pre_topc(A))) & v2_orders_2(k2_yellow_1(u1_pre_topc(A))) & v3_orders_2(k2_yellow_1(u1_pre_topc(A))) & v4_orders_2(k2_yellow_1(u1_pre_topc(A))) & v1_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v2_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v3_yellow_0(k2_yellow_1(u1_pre_topc(A))) & v1_lattice3(k2_yellow_1(u1_pre_topc(A))) & v2_lattice3(k2_yellow_1(u1_pre_topc(A))) & v3_lattice3(k2_yellow_1(u1_pre_topc(A))) & ~ v3_realset2(k2_yellow_1(u1_pre_topc(A))) ) ) ), file(yellow_1,fc9_yellow_1), []). fof(fraenkel_a_2_0_waybel14,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_waybel_0(B,D) & r2_hidden(D,C) ) ) ) ), file(waybel14,a_2_0_waybel14), []). fof(fraenkel_a_2_0_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) ), file(waybel_3,a_2_0_waybel_3), []). fof(fraenkel_a_2_10_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_10_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_waybel_0(B,D) & r2_hidden(D,C) ) ) ) ), file(waybel14,a_2_10_waybel14), []). fof(fraenkel_a_2_2_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) & v2_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_waybel_0(B,D) & r2_hidden(D,C) ) ) ) ), file(waybel14,a_2_2_waybel14), []). fof(fraenkel_a_2_9_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,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_9_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(B)) ) ) ) ), file(waybel14,a_2_9_waybel14), []). 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(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(involutiveness_k7_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k7_setfam_1(A,k7_setfam_1(A,B)) = B ) ), file(setfam_1,k7_setfam_1), []). fof(l26_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] : ( ( v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k5_waybel11(A))))) => ( ( C = a_2_2_waybel14(A,B) & D = k7_setfam_1(u1_struct_0(A),C) ) => v1_waybel_0(D,k2_yellow_1(k5_waybel11(A))) ) ) ) ) ) ), file(waybel14,l26_waybel14), []). 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_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_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). 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_waybel11,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) ) ) ), file(waybel11,rc1_waybel11), []). 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_waybel_6,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel_1(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ), file(waybel_6,rc1_waybel_6), []). 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_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(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_waybel11,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))) & v2_waybel11(B,A) & v3_waybel11(B,A) ) ) ), file(waybel11,rc4_waybel11), []). 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_waybel11,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))) & v12_waybel_0(B,A) & v13_waybel_0(B,A) & v1_waybel11(B,A) & v2_waybel11(B,A) ) ) ), file(waybel11,rc6_waybel11), []). 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_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_k1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => k1_struct_0(A,B) = k1_tarski(B) ) ), file(struct_0,k1_struct_0), []). fof(redefinition_k1_yellow_1,axiom,( ! [A] : k1_yellow_1(A) = k1_wellord2(A) ), file(yellow_1,k1_yellow_1), []). fof(redefinition_k5_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A,B) = k3_tarski(B) ) ), file(setfam_1,k5_setfam_1), []). fof(redefinition_k6_setfam_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k6_setfam_1(A,B) = k1_setfam_1(B) ) ), file(setfam_1,k6_setfam_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(t10_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r2_hidden(C,B) <=> r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) ) ) ) ) ), file(yellow_6,t10_yellow_6), []). fof(t12_tops_2,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( B != k1_xboole_0 => k5_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k6_setfam_1(A,B)) ) ) ), file(tops_2,t12_tops_2), []). fof(t12_waybel11,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v24_waybel_0(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_pre_topc(k3_subset_1(u1_struct_0(A),k6_waybel_0(A,B)),A) ) ) ), file(waybel11,t12_waybel11), []). fof(t14_yellow_8,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(k3_subset_1(u1_struct_0(A),C),k7_setfam_1(u1_struct_0(A),B)) <=> r2_hidden(C,B) ) ) ) ) ), file(yellow_8,t14_yellow_8), []). fof(t15_waybel14,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k6_waybel_0(A,k2_yellow_0(A,B)) = k1_setfam_1(a_2_0_waybel14(A,B)) ) ) ), file(waybel14,t15_waybel14), []). fof(t17_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(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(C,k6_waybel_0(A,B)) <=> r1_orders_2(A,C,B) ) ) ) ) ), file(waybel_0,t17_waybel_0), []). 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_yellow_1,axiom,( ! [A] : ( u1_struct_0(k2_yellow_1(A)) = A & u1_orders_2(k2_yellow_1(A)) = k1_yellow_1(A) ) ), file(yellow_1,t1_yellow_1), []). fof(t21_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(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)) => ( r1_orders_2(A,B,C) => r1_tarski(k6_waybel_0(A,B),k6_waybel_0(A,C)) ) ) ) ) ), file(waybel_0,t21_waybel_0), []). fof(t21_yellow_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_yellow_8(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) => ( v3_pre_topc(D,A) & r2_hidden(B,D) ) ) ) ) ) ) ), file(yellow_8,t21_yellow_8), []). fof(t22_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_pre_topc(A))))) => k1_yellow_0(k2_yellow_1(u1_pre_topc(A)),B) = k3_tarski(B) ) ) ), file(yellow_1,t22_yellow_1), []). fof(t23_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) ) => k5_waybel11(A) = u1_pre_topc(A) ) ), file(waybel14,t23_waybel14), []). fof(t24_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))) => ( r2_hidden(B,k5_waybel11(A)) <=> v3_pre_topc(B,A) ) ) ) ), file(waybel14,t24_waybel14), []). fof(t25_orders_2,axiom,( ! [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_orders_2(A,B,C) & r1_orders_2(A,C,B) ) => B = C ) ) ) ) ), file(orders_2,t25_orders_2), []). 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(t31_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(B,C) <=> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) ) ) ) ), file(subset_1,t31_subset_1), []). fof(t32_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( B = k1_yellow_0(A,C) <=> ( r2_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,C,D) => r1_orders_2(A,B,D) ) ) ) ) ) ) ), file(yellow_0,t32_yellow_0), []). fof(t33_yellow_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v4_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( B = k2_yellow_0(A,C) <=> ( r1_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,C,D) => r1_orders_2(A,D,B) ) ) ) ) ) ) ), file(yellow_0,t33_yellow_0), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) => ( r3_orders_2(k2_yellow_1(A),B,C) <=> r1_tarski(B,C) ) ) ) ) ), file(yellow_1,t3_yellow_1), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t54_waybel_4,axiom,( ! [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) & 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) <=> ! [D] : ( ( ~ v1_xboole_0(D) & v1_waybel_0(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r1_waybel_3(A,B,E) ) ) ) ) ) ) ) ) ), file(waybel_4,t54_waybel_4), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_waybel_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,k1_waybel_3(A,C)) <=> r1_waybel_3(A,B,C) ) ) ) ) ), file(waybel_3,t7_waybel_3), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []).