% Mizar problem: t16_waybel18,waybel18,2018,69 fof(t16_waybel18,conjecture,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1)))) ) => u1_pre_topc(B) = u1_pre_topc(k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v3_lattices,antisymmetry_r2_hidden,cc10_waybel_0,cc11_waybel_0,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc1_funct_1,cc1_lattice3,cc1_monoid_0,cc1_relset_1,cc1_waybel18,cc1_waybel_8,cc1_yellow_1,cc1_yellow_9,cc2_funct_1,cc2_lattice3,cc2_waybel_8,cc2_yellow_9,cc3_yellow_9,cc4_waybel11,cc4_waybel_3,cc4_yellow_9,cc5_waybel_3,cc5_yellow_9,cc6_yellow_9,cc8_waybel_0,cc9_waybel_0,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k3_xboole_0,commutativity_k4_subset_1,commutativity_k5_subset_1,d10_xboole_0,d12_funct_1,d13_pralg_1,d18_waybel_0,d1_funct_2,d1_lattice3,d1_tarski,d1_waybel_8,d2_funcop_1,d2_lattice3,d2_tarski,d2_yellow_1,d3_funct_3,d3_pboole,d3_tarski,d3_waybel18,d4_cantor_1,d4_yellow_1,d4_yellow_9,d5_card_3,d5_funct_1,d9_waybel18,dt_g1_orders_2,dt_g1_pre_topc,dt_g3_lattices,dt_k12_pralg_1,dt_k1_binop_1,dt_k1_enumset1,dt_k1_funct_1,dt_k1_lattice3,dt_k1_relat_1,dt_k1_struct_0,dt_k1_tarski,dt_k1_waybel_0,dt_k1_waybel_8,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_cantor_1,dt_k2_funcop_1,dt_k2_funct_7,dt_k2_lattice3,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_tarski,dt_k2_waybel18,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_lattice3,dt_k3_waybel18,dt_k3_xboole_0,dt_k3_yellow_1,dt_k4_card_3,dt_k4_funct_3,dt_k4_relset_1,dt_k4_subset_1,dt_k4_waybel_0,dt_k5_funct_3,dt_k5_subset_1,dt_k5_waybel_0,dt_k5_yellow_1,dt_k6_waybel_3,dt_k7_waybel_0,dt_k8_setfam_1,dt_k8_yellow_2,dt_k9_filter_1,dt_k9_relat_1,dt_k9_waybel18,dt_l1_lattices,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_9,dt_l2_lattices,dt_l3_lattices,dt_m1_cantor_1,dt_m1_pboole,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_u1_lattices,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,dt_u2_lattices,existence_l1_lattices,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_9,existence_l2_lattices,existence_l3_lattices,existence_m1_cantor_1,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m1_yellow_0,existence_m1_yellow_9,existence_m2_cantor_1,existence_m2_relset_1,fc10_waybel18,fc10_waybel_0,fc10_waybel_8,fc10_yellow_1,fc11_waybel18,fc11_waybel_0,fc11_waybel_8,fc12_waybel18,fc12_waybel_0,fc13_waybel18,fc14_waybel18,fc14_waybel_0,fc14_waybel_8,fc17_waybel_0,fc1_funcop_1,fc1_lattice3,fc1_struct_0,fc1_subset_1,fc1_waybel18,fc1_waybel_8,fc1_xboole_0,fc1_yellow_1,fc2_funcop_1,fc2_lattice3,fc2_subset_1,fc2_waybel18,fc2_xboole_0,fc2_yellow_1,fc3_card_3,fc3_funcop_1,fc3_lattice3,fc3_subset_1,fc3_waybel_8,fc3_xboole_0,fc3_yellow_1,fc4_card_3,fc4_lattice3,fc4_subset_1,fc4_waybel_8,fc5_card_3,fc5_waybel18,fc5_waybel_8,fc6_funct_1,fc6_waybel18,fc6_waybel_8,fc7_waybel18,fc7_waybel_0,fc7_waybel_3,fc7_waybel_8,fc7_yellow_1,fc8_waybel18,fc8_waybel_0,fc8_waybel_3,fc8_waybel_8,fc8_yellow_1,fc9_funcop_1,fc9_waybel18,fc9_waybel_3,fc9_waybel_8,fraenkel_a_0_42_fraenkel,fraenkel_a_1_0_waybel14,fraenkel_a_1_0_waybel18,fraenkel_a_1_1_waybel18,fraenkel_a_2_0_waybel18,fraenkel_a_2_1_waybel18,free_g1_orders_2,free_g1_pre_topc,free_g3_lattices,idempotence_k2_xboole_0,idempotence_k3_xboole_0,idempotence_k4_subset_1,idempotence_k5_subset_1,rc10_waybel_0,rc13_waybel_0,rc1_funct_1,rc1_lattice3,rc1_monoid_0,rc1_pre_topc,rc1_subset_1,rc1_waybel18,rc1_xboole_0,rc1_yellow_1,rc2_funct_1,rc2_lattice3,rc2_pre_topc,rc2_subset_1,rc2_waybel18,rc2_waybel_3,rc2_xboole_0,rc3_funct_1,rc3_struct_0,rc3_waybel_3,rc5_funct_1,rc5_struct_0,rc7_waybel_0,rc8_waybel_0,redefinition_k1_struct_0,redefinition_k1_waybel_0,redefinition_k2_lattice3,redefinition_k2_pre_circ,redefinition_k4_relset_1,redefinition_k4_subset_1,redefinition_k5_funct_3,redefinition_k5_subset_1,redefinition_k6_waybel_3,redefinition_k8_yellow_2,redefinition_m2_relset_1,redefinition_r3_orders_2,redefinition_r6_pboole,reflexivity_r1_tarski,reflexivity_r3_orders_2,reflexivity_r6_pboole,s21_fraenkel__e20_47_5__waybel18,s3_funct_1__e7_47_6__waybel18,spc0_boole,spc1_boole,spc2_boole,symmetry_r6_pboole,t13_funcop_1,t13_waybel_0,t14_waybel18,t15_waybel18,t17_waybel_8,t18_waybel_0,t195_orders_1,t1_boole,t1_card_5,t1_subset,t1_xboole_1,t23_yellow_9,t26_yellow_9,t28_waybel13,t28_waybel_8,t2_boole,t2_subset,t2_tarski,t2_xboole_1,t2_yellow_1,t30_waybel_8,t30_zfmisc_1,t32_funct_7,t33_funct_7,t34_funct_7,t3_subset,t42_waybel14,t4_subset,t58_setfam_1,t5_subset,t66_waybel_0,t6_boole,t7_boole,t8_boole,t9_funct_1,t9_waybel_8]), [file(waybel18,t16_waybel18)]). 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_v3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( v3_lattices(A) => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ), file(lattices,v3_lattices), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_0,cc10_waybel_0), []). fof(cc11_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_yellow_0(A) ) ) ) ), file(waybel_0,cc11_waybel_0), []). fof(cc12_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(waybel_0,cc12_waybel_0), []). fof(cc13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) ) ) ) ), file(waybel_0,cc13_waybel_0), []). fof(cc14_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc14_waybel_0), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc1_lattice3), []). fof(cc1_monoid_0,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(monoid_0,cc1_monoid_0), []). fof(cc1_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_waybel18,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel18(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) ), file(waybel18,cc1_waybel18), []). fof(cc1_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v2_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ) ) ), file(waybel_8,cc1_waybel_8), []). fof(cc1_yellow_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_yellow_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) ), file(yellow_1,cc1_yellow_1), []). fof(cc1_yellow_9,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ~ v3_struct_0(B) ) ) ), file(yellow_9,cc1_yellow_9), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v3_struct_0(A) ) ) ), file(lattice3,cc2_lattice3), []). fof(cc2_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_8(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v1_waybel_8(A) ) ) ) ), file(waybel_8,cc2_waybel_8), []). fof(cc2_yellow_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_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_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_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_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) ) ) ) ), file(waybel_3,cc5_waybel_3), []). fof(cc5_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(cc8_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) => ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v23_waybel_0(C,A,B) ) => ( v1_funct_1(C) & v2_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) ) ) ), file(waybel_0,cc8_waybel_0), []). fof(cc9_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v1_lattice3(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc9_waybel_0), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), []). fof(commutativity_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k4_subset_1(A,C,B) ) ), file(subset_1,k4_subset_1), []). fof(commutativity_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ), file(subset_1,k5_subset_1), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d12_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( C = k9_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,k1_relat_1(A)) & r2_hidden(E,B) & D = k1_funct_1(A,E) ) ) ) ) ), file(funct_1,d12_funct_1), []). fof(d13_pralg_1,axiom,( ! [A,B] : ( ( v2_pralg_1(B) & m1_pboole(B,A) ) => ! [C] : ( m1_pboole(C,A) => ( C = k12_pralg_1(A,B) <=> ! [D] : ~ ( r2_hidden(D,A) & ! [E] : ( l1_struct_0(E) => ~ ( E = k1_funct_1(B,D) & k1_funct_1(C,D) = u1_struct_0(E) ) ) ) ) ) ) ), file(pralg_1,d13_pralg_1), []). 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_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_lattice3,axiom,( ! [A,B] : ( ( v3_lattices(B) & l3_lattices(B) ) => ( B = k1_lattice3(A) <=> ( u1_struct_0(B) = k1_zfmisc_1(A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( k1_binop_1(u2_lattices(B),C,D) = k4_subset_1(A,C,D) & k1_binop_1(u1_lattices(B),C,D) = k5_subset_1(A,C,D) ) ) ) ) ) ) ), file(lattice3,d1_lattice3), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d1_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_orders_2(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( B = k1_waybel_8(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,u1_struct_0(B)) <=> v1_waybel_3(C,A) ) ) ) ) ) ), file(waybel_8,d1_waybel_8), []). fof(d2_funcop_1,axiom,( ! [A,B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) ), file(funcop_1,d2_funcop_1), []). fof(d2_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)) ) ), file(lattice3,d2_lattice3), []). fof(d2_tarski,axiom,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), []). fof(d2_yellow_1,axiom,( ! [A] : k3_yellow_1(A) = k3_lattice3(k1_lattice3(A)) ), file(yellow_1,d2_yellow_1), []). fof(d3_funct_3,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k4_funct_3(A,B) <=> ( k1_relat_1(C) = B & ! [D] : ( r2_hidden(D,B) => ( ( r2_hidden(D,A) => k1_funct_1(C,D) = 1 ) & ( ~ r2_hidden(D,A) => k1_funct_1(C,D) = 0 ) ) ) ) ) ) ), file(funct_3,d3_funct_3), []). fof(d3_pboole,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_pboole(B,A) <=> k1_relat_1(B) = A ) ) ), file(pboole,d3_pboole), []). 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_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ! [C] : ( ( v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = k3_waybel18(A,B) <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B)) & m2_cantor_1(k2_waybel18(A,B),C) ) ) ) ) ), file(waybel18,d3_waybel18), []). fof(d4_cantor_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 = k2_cantor_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) & r1_tarski(E,B) & v1_finset_1(E) & D = k8_setfam_1(A,E) ) ) ) ) ) ) ), file(cantor_1,d4_cantor_1), []). fof(d4_yellow_1,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & m1_pboole(B,A) ) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k5_yellow_1(A,B) <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( r2_hidden(D,k4_card_3(k12_pralg_1(A,B))) => ( r1_orders_2(C,D,E) <=> ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & F = D & G = E & ! [H] : ~ ( r2_hidden(H,A) & ! [I] : ( l1_orders_2(I) => ! [J] : ( m1_subset_1(J,u1_struct_0(I)) => ! [K] : ( m1_subset_1(K,u1_struct_0(I)) => ~ ( I = k1_funct_1(B,H) & J = k1_funct_1(F,H) & K = k1_funct_1(G,H) & r1_orders_2(I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(yellow_1,d4_yellow_1), []). 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_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k4_card_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & C = D & k1_relat_1(D) = k1_relat_1(A) & ! [E] : ( r2_hidden(E,k1_relat_1(A)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) ), file(card_3,d5_card_3), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d9_waybel18,axiom,( ! [A] : ( ( v1_pre_topc(A) & l1_pre_topc(A) ) => ( A = k9_waybel18 <=> ( u1_struct_0(A) = k2_tarski(0,1) & u1_pre_topc(A) = k1_enumset1(k1_xboole_0,k1_tarski(1),k2_tarski(0,1)) ) ) ) ), file(waybel18,d9_waybel18), []). 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_g3_lattices,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) ) => ( v3_lattices(g3_lattices(A,B,C)) & l3_lattices(g3_lattices(A,B,C)) ) ) ), file(lattices,g3_lattices), []). fof(dt_k12_pralg_1,axiom,( ! [A,B] : ( ( v2_pralg_1(B) & m1_pboole(B,A) ) => m1_pboole(k12_pralg_1(A,B),A) ) ), file(pralg_1,k12_pralg_1), []). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), []). fof(dt_k1_enumset1,axiom,( $true ), file(enumset1,k1_enumset1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_lattice3,axiom,( ! [A] : ( v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)) ) ), file(lattice3,k1_lattice3), []). 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_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) & m1_yellow_0(k1_waybel_8(A),A) ) ) ), file(waybel_8,k1_waybel_8), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_cantor_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k2_cantor_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ), file(cantor_1,k2_cantor_1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). fof(dt_k2_funct_7,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_7(A,B,C)) & v1_funct_1(k2_funct_7(A,B,C)) ) ) ), file(funct_7,k2_funct_7), []). fof(dt_k2_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_relat_2(k2_lattice3(A)) & v4_relat_2(k2_lattice3(A)) & v8_relat_2(k2_lattice3(A)) & v1_partfun1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) & m2_relset_1(k2_lattice3(A),u1_struct_0(A),u1_struct_0(A)) ) ) ), file(lattice3,k2_lattice3), []). fof(dt_k2_pre_circ,axiom,( ! [A,B] : m1_pboole(k2_pre_circ(A,B),A) ), file(pre_circ,k2_pre_circ), []). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_waybel18,axiom,( ! [A,B] : ( ( v1_waybel18(B) & m1_pboole(B,A) ) => m1_subset_1(k2_waybel18(A,B),k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) ) ), file(waybel18,k2_waybel18), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & l1_orders_2(k3_lattice3(A)) ) ) ), file(lattice3,k3_lattice3), []). fof(dt_k3_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ( v1_pre_topc(k3_waybel18(A,B)) & v2_pre_topc(k3_waybel18(A,B)) & l1_pre_topc(k3_waybel18(A,B)) ) ) ), file(waybel18,k3_waybel18), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). fof(dt_k3_yellow_1,axiom,( ! [A] : ( v1_orders_2(k3_yellow_1(A)) & l1_orders_2(k3_yellow_1(A)) ) ), file(yellow_1,k3_yellow_1), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_funct_3,axiom,( ! [A,B] : ( v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)) ) ), file(funct_3,k4_funct_3), []). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), []). fof(dt_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k4_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k4_subset_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_k5_funct_3,axiom,( ! [A,B] : ( v1_funct_1(k5_funct_3(A,B)) & v1_funct_2(k5_funct_3(A,B),B,k2_tarski(0,1)) & m2_relset_1(k5_funct_3(A,B),B,k2_tarski(0,1)) ) ), file(funct_3,k5_funct_3), []). fof(dt_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k5_subset_1), []). fof(dt_k5_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_1,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & m1_pboole(B,A) ) => ( v1_orders_2(k5_yellow_1(A,B)) & l1_orders_2(k5_yellow_1(A,B)) ) ) ), file(yellow_1,k5_yellow_1), []). fof(dt_k6_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k6_waybel_3(A,B,C)) & v2_orders_2(k6_waybel_3(A,B,C)) & l1_orders_2(k6_waybel_3(A,B,C)) ) ) ), file(waybel_3,k6_waybel_3), []). 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_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_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_k9_filter_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => v1_relat_1(k9_filter_1(A)) ) ), file(filter_1,k9_filter_1), []). fof(dt_k9_relat_1,axiom,( $true ), file(relat_1,k9_relat_1), []). fof(dt_k9_waybel18,axiom, ( v1_pre_topc(k9_waybel18) & l1_pre_topc(k9_waybel18) ), file(waybel18,k9_waybel18), []). fof(dt_l1_lattices,axiom,( ! [A] : ( l1_lattices(A) => l1_struct_0(A) ) ), file(lattices,l1_lattices), []). 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_l2_lattices,axiom,( ! [A] : ( l2_lattices(A) => l1_struct_0(A) ) ), file(lattices,l2_lattices), []). fof(dt_l3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( l1_lattices(A) & l2_lattices(A) ) ) ), file(lattices,l3_lattices), []). fof(dt_m1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_cantor_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ), file(cantor_1,m1_cantor_1), []). fof(dt_m1_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ), file(pboole,m1_pboole), []). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), []). fof(dt_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_u1_lattices,axiom,( ! [A] : ( l1_lattices(A) => ( v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u1_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(lattices,u1_lattices), []). 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_u2_lattices,axiom,( ! [A] : ( l2_lattices(A) => ( v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) & m2_relset_1(u2_lattices(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ), file(lattices,u2_lattices), []). fof(existence_l1_lattices,axiom,( ? [A] : l1_lattices(A) ), file(lattices,l1_lattices), []). 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_l2_lattices,axiom,( ? [A] : l2_lattices(A) ), file(lattices,l2_lattices), []). fof(existence_l3_lattices,axiom,( ? [A] : l3_lattices(A) ), file(lattices,l3_lattices), []). fof(existence_m1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_cantor_1(B,A) ) ), file(cantor_1,m1_cantor_1), []). fof(existence_m1_pboole,axiom,( ! [A] : ? [B] : m1_pboole(B,A) ), file(pboole,m1_pboole), []). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_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(fc10_waybel18,axiom,( ! [A,B] : ( ( v2_orders_2(B) & l1_orders_2(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) & v5_waybel_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc10_waybel18), []). fof(fc10_waybel_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_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc10_waybel_8), []). fof(fc10_yellow_1,axiom,( ! [A,B] : ( l1_orders_2(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_yellow_1(k2_funcop_1(A,B)) ) ) ), file(yellow_1,fc10_yellow_1), []). fof(fc11_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc11_waybel18), []). fof(fc11_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_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc12_waybel18), []). fof(fc12_waybel_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(fc13_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc13_waybel18), []). fof(fc14_waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_yellow_0(B) & v2_waybel_8(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v4_orders_2(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_yellow_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v24_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v25_waybel_0(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_waybel_3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_waybel_8(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v2_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v3_lattice3(k5_yellow_1(A,k2_pre_circ(A,B))) & v1_monoid_0(k5_yellow_1(A,k2_pre_circ(A,B))) ) ) ), file(waybel18,fc14_waybel18), []). fof(fc14_waybel_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_8,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & v2_waybel_1(k3_yellow_1(A)) & v9_waybel_1(k3_yellow_1(A)) & v10_waybel_1(k3_yellow_1(A)) & v11_waybel_1(k3_yellow_1(A)) & v2_waybel_3(k3_yellow_1(A)) & v3_waybel_3(k3_yellow_1(A)) & v1_waybel_8(k3_yellow_1(A)) & v2_waybel_8(k3_yellow_1(A)) ) ), file(waybel_8,fc14_waybel_8), []). fof(fc17_waybel_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_waybel_0(k5_waybel_0(A,B),A) & v13_waybel_0(k5_waybel_0(A,B),A) ) ) ), file(waybel_0,fc17_waybel_0), []). fof(fc1_funcop_1,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ), file(funcop_1,fc1_funcop_1), []). fof(fc1_lattice3,axiom,( ! [A] : ( ~ v3_struct_0(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) ) ), file(lattice3,fc1_lattice3), []). 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_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k3_waybel18(A,B)) & v1_pre_topc(k3_waybel18(A,B)) & v2_pre_topc(k3_waybel18(A,B)) ) ) ), file(waybel18,fc1_waybel18), []). fof(fc1_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(k1_waybel_8(A)) & v1_orders_2(k1_waybel_8(A)) & v2_orders_2(k1_waybel_8(A)) & v4_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) ) ) ), file(waybel_8,fc1_waybel_8), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc1_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ~ v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) ) ) ), file(yellow_1,fc1_yellow_1), []). fof(fc2_funcop_1,axiom,( ! [A] : ( v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) & v1_relat_1(k2_funcop_1(k1_xboole_0,A)) & v1_funct_1(k2_funcop_1(k1_xboole_0,A)) & v2_funct_1(k2_funcop_1(k1_xboole_0,A)) ) ), file(funcop_1,fc2_funcop_1), []). fof(fc2_lattice3,axiom,( ! [A] : ( ~ v3_struct_0(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) ) ), file(lattice3,fc2_lattice3), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_waybel18,axiom,( ! [A,B] : ( ( v4_waybel_3(B) & v1_waybel18(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k3_waybel18(A,B)) & v1_pre_topc(k3_waybel18(A,B)) & v2_pre_topc(k3_waybel18(A,B)) & v1_monoid_0(k3_waybel18(A,B)) ) ) ), file(waybel18,fc2_waybel18), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc2_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ( ~ v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v2_yellow_0(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) ) ) ), file(yellow_1,fc2_yellow_1), []). fof(fc3_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(card_3,fc3_card_3), []). fof(fc3_funcop_1,axiom,( ! [A,B] : ( v1_xboole_0(B) => ( v1_xboole_0(k2_funcop_1(B,A)) & v1_relat_1(k2_funcop_1(B,A)) & v1_funct_1(k2_funcop_1(B,A)) & v2_funct_1(k2_funcop_1(B,A)) ) ) ), file(funcop_1,fc3_funcop_1), []). fof(fc3_lattice3,axiom,( ! [A] : ( ~ v3_struct_0(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) & v4_lattices(k1_lattice3(A)) & v5_lattices(k1_lattice3(A)) & v6_lattices(k1_lattice3(A)) & v7_lattices(k1_lattice3(A)) & v8_lattices(k1_lattice3(A)) & v9_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) & v11_lattices(k1_lattice3(A)) & v12_lattices(k1_lattice3(A)) & v13_lattices(k1_lattice3(A)) & v14_lattices(k1_lattice3(A)) & v15_lattices(k1_lattice3(A)) & v16_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A)) ) ), file(lattice3,fc3_lattice3), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_waybel_8(A)) & v2_orders_2(k1_waybel_8(A)) & v3_orders_2(k1_waybel_8(A)) & v4_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) & v6_yellow_0(k1_waybel_8(A),A) ) ) ), file(waybel_8,fc3_waybel_8), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc3_yellow_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ( ~ v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) & v1_yellow_0(k3_lattice3(A)) & v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) ) ) ), file(yellow_1,fc3_yellow_1), []). fof(fc4_card_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( ~ v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)) ) ) ), file(card_3,fc4_card_3), []). fof(fc4_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ~ v3_struct_0(k3_lattice3(A)) & v1_orders_2(k3_lattice3(A)) & v2_orders_2(k3_lattice3(A)) & v3_orders_2(k3_lattice3(A)) & v4_orders_2(k3_lattice3(A)) ) ) ), file(lattice3,fc4_lattice3), []). 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_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_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k4_card_3(A)) & v1_fraenkel(k4_card_3(A)) ) ) ), file(card_3,fc5_card_3), []). fof(fc5_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) ), file(waybel18,fc5_waybel18), []). 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(fc6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k2_relat_1(A)) ) ), file(funct_1,fc6_funct_1), []). fof(fc6_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) ), file(waybel18,fc6_waybel18), []). 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(fc7_waybel18,axiom, ( ~ v3_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) & v2_t_0topsp(k9_waybel18) & v2_waybel18(k9_waybel18) ), file(waybel18,fc7_waybel18), []). 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_3,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) ) ) ), file(waybel_3,fc7_waybel_3), []). fof(fc7_waybel_8,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc7_waybel_8), []). fof(fc7_yellow_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) ) ), file(yellow_1,fc7_yellow_1), []). fof(fc8_waybel18,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v4_waybel_3(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc8_waybel18), []). fof(fc8_waybel_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_3,axiom,( ! [A,B] : ( ( v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(waybel_3,fc8_waybel_3), []). fof(fc8_waybel_8,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc8_waybel_8), []). fof(fc8_yellow_1,axiom,( ! [A] : ( ~ v3_struct_0(k3_yellow_1(A)) & v1_orders_2(k3_yellow_1(A)) & v2_orders_2(k3_yellow_1(A)) & v3_orders_2(k3_yellow_1(A)) & v4_orders_2(k3_yellow_1(A)) & v1_yellow_0(k3_yellow_1(A)) & v2_yellow_0(k3_yellow_1(A)) & v3_yellow_0(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(yellow_1,fc8_yellow_1), []). fof(fc9_funcop_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v2_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) ) ), file(funcop_1,fc9_funcop_1), []). fof(fc9_waybel18,axiom,( ! [A,B] : ( l1_pre_topc(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) & v1_waybel18(k2_funcop_1(A,B)) ) ) ), file(waybel18,fc9_waybel18), []). fof(fc9_waybel_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) ) => ( ~ v3_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) & v2_orders_2(k5_yellow_1(A,B)) & v1_monoid_0(k5_yellow_1(A,B)) ) ) ), file(waybel_3,fc9_waybel_3), []). fof(fc9_waybel_8,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) & v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(waybel_8,fc9_waybel_8), []). fof(fraenkel_a_0_42_fraenkel,axiom,( ! [A] : ( r2_hidden(A,a_0_42_fraenkel) <=> ? [B] : ( m1_subset_1(B,f1_s21_fraenkel) & A = f3_s21_fraenkel(B) & r2_hidden(B,f2_s21_fraenkel) ) ) ), file(fraenkel,a_0_42_fraenkel), []). fof(fraenkel_a_1_0_waybel14,axiom,( ! [A,B] : ( ( 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) ) => ( r2_hidden(A,a_1_0_waybel14(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k7_waybel_0(B,C) & r2_hidden(C,u1_struct_0(k1_waybel_8(B))) ) ) ) ), file(waybel14,a_1_0_waybel14), []). fof(fraenkel_a_1_0_waybel18,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_waybel18(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k4_card_3(k2_funct_7(k12_pralg_1(B,k2_pre_circ(B,k9_waybel18)),C,k1_tarski(1))) ) ) ) ), file(waybel18,a_1_0_waybel18), []). fof(fraenkel_a_1_1_waybel18,axiom,( ! [A,B] : ( ( v2_pre_topc(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v4_waybel11(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_1_waybel18(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k7_waybel_0(B,C) & r2_hidden(C,u1_struct_0(k1_waybel_8(B))) ) ) ) ), file(waybel18,a_1_1_waybel18), []). fof(fraenkel_a_2_0_waybel18,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,u1_struct_0(k3_yellow_1(B))) ) => ( r2_hidden(A,a_2_0_waybel18(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k4_card_3(k2_funct_7(k12_pralg_1(B,k2_pre_circ(B,k9_waybel18)),D,k1_tarski(1))) & r2_hidden(D,C) ) ) ) ), file(waybel18,a_2_0_waybel18), []). fof(fraenkel_a_2_1_waybel18,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_1_waybel18(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k4_card_3(k2_funct_7(k12_pralg_1(B,k2_pre_circ(B,k9_waybel18)),D,k1_tarski(1))) & r2_hidden(D,C) ) ) ) ), file(waybel18,a_2_1_waybel18), []). 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_g3_lattices,axiom,( ! [A,B,C] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & m1_relset_1(B,k2_zfmisc_1(A,A),A) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,A),A) & m1_relset_1(C,k2_zfmisc_1(A,A),A) ) => ! [D,E,F] : ( g3_lattices(A,B,C) = g3_lattices(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(lattices,g3_lattices), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(idempotence_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) ), file(subset_1,k4_subset_1), []). fof(idempotence_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,B) = B ) ), file(subset_1,k5_subset_1), []). fof(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(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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_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_monoid_0,axiom,( ? [A] : ( l1_struct_0(A) & v1_monoid_0(A) ) ), file(monoid_0,rc1_monoid_0), []). fof(rc1_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) ), file(pre_topc,rc1_pre_topc), []). 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_waybel18,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_waybel18(B) ) ), file(waybel18,rc1_waybel18), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_yellow_1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_yellow_1(B) ) ), file(yellow_1,rc1_yellow_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_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_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v3_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) ), file(pre_topc,rc2_pre_topc), []). 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_waybel18,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v4_waybel_3(B) & v2_pralg_1(B) & v1_waybel18(B) ) ), file(waybel18,rc2_waybel18), []). fof(rc2_waybel_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ), file(waybel_3,rc2_waybel_3), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_waybel_3,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_yellow_1(B) & v2_pralg_1(B) & v4_waybel_3(B) & v5_waybel_3(B) ) ), file(waybel_3,rc3_waybel_3), []). fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc5_funct_1), []). fof(rc5_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) ), file(struct_0,rc5_struct_0), []). fof(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(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_k2_lattice3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k2_lattice3(A) = k9_filter_1(A) ) ), file(lattice3,k2_lattice3), []). fof(redefinition_k2_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). fof(redefinition_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), []). fof(redefinition_k4_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,C) = k2_xboole_0(B,C) ) ), file(subset_1,k4_subset_1), []). fof(redefinition_k5_funct_3,axiom,( ! [A,B] : k5_funct_3(A,B) = k4_funct_3(A,B) ), file(funct_3,k5_funct_3), []). fof(redefinition_k5_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ), file(subset_1,k5_subset_1), []). fof(redefinition_k6_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & v5_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k6_waybel_3(A,B,C) = k1_funct_1(B,C) ) ), file(waybel_3,k6_waybel_3), []). 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(redefinition_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). 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(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(s21_fraenkel__e20_47_5__waybel18,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) ) => ( v1_finset_1(B) => v1_finset_1(a_0_42_fraenkel) ) ) ), file(waybel18,s21_fraenkel__e20_47_5__waybel18), []). fof(s3_funct_1__e7_47_6__waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k1_relat_1(B) = A & ! [C] : ( r2_hidden(C,A) => k1_funct_1(B,C) = k4_card_3(k2_funct_7(k12_pralg_1(A,k2_pre_circ(A,k9_waybel18)),C,k1_tarski(1))) ) ) ) ), file(waybel18,s3_funct_1__e7_47_6__waybel18), []). fof(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc2_boole,axiom,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), []). fof(symmetry_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(t13_funcop_1,axiom,( ! [A,B,C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) ), file(funcop_1,t13_funcop_1), []). fof(t13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( k4_waybel_0(A,C) = k4_waybel_0(B,D) & k5_waybel_0(A,C) = k5_waybel_0(B,D) ) ) ) ) ) ) ) ), file(waybel_0,t13_waybel_0), []). fof(t14_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_cantor_1(a_1_0_waybel18(A),k3_waybel18(A,k2_pre_circ(A,k9_waybel18))) ) ), file(waybel18,t14_waybel18), []). fof(t15_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1))))) & m2_relset_1(B,u1_struct_0(k3_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1))))) & v23_waybel_0(B,k3_yellow_1(A),k5_yellow_1(A,k2_pre_circ(A,k3_yellow_1(1)))) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_funct_1(B,C) = k5_funct_3(C,A) ) ) ) ), file(waybel18,t15_waybel18), []). fof(t17_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & v2_waybel_8(A) ) => v2_waybel_8(B) ) ) ) ), file(waybel_8,t17_waybel_8), []). 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(t195_orders_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ~ ( v1_finset_1(B) & r1_tarski(B,k2_relat_1(A)) & ! [C] : ~ ( r1_tarski(C,k1_relat_1(A)) & v1_finset_1(C) & k9_relat_1(A,C) = B ) ) ) ), file(orders_1,t195_orders_1), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_card_5,axiom, ( 1 = k1_tarski(0) & 2 = k2_tarski(0,1) ), file(card_5,t1_card_5), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t1_xboole_1,axiom,( ! [A,B,C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) ), file(xboole_1,t1_xboole_1), []). fof(t23_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m2_cantor_1(B,A) <=> m1_cantor_1(k2_cantor_1(u1_struct_0(A),B),A) ) ) ) ), file(yellow_9,t23_yellow_9), []). fof(t26_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m2_cantor_1(C,A) => ( ( u1_struct_0(A) = u1_struct_0(B) & m2_cantor_1(C,B) ) => u1_pre_topc(A) = u1_pre_topc(B) ) ) ) ) ), file(yellow_9,t26_yellow_9), []). fof(t28_waybel13,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v23_waybel_0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_waybel_3(D,A) <=> v1_waybel_3(k1_waybel_0(A,B,C,D),B) ) ) ) ) ) ) ), file(waybel13,t28_waybel13), []). fof(t28_waybel_8,axiom,( ! [A,B] : ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) <=> r1_tarski(B,A) ) ), file(waybel_8,t28_waybel_8), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t2_xboole_1,axiom,( ! [A] : r1_tarski(k1_xboole_0,A) ), file(xboole_1,t2_xboole_1), []). fof(t2_yellow_1,axiom,( ! [A,B] : ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_1(A))) => ( r3_orders_2(k3_yellow_1(A),B,C) <=> r1_tarski(B,C) ) ) ) ), file(yellow_1,t2_yellow_1), []). fof(t30_waybel_8,axiom,( ! [A,B] : ( m1_subset_1(B,u1_struct_0(k3_yellow_1(A))) => ( v1_finset_1(B) <=> v1_waybel_3(B,k3_yellow_1(A)) ) ) ), file(waybel_8,t30_waybel_8), []). fof(t30_zfmisc_1,axiom,( ! [A] : k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) ), file(zfmisc_1,t30_zfmisc_1), []). fof(t32_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_relat_1(k2_funct_7(A,C,B)) = k1_relat_1(A) ) ), file(funct_7,t32_funct_7), []). fof(t33_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(k2_funct_7(A,C,B),C) = B ) ) ), file(funct_7,t33_funct_7), []). fof(t34_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C,D] : ( C != D => k1_funct_1(k2_funct_7(A,C,B),D) = k1_funct_1(A,D) ) ) ), file(funct_7,t34_funct_7), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t42_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) ) => ~ ( v2_waybel_8(A) & ! [B] : ( m1_cantor_1(B,A) => B != a_1_0_waybel14(A) ) ) ) ), file(waybel14,t42_waybel14), []). 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(t58_setfam_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( r2_hidden(B,A) => ( r2_hidden(B,k8_setfam_1(A,C)) <=> ! [D] : ( r2_hidden(D,C) => r2_hidden(B,D) ) ) ) ) ), file(setfam_1,t58_setfam_1), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t66_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) => ( v23_waybel_0(C,A,B) <=> ( v2_funct_1(C) & k2_relat_1(C) = u1_struct_0(B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_orders_2(A,D,E) <=> r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) ) ), file(waybel_0,t66_waybel_0), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []). fof(t9_waybel_8,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & v24_waybel_0(A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( C = D & v1_waybel_3(C,A) ) => v1_waybel_3(D,B) ) ) ) ) ) ) ), file(waybel_8,t9_waybel_8), []).