% Mizar problem: t43_waybel19,waybel19,1771,29 fof(t43_waybel19,conjecture,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_pre_topc(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v2_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k11_yellow_6(A,k3_yellow_9(A,B)) = k1_struct_0(A,k2_yellow_0(A,B)) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v6_waybel_0,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_yellow_3,cc1_yellow_9,cc20_membered,cc2_finset_1,cc2_lattice3,cc2_membered,cc2_yellow_3,cc2_yellow_9,cc3_membered,cc3_waybel19,cc3_waybel_0,cc3_yellow_3,cc3_yellow_9,cc4_membered,cc4_waybel11,cc4_waybel_0,cc4_yellow_9,cc5_yellow_9,cc6_yellow_9,cc7_yellow_6,cc9_waybel_0,commutativity_k2_xboole_0,d10_xboole_0,d11_waybel_0,d12_waybel11,d17_waybel_0,d18_waybel_0,d1_tarski,d20_waybel_0,d2_xboole_0,d2_yellow_9,d3_tarski,d3_yellow_9,d4_waybel11,d4_yellow_9,d5_lattice3,d5_pre_topc,d6_lattice3,d8_lattice3,d8_waybel_0,dt_g1_orders_2,dt_g1_pre_topc,dt_g1_waybel_0,dt_k11_yellow_6,dt_k14_yellow_6,dt_k1_funct_1,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_waybel_0,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_yellow_9,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_waybel11,dt_k2_xboole_0,dt_k2_yellow_0,dt_k2_yellow_9,dt_k2_zfmisc_1,dt_k3_subset_1,dt_k3_waybel_0,dt_k3_waybel_9,dt_k3_yellow_9,dt_k4_relat_1,dt_k4_waybel_0,dt_k4_waybel_9,dt_k5_waybel11,dt_k5_waybel_0,dt_k5_yellow_0,dt_k6_pre_topc,dt_k6_relat_1,dt_k6_relset_1,dt_k6_waybel_0,dt_k7_lattice3,dt_k7_waybel_0,dt_k7_waybel_9,dt_k8_lattice3,dt_k8_yellow_2,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_0,dt_l1_waybel_9,dt_m1_relset_1,dt_m1_subset_1,dt_m1_yellow_0,dt_m1_yellow_9,dt_m2_cantor_1,dt_m2_relset_1,dt_m4_yellow_6,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,dt_u1_waybel_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_0,existence_l1_waybel_9,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m1_yellow_9,existence_m2_cantor_1,existence_m2_relset_1,existence_m4_yellow_6,fc10_membered,fc10_waybel_0,fc10_waybel_9,fc11_membered,fc11_waybel_0,fc11_waybel_9,fc12_waybel11,fc12_waybel_0,fc12_waybel_9,fc13_waybel11,fc13_waybel_0,fc13_waybel_9,fc13_yellow_3,fc14_finset_1,fc14_waybel_0,fc14_waybel_9,fc15_waybel_9,fc15_yellow_6,fc16_waybel_0,fc16_waybel_9,fc17_waybel_0,fc17_waybel_9,fc18_waybel_9,fc19_waybel_9,fc1_finset_1,fc1_struct_0,fc1_subset_1,fc1_yellow_9,fc20_waybel_9,fc22_membered,fc23_membered,fc24_membered,fc24_yellow_6,fc25_membered,fc25_yellow_6,fc26_membered,fc27_waybel_9,fc28_waybel_9,fc29_waybel_9,fc2_subset_1,fc2_yellow_9,fc30_waybel_9,fc31_waybel_9,fc3_waybel11,fc3_yellow_9,fc4_subset_1,fc4_yellow_9,fc5_lattice3,fc5_waybel11,fc5_yellow12,fc5_yellow_3,fc5_yellow_9,fc6_lattice3,fc6_membered,fc6_waybel11,fc6_waybel_0,fc6_yellow12,fc6_yellow_3,fc6_yellow_6,fc6_yellow_9,fc7_membered,fc7_waybel_0,fc7_yellow_6,fc7_yellow_9,fc8_membered,fc8_waybel_0,fc8_waybel_9,fc8_yellow_9,fc9_finset_1,fc9_membered,fc9_waybel_0,fc9_waybel_9,fc9_yellow_9,fraenkel_a_1_11_waybel19,free_g1_orders_2,free_g1_pre_topc,free_g1_waybel_0,idempotence_k2_xboole_0,involutiveness_k3_subset_1,involutiveness_k4_relat_1,involutiveness_k6_relset_1,rc10_waybel_0,rc11_waybel_0,rc13_waybel_0,rc1_finset_1,rc1_lattice3,rc1_membered,rc1_subset_1,rc1_waybel11,rc1_waybel_0,rc1_yellow_3,rc2_lattice3,rc2_subset_1,rc2_waybel_0,rc3_finset_1,rc3_struct_0,rc4_finset_1,rc4_waybel11,rc4_waybel_0,rc4_yellow_6,rc5_struct_0,rc5_waybel_0,rc6_waybel11,rc6_waybel_0,rc7_waybel11,rc7_waybel_0,rc8_waybel_0,rc9_waybel_0,redefinition_k1_struct_0,redefinition_k1_waybel_0,redefinition_k6_relset_1,redefinition_k8_yellow_2,redefinition_m2_relset_1,redefinition_r3_orders_2,reflexivity_r1_tarski,reflexivity_r3_orders_2,t17_waybel_0,t18_waybel_0,t1_boole,t1_subset,t1_yellow_9,t24_waybel_9,t24_yellow_2,t25_orders_2,t25_waybel19,t25_waybel_0,t26_orders_2,t26_waybel19,t27_waybel19,t2_subset,t2_tarski,t2_yellow_2,t30_waybel19,t33_yellow_0,t37_zfmisc_1,t38_waybel19,t3_subset,t49_pre_topc,t4_subset,t51_yellow_9,t52_pre_topc,t5_subset,t60_yellow_0,t6_boole,t71_relat_1,t7_boole,t7_yellow_9,t8_boole,t9_lattice3]), [file(waybel19,t43_waybel19)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(abstractness_v1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(A) => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ), file(pre_topc,v1_pre_topc), []). fof(abstractness_v6_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v6_waybel_0(B,A) => B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) ) ) ), file(waybel_0,v6_waybel_0), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_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_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(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_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_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). 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_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & v8_waybel_0(B,A) ) => ( ~ v3_struct_0(B) & v7_waybel_0(B) & v10_waybel_0(B,A) ) ) ) ) ), file(waybel_0,cc3_waybel_0), []). fof(cc3_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_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_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => ( ( ~ v3_struct_0(B) & v7_waybel_0(B) & v9_waybel_0(B,A) ) => ( ~ v3_struct_0(B) & v7_waybel_0(B) & v11_waybel_0(B,A) ) ) ) ) ), file(waybel_0,cc4_waybel_0), []). fof(cc4_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_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_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_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => v1_relat_1(B) ) ) ), file(yellow_6,cc7_yellow_6), []). fof(cc9_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v1_lattice3(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc9_waybel_0), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d11_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r1_waybel_0(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,D,E) => r2_hidden(k3_waybel_0(A,B,E),C) ) ) ) ) ) ) ), file(waybel_0,d11_waybel_0), []). fof(d12_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => k5_waybel11(A) = u1_pre_topc(k14_yellow_6(A,k2_waybel11(A))) ) ), file(waybel11,d12_waybel11), []). 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(d18_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_0(A,B) = k5_waybel_0(A,k1_struct_0(A,B)) ) ) ), file(waybel_0,d18_waybel_0), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d20_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v13_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r1_orders_2(A,C,D) ) => r2_hidden(D,B) ) ) ) ) ) ) ), file(waybel_0,d20_waybel_0), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d2_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k2_yellow_9(A,B) = k7_waybel_9(k5_yellow_0(A,B),A,k1_yellow_9(A,k5_yellow_0(A,B)),k3_waybel_9(k5_yellow_0(A,B))) ) ) ), file(yellow_9,d2_yellow_9), []). 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_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k3_yellow_9(A,B) = k7_waybel_9(k5_yellow_0(A,B),A,k1_yellow_9(A,k5_yellow_0(A,B)),k4_waybel_9(k5_yellow_0(A,B))) ) ) ), file(yellow_9,d3_yellow_9), []). fof(d4_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_waybel_9(A) ) => ( v4_waybel11(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> ( v1_waybel11(B,A) & v13_waybel_0(B,A) ) ) ) ) ) ), file(waybel11,d4_waybel11), []). 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_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => k7_lattice3(A) = g1_orders_2(u1_struct_0(A),k6_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A))) ) ), file(lattice3,d5_lattice3), []). 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(d6_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_lattice3(A,B) = B ) ) ), file(lattice3,d6_lattice3), []). 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_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_waybel_0(A,B,C) = k1_waybel_0(B,A,u1_waybel_0(A,B),C) ) ) ) ), file(waybel_0,d8_waybel_0), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(pre_topc,g1_pre_topc), []). fof(dt_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( v6_waybel_0(g1_waybel_0(A,B,C,D),A) & l1_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,g1_waybel_0), []). fof(dt_k11_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(k11_yellow_6(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(yellow_6,k11_yellow_6), []). fof(dt_k14_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( v1_pre_topc(k14_yellow_6(A,B)) & l1_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,k14_yellow_6), []). 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_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k1_struct_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(struct_0,k1_struct_0), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ), file(waybel_0,k1_waybel_0), []). fof(dt_k1_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_9,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ( v1_funct_1(k1_yellow_9(A,B)) & v1_funct_2(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(yellow_9,k1_yellow_9), []). 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_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => m4_yellow_6(k2_waybel11(A),A) ) ), file(waybel11,k2_waybel11), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). 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_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k2_yellow_9(A,B)) & v6_waybel_0(k2_yellow_9(A,B),A) & l1_waybel_0(k2_yellow_9(A,B),A) ) ) ), file(yellow_9,k2_yellow_9), []). 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_waybel_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)) ) ), file(waybel_0,k3_waybel_0), []). fof(dt_k3_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ( v6_waybel_0(k3_waybel_9(A),A) & l1_waybel_0(k3_waybel_9(A),A) ) ) ), file(waybel_9,k3_waybel_9), []). fof(dt_k3_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) & l1_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(yellow_9,k3_yellow_9), []). fof(dt_k4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k4_relat_1(A)) ) ), file(relat_1,k4_relat_1), []). 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_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ( v6_waybel_0(k4_waybel_9(A),A) & l1_waybel_0(k4_waybel_9(A),A) ) ) ), file(waybel_9,k4_waybel_9), []). fof(dt_k5_waybel11,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => m1_subset_1(k5_waybel11(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(waybel11,k5_waybel11), []). fof(dt_k5_waybel_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k5_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k5_waybel_0), []). fof(dt_k5_yellow_0,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_orders_2(k5_yellow_0(A,B)) & v4_yellow_0(k5_yellow_0(A,B),A) & m1_yellow_0(k5_yellow_0(A,B),A) ) ) ), file(yellow_0,k5_yellow_0), []). fof(dt_k6_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k6_pre_topc), []). fof(dt_k6_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), []). fof(dt_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m2_relset_1(k6_relset_1(A,B,C),B,A) ) ), file(relset_1,k6_relset_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_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)) ) ) ), file(lattice3,k7_lattice3), []). fof(dt_k7_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k7_waybel_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(waybel_0,k7_waybel_0), []). fof(dt_k7_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & l1_waybel_0(D,A) ) => ( v6_waybel_0(k7_waybel_9(A,B,C,D),B) & l1_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,k7_waybel_9), []). fof(dt_k8_lattice3,axiom,( ! [A,B] : ( ( l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k8_lattice3(A,B),u1_struct_0(k7_lattice3(A))) ) ), file(lattice3,k8_lattice3), []). fof(dt_k8_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ), file(yellow_2,k8_yellow_2), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => l1_orders_2(B) ) ) ), file(waybel_0,l1_waybel_0), []). fof(dt_l1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( l1_pre_topc(A) & l1_orders_2(A) ) ) ), file(waybel_9,l1_waybel_9), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) ), file(yellow_0,m1_yellow_0), []). fof(dt_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_9(B,A) => l1_waybel_9(B) ) ) ), file(yellow_9,m1_yellow_9), []). fof(dt_m2_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_cantor_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(cantor_1,m2_cantor_1), []). fof(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), []). fof(dt_m4_yellow_6,axiom,( $true ), file(yellow_6,m4_yellow_6), []). 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(dt_u1_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(waybel_0,u1_waybel_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_waybel_0(B,A) ) ), file(waybel_0,l1_waybel_0), []). fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) ), file(waybel_9,l1_waybel_9), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) ), file(yellow_0,m1_yellow_0), []). fof(existence_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_9(B,A) ) ), file(yellow_9,m1_yellow_9), []). fof(existence_m2_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m2_cantor_1(B,A) ) ), file(cantor_1,m2_cantor_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m4_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : m4_yellow_6(B,A) ) ), file(yellow_6,m4_yellow_6), []). 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_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k7_waybel_0(A,B)) & v2_waybel_0(k7_waybel_0(A,B),A) ) ) ), file(waybel_0,fc10_waybel_0), []). fof(fc10_waybel_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v4_orders_2(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) ), file(waybel_9,fc10_waybel_9), []). 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_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v3_orders_2(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) ), file(waybel_9,fc11_waybel_9), []). fof(fc12_waybel11,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_relat_1(k2_waybel11(A)) & v4_yellow_6(k2_waybel11(A),A) ) ) ), file(waybel11,fc12_waybel11), []). 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_9,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) & v7_waybel_0(k3_waybel_9(A)) ) ) ), file(waybel_9,fc12_waybel_9), []). fof(fc13_waybel11,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_relat_1(k2_waybel11(A)) & v4_yellow_6(k2_waybel11(A),A) & v5_yellow_6(k2_waybel11(A),A) ) ) ), file(waybel11,fc13_waybel11), []). 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(fc13_waybel_9,axiom,( ! [A] : ( ( v7_waybel_0(A) & l1_orders_2(A) ) => ( v6_waybel_0(k3_waybel_9(A),A) & v7_waybel_0(k3_waybel_9(A)) ) ) ), file(waybel_9,fc13_waybel_9), []). 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(fc14_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v13_waybel_0(k7_waybel_0(A,B),A) ) ), file(waybel_0,fc14_waybel_0), []). fof(fc14_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) & v8_waybel_0(k3_waybel_9(A),A) & v10_waybel_0(k3_waybel_9(A),A) ) ) ), file(waybel_9,fc14_waybel_9), []). fof(fc15_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k4_waybel_9(A)) & v6_waybel_0(k4_waybel_9(A),A) ) ) ), file(waybel_9,fc15_waybel_9), []). fof(fc15_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ( ~ v1_xboole_0(u1_waybel_0(A,B)) & v1_relat_1(u1_waybel_0(A,B)) & v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(yellow_6,fc15_yellow_6), []). fof(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(fc16_waybel_9,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ( v2_orders_2(k4_waybel_9(A)) & v6_waybel_0(k4_waybel_9(A),A) ) ) ), file(waybel_9,fc16_waybel_9), []). fof(fc17_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_waybel_0(k5_waybel_0(A,B),A) & v13_waybel_0(k5_waybel_0(A,B),A) ) ) ), file(waybel_0,fc17_waybel_0), []). fof(fc17_waybel_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v4_orders_2(k4_waybel_9(A)) & v6_waybel_0(k4_waybel_9(A),A) ) ) ), file(waybel_9,fc17_waybel_9), []). fof(fc18_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v3_orders_2(k4_waybel_9(A)) & v6_waybel_0(k4_waybel_9(A),A) ) ) ), file(waybel_9,fc18_waybel_9), []). fof(fc19_waybel_9,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k4_waybel_9(A)) & v6_waybel_0(k4_waybel_9(A),A) & v7_waybel_0(k4_waybel_9(A)) ) ) ), file(waybel_9,fc19_waybel_9), []). 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_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & m1_yellow_0(B,A) ) => ( v1_relat_1(k1_yellow_9(A,B)) & v1_funct_1(k1_yellow_9(A,B)) & ~ v1_xboole_0(k1_yellow_9(A,B)) & v1_funct_2(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A)) & v1_partfun1(k1_yellow_9(A,B),u1_struct_0(B),u1_struct_0(A)) & v5_orders_3(k1_yellow_9(A,B),B,A) ) ) ), file(yellow_9,fc1_yellow_9), []). fof(fc20_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k4_waybel_9(A)) & v6_waybel_0(k4_waybel_9(A),A) & v9_waybel_0(k4_waybel_9(A),A) & v11_waybel_0(k4_waybel_9(A),A) ) ) ), file(waybel_9,fc20_waybel_9), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). fof(fc23_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc24_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( ~ v3_struct_0(k14_yellow_6(A,B)) & v1_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,fc24_yellow_6), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc25_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( ~ v3_struct_0(k14_yellow_6(A,B)) & v1_pre_topc(k14_yellow_6(A,B)) & v2_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,fc25_yellow_6), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(fc27_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & ~ v3_struct_0(D) & l1_waybel_0(D,A) ) => ( ~ v3_struct_0(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc27_waybel_9), []). fof(fc28_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v2_orders_2(D) & l1_waybel_0(D,A) ) => ( v2_orders_2(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc28_waybel_9), []). fof(fc29_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v4_orders_2(D) & l1_waybel_0(D,A) ) => ( v4_orders_2(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc29_waybel_9), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k2_yellow_9(A,B)) & v2_orders_2(k2_yellow_9(A,B)) & v6_waybel_0(k2_yellow_9(A,B),A) ) ) ), file(yellow_9,fc2_yellow_9), []). fof(fc30_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v3_orders_2(D) & l1_waybel_0(D,A) ) => ( v3_orders_2(k7_waybel_9(A,B,C,D)) & v6_waybel_0(k7_waybel_9(A,B,C,D),B) ) ) ), file(waybel_9,fc30_waybel_9), []). fof(fc31_waybel_9,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ( v6_waybel_0(k7_waybel_9(A,B,C,D),B) & v7_waybel_0(k7_waybel_9(A,B,C,D)) ) ) ), file(waybel_9,fc31_waybel_9), []). fof(fc3_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_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v2_orders_2(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(yellow_9,fc3_yellow_9), []). fof(fc4_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_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k2_yellow_9(A,B)) & v3_orders_2(k2_yellow_9(A,B)) & v6_waybel_0(k2_yellow_9(A,B),A) ) ) ), file(yellow_9,fc4_yellow_9), []). fof(fc5_lattice3,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v2_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)) ) ) ), file(lattice3,fc5_lattice3), []). 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_yellow12,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_pre_topc(A) ) => ( ~ v3_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ), file(yellow12,fc5_yellow12), []). 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(fc5_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v3_orders_2(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) ) ) ), file(yellow_9,fc5_yellow_9), []). fof(fc6_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)) ) ) ), file(lattice3,fc6_lattice3), []). 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_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & ~ v1_xboole_0(B) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( ~ v3_struct_0(g1_waybel_0(A,B,C,D)) & v6_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,fc6_waybel_0), []). fof(fc6_yellow12,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) & v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) ) ) ), file(yellow12,fc6_yellow12), []). 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(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(fc6_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_orders_2(k5_yellow_0(A,B)) & v2_orders_2(k5_yellow_0(A,B)) & v4_yellow_0(k5_yellow_0(A,B),A) & v7_waybel_0(k5_yellow_0(A,B)) ) ) ), file(yellow_9,fc6_yellow_9), []). 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_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(fc7_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k2_yellow_9(A,B)) & v2_orders_2(k2_yellow_9(A,B)) & v6_waybel_0(k2_yellow_9(A,B),A) & v7_waybel_0(k2_yellow_9(A,B)) ) ) ), file(yellow_9,fc7_yellow_9), []). 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_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_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) ), file(waybel_9,fc8_waybel_9), []). fof(fc8_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k4_waybel_9(k5_yellow_0(A,B))) & v2_orders_2(k4_waybel_9(k5_yellow_0(A,B))) & v6_waybel_0(k4_waybel_9(k5_yellow_0(A,B)),k5_yellow_0(A,B)) & v7_waybel_0(k4_waybel_9(k5_yellow_0(A,B))) & v9_waybel_0(k4_waybel_9(k5_yellow_0(A,B)),k5_yellow_0(A,B)) & v11_waybel_0(k4_waybel_9(k5_yellow_0(A,B)),k5_yellow_0(A,B)) ) ) ), file(yellow_9,fc8_yellow_9), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). 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_9,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => ( v2_orders_2(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) ), file(waybel_9,fc9_waybel_9), []). fof(fc9_yellow_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v3_struct_0(k3_yellow_9(A,B)) & v2_orders_2(k3_yellow_9(A,B)) & v6_waybel_0(k3_yellow_9(A,B),A) & v7_waybel_0(k3_yellow_9(A,B)) ) ) ), file(yellow_9,fc9_yellow_9), []). fof(fraenkel_a_1_11_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_11_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k7_waybel_0(B,C)) ) ) ) ), file(waybel19,a_1_11_waybel19), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). fof(free_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ! [E,F,G,H] : ( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(waybel_0,g1_waybel_0), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). 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_k4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k4_relat_1(k4_relat_1(A)) = A ) ), file(relat_1,k4_relat_1), []). fof(involutiveness_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k6_relset_1(A,B,k6_relset_1(A,B,C)) = C ) ), file(relset_1,k6_relset_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(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_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_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(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(rc4_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) ) ) ), file(waybel_0,rc4_waybel_0), []). fof(rc4_yellow_6,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v7_waybel_0(A) ) ), file(yellow_6,rc4_yellow_6), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(rc5_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) ) ) ), file(waybel_0,rc5_waybel_0), []). fof(rc6_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(rc6_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) & v9_waybel_0(B,A) & v10_waybel_0(B,A) & v11_waybel_0(B,A) ) ) ), file(waybel_0,rc6_waybel_0), []). fof(rc7_waybel11,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] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) & v10_waybel_0(B,A) ) ) ), file(waybel11,rc7_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_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => k1_waybel_0(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_0,k1_waybel_0), []). fof(redefinition_k6_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k6_relset_1(A,B,C) = k4_relat_1(C) ) ), file(relset_1,k6_relset_1), []). fof(redefinition_k8_yellow_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(B)) & m1_relset_1(C,A,u1_struct_0(B)) ) => k8_yellow_2(A,B,C) = k2_relat_1(C) ) ), file(yellow_2,k8_yellow_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r3_orders_2(A,B,C) <=> r1_orders_2(A,B,C) ) ) ), file(orders_2,r3_orders_2), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r3_orders_2(A,B,B) ) ), file(orders_2,r3_orders_2), []). fof(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(t18_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,k7_waybel_0(A,B)) <=> r1_orders_2(A,B,C) ) ) ) ) ), file(waybel_0,t18_waybel_0), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_yellow_9,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,k3_subset_1(u1_struct_0(A),k7_waybel_0(A,B))) <=> ~ r1_orders_2(A,B,C) ) ) ) ) ), file(yellow_9,t1_yellow_9), []). fof(t24_waybel_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( r2_hidden(B,k11_yellow_6(A,C)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k8_yellow_2(u1_struct_0(C),A,u1_waybel_0(A,C)) => r2_hidden(B,k6_pre_topc(A,D)) ) ) ) ) ) ) ), file(waybel_9,t24_waybel_9), []). fof(t24_yellow_2,axiom,( ! [A,B] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r2_hidden(C,A) => ( r3_orders_2(B,C,k1_yellow_0(B,A)) & r3_orders_2(B,k2_yellow_0(B,A),C) ) ) ) ) ), file(yellow_2,t24_yellow_2), []). 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(t25_waybel19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_cantor_1(B,A) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(D,E) & r2_hidden(E,B) ) => r1_waybel_0(A,C,E) ) ) => r2_hidden(D,k11_yellow_6(A,C)) ) ) ) ) ) ), file(waybel19,t25_waybel19), []). fof(t25_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 => ( ( v12_waybel_0(C,A) => v12_waybel_0(D,B) ) & ( v13_waybel_0(C,A) => v13_waybel_0(D,B) ) ) ) ) ) ) ) ) ), file(waybel_0,t25_waybel_0), []). fof(t26_orders_2,axiom,( ! [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)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,D) ) => r1_orders_2(A,B,D) ) ) ) ) ) ), file(orders_2,t26_orders_2), []). fof(t26_waybel19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_waybel_0(A,B,C) => r1_tarski(k11_yellow_6(A,B),k6_pre_topc(A,C)) ) ) ) ) ), file(waybel19,t26_waybel19), []). fof(t27_waybel19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( u1_waybel_0(A,k2_yellow_9(A,B)) = k6_relat_1(B) & u1_waybel_0(A,k3_yellow_9(A,B)) = k6_relat_1(B) ) ) ) ), file(waybel19,t27_waybel19), []). 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_yellow_2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,k7_waybel_0(A,B)) <=> r1_lattice3(A,C,B) ) ) ) ) ), file(yellow_2,t2_yellow_2), []). fof(t30_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) ) => m2_cantor_1(k2_xboole_0(k5_waybel11(A),a_1_11_waybel19(A)),A) ) ), file(waybel19,t30_waybel19), []). 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(t37_zfmisc_1,axiom,( ! [A,B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) ), file(zfmisc_1,t37_zfmisc_1), []). fof(t38_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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_pre_topc(k7_waybel_0(A,B),A) & v4_pre_topc(k6_waybel_0(A,B),A) & v4_pre_topc(k1_struct_0(A,B),A) ) ) ) ), file(waybel19,t38_waybel19), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t49_pre_topc,axiom,( ! [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))) => ( r1_tarski(B,C) => r1_tarski(k6_pre_topc(A,B),k6_pre_topc(A,C)) ) ) ) ) ), file(pre_topc,t49_pre_topc), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t51_yellow_9,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => u1_pre_topc(B) = k5_waybel11(A) ) ) ), file(yellow_9,t51_yellow_9), []). fof(t52_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_pre_topc(B,A) => k6_pre_topc(A,B) = B ) & ( ( v2_pre_topc(A) & k6_pre_topc(A,B) = B ) => v4_pre_topc(B,A) ) ) ) ) ), file(pre_topc,t52_pre_topc), []). 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(t60_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,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)) => ( ( E = C & F = D & r1_orders_2(B,E,F) ) => r1_orders_2(A,C,D) ) ) ) ) ) ) ) ), file(yellow_0,t60_yellow_0), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t71_relat_1,axiom,( ! [A] : ( k1_relat_1(k6_relat_1(A)) = A & k2_relat_1(k6_relat_1(A)) = A ) ), file(relat_1,t71_relat_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( u1_struct_0(k3_yellow_9(A,B)) = B & v4_yellow_0(k3_yellow_9(A,B),k7_lattice3(A)) & m1_yellow_0(k3_yellow_9(A,B),k7_lattice3(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_9(A,B))) => k3_waybel_0(A,k3_yellow_9(A,B),C) = C ) ) ) ) ), file(yellow_9,t7_yellow_9), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r1_orders_2(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B)) ) ) ) ) ), file(lattice3,t9_lattice3), []).