% Mizar problem: t13_waybel33,waybel33,802,33 fof(t13_waybel33,conjecture,( ! [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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => k1_waybel33(A,k2_pre_topc(A),B) = k1_waybel11(A,k3_yellow19(A,k2_pre_topc(A),B)) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v6_waybel_0,antisymmetry_r2_hidden,cc10_waybel_0,cc11_waybel_0,cc12_waybel_0,cc13_waybel_0,cc14_waybel_0,cc1_finset_1,cc1_funct_1,cc1_lattice3,cc1_relat_1,cc1_relset_1,cc1_waybel_3,cc1_yellow11,cc1_yellow13,cc2_finset_1,cc2_funct_1,cc2_lattice3,cc2_waybel_3,cc2_yellow13,cc3_waybel_3,cc3_yellow13,cc4_waybel_3,cc4_yellow11,cc5_waybel_0,cc5_waybel_3,cc5_yellow11,cc6_waybel_3,cc9_waybel_0,commutativity_k2_tarski,d10_xboole_0,d1_waybel33,d2_mcart_1,d3_pre_topc,d3_tarski,d4_yellow19,d5_tarski,d8_waybel_0,dt_g1_orders_2,dt_g1_waybel_0,dt_k1_funct_1,dt_k1_mcart_1,dt_k1_tarski,dt_k1_waybel11,dt_k1_waybel33,dt_k1_waybel_0,dt_k1_xboole_0,dt_k1_yellow_0,dt_k1_zfmisc_1,dt_k2_mcart_1,dt_k2_pre_topc,dt_k2_tarski,dt_k2_waybel_9,dt_k2_yellow_0,dt_k2_zfmisc_1,dt_k3_waybel_0,dt_k3_yellow19,dt_k3_yellow_0,dt_k3_yellow_1,dt_k4_tarski,dt_k5_waybel_9,dt_k6_waybel_9,dt_l1_orders_2,dt_l1_struct_0,dt_l1_waybel_0,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m2_relset_1,dt_m2_yellow_6,dt_u1_orders_2,dt_u1_struct_0,dt_u1_waybel_0,existence_l1_orders_2,existence_l1_struct_0,existence_l1_waybel_0,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m2_relset_1,existence_m2_yellow_6,fc12_relat_1,fc14_finset_1,fc15_waybel_0,fc15_yellow_6,fc1_finset_1,fc1_struct_0,fc1_subset_1,fc1_waybel28,fc1_waybel_7,fc1_yellow13,fc2_finset_1,fc2_subset_1,fc2_waybel_0,fc2_waybel_7,fc2_yellow13,fc3_subset_1,fc3_waybel_0,fc4_relat_1,fc4_subset_1,fc4_waybel_0,fc4_yellow19,fc5_waybel_0,fc5_yellow19,fc6_waybel_0,fc8_yellow_6,fraenkel_a_2_2_waybel33,fraenkel_a_2_4_waybel33,fraenkel_a_2_5_waybel33,fraenkel_a_2_6_waybel33,fraenkel_a_3_0_waybel33,fraenkel_a_3_1_yellow19,free_g1_orders_2,free_g1_waybel_0,rc10_waybel_0,rc11_waybel_0,rc12_waybel_0,rc13_waybel_0,rc1_finset_1,rc1_funct_1,rc1_lattice3,rc1_relat_1,rc1_subset_1,rc1_waybel_0,rc1_waybel_3,rc1_waybel_7,rc1_yellow11,rc2_funct_1,rc2_lattice3,rc2_relat_1,rc2_subset_1,rc2_waybel_0,rc2_waybel_3,rc2_waybel_7,rc2_yellow13,rc3_finset_1,rc3_funct_1,rc3_relat_1,rc3_struct_0,rc3_waybel28,rc3_waybel_7,rc4_finset_1,rc4_funct_1,rc4_waybel_0,rc4_waybel_7,rc4_yellow_6,rc5_struct_0,rc5_waybel_0,rc7_waybel_0,rc8_waybel_0,rc9_waybel_0,redefinition_k1_waybel_0,redefinition_k6_waybel_9,redefinition_m1_struct_0,redefinition_m2_relset_1,reflexivity_r1_tarski,t10_subset_1,t11_waybel33,t12_waybel33,t18_yellow_1,t1_subset,t2_subset,t2_tarski,t3_subset,t4_subset,t4_waybel_7,t5_subset,t6_boole,t7_boole,t8_boole,t8_waybel_7]), [file(waybel33,t13_waybel33)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(abstractness_v6_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v6_waybel_0(B,A) => B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) ) ) ), file(waybel_0,v6_waybel_0), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_lattice3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_0,cc10_waybel_0), []). fof(cc11_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_yellow_0(A) ) ) ) ), file(waybel_0,cc11_waybel_0), []). fof(cc12_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(waybel_0,cc12_waybel_0), []). fof(cc13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) ) ) ) ), file(waybel_0,cc13_waybel_0), []). fof(cc14_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & v25_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc14_waybel_0), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). fof(cc1_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_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_waybel_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ) ), file(waybel_3,cc1_waybel_3), []). fof(cc1_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v2_waybel_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v1_yellow11(A) ) ) ) ), file(yellow11,cc1_yellow11), []). fof(cc1_yellow13,axiom,( ! [A] : ( v1_realset1(A) => v1_finset_1(A) ) ), file(yellow13,cc1_yellow13), []). 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_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_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ) ) ), file(waybel_3,cc2_waybel_3), []). fof(cc2_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_realset2(A) => v6_group_1(A) ) ) ), file(yellow13,cc2_yellow13), []). fof(cc3_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v3_realset2(A) & v2_orders_2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc3_waybel_3), []). fof(cc3_yellow13,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v3_realset2(A) => ~ v3_struct_0(A) ) ) ), file(yellow13,cc3_yellow13), []). 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_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v6_group_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) ) ) ) ), file(yellow11,cc4_yellow11), []). fof(cc5_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_realset2(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v16_waybel_0(A) ) ) ) ), file(waybel_0,cc5_waybel_0), []). fof(cc5_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v24_waybel_0(A) & v2_waybel_3(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & v3_waybel_3(A) ) ) ) ), file(waybel_3,cc5_waybel_3), []). fof(cc5_yellow11,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v6_group_1(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) ) ) ) ), file(yellow11,cc5_yellow11), []). fof(cc6_waybel_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v3_lattice3(A) & v16_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) & v2_waybel_3(A) ) ) ) ), file(waybel_3,cc6_waybel_3), []). fof(cc9_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v2_orders_2(A) & v1_lattice3(A) & v24_waybel_0(A) ) => ( ~ v3_struct_0(A) & v2_orders_2(A) & v1_lattice3(A) & v2_yellow_0(A) ) ) ) ), file(waybel_0,cc9_waybel_0), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(d10_xboole_0,axiom,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), []). fof(d1_waybel33,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) ), file(waybel33,d1_waybel33), []). fof(d2_mcart_1,axiom,( ! [A] : ( ? [B,C] : A = k4_tarski(B,C) => ! [B] : ( B = k2_mcart_1(A) <=> ! [C,D] : ( A = k4_tarski(C,D) => B = D ) ) ) ), file(mcart_1,d2_mcart_1), []). fof(d3_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => k2_pre_topc(A) = u1_struct_0(A) ) ), file(pre_topc,d3_pre_topc), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d4_yellow19,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ! [D] : ( ( ~ v3_struct_0(D) & v6_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( D = k3_yellow19(A,B,C) <=> ( u1_struct_0(D) = a_3_1_yellow19(A,B,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( r1_orders_2(D,E,F) <=> r1_tarski(k2_mcart_1(F),k2_mcart_1(E)) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => k3_waybel_0(A,D,E) = k1_mcart_1(E) ) ) ) ) ) ) ) ), file(yellow19,d4_yellow19), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). 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_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( v6_waybel_0(g1_waybel_0(A,B,C,D),A) & l1_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,g1_waybel_0), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_mcart_1,axiom,( $true ), file(mcart_1,k1_mcart_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel11,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(k1_waybel11(A,B),u1_struct_0(A)) ) ), file(waybel11,k1_waybel11), []). fof(dt_k1_waybel33,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_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(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) ), file(waybel33,k1_waybel33), []). fof(dt_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ), file(waybel_0,k1_waybel_0), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k1_yellow_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_mcart_1,axiom,( $true ), file(mcart_1,k2_mcart_1), []). fof(dt_k2_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k2_pre_topc), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_waybel_9,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & l1_waybel_0(B,A) ) => m1_subset_1(k2_waybel_9(A,B),u1_struct_0(A)) ) ), file(waybel_9,k2_waybel_9), []). fof(dt_k2_yellow_0,axiom,( ! [A,B] : ( l1_orders_2(A) => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) ), file(yellow_0,k2_yellow_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_waybel_0,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(k3_waybel_0(A,B,C),u1_struct_0(A)) ) ), file(waybel_0,k3_waybel_0), []). fof(dt_k3_yellow19,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ( ~ v3_struct_0(k3_yellow19(A,B,C)) & v6_waybel_0(k3_yellow19(A,B,C),A) & l1_waybel_0(k3_yellow19(A,B,C),A) ) ) ), file(yellow19,k3_yellow19), []). fof(dt_k3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) ), file(yellow_0,k3_yellow_0), []). fof(dt_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_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k5_waybel_9,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)) ) => ( v6_waybel_0(k5_waybel_9(A,B,C),A) & l1_waybel_0(k5_waybel_9(A,B,C),A) ) ) ), file(waybel_9,k5_waybel_9), []). fof(dt_k6_waybel_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => ( v6_waybel_0(k6_waybel_9(A,B,C),A) & m2_yellow_6(k6_waybel_9(A,B,C),A,B) ) ) ), file(waybel_9,k6_waybel_9), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). 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_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), []). fof(dt_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ), file(struct_0,m1_struct_0), []). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_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_m2_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) ) ) ), file(yellow_6,m2_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_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_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_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), []). fof(existence_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_struct_0(C,A,B) ) ), file(struct_0,m1_struct_0), []). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : m2_yellow_6(C,A,B) ) ), file(yellow_6,m2_yellow_6), []). fof(fc12_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc15_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v12_waybel_0(k2_pre_topc(A),A) & v13_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc15_waybel_0), []). fof(fc15_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ( ~ v1_xboole_0(u1_waybel_0(A,B)) & v1_relat_1(u1_waybel_0(A,B)) & v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(yellow_6,fc15_yellow_6), []). fof(fc1_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_1), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_waybel28,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) ) => ( ~ v3_struct_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) & v3_orders_2(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) & v6_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A) & v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) ) ) ), file(waybel28,fc1_waybel28), []). fof(fc1_waybel_7,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)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & ~ v1_yellow_3(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)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(waybel_7,fc1_waybel_7), []). fof(fc1_yellow13,axiom,( ! [A] : ( ( v6_group_1(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) ), file(yellow13,fc1_yellow13), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_waybel_0,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v1_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc2_waybel_0), []). fof(fc2_waybel_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v3_struct_0(k3_yellow_1(A)) & ~ v3_realset2(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)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & ~ v1_yellow_3(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)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ) ), file(waybel_7,fc2_waybel_7), []). fof(fc2_yellow13,axiom,( ! [A] : ( ( v3_realset2(A) & l1_struct_0(A) ) => v1_realset1(u1_struct_0(A)) ) ), file(yellow13,fc2_yellow13), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v1_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc3_waybel_0), []). fof(fc4_relat_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), []). fof(fc4_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_waybel_0,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v2_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc4_waybel_0), []). fof(fc4_yellow19,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ( ~ v3_struct_0(k3_yellow19(A,B,C)) & v2_orders_2(k3_yellow19(A,B,C)) & v3_orders_2(k3_yellow19(A,B,C)) & v6_waybel_0(k3_yellow19(A,B,C),A) ) ) ), file(yellow19,fc4_yellow19), []). fof(fc5_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(k2_pre_topc(A)) & v2_waybel_0(k2_pre_topc(A),A) ) ) ), file(waybel_0,fc5_waybel_0), []). fof(fc5_yellow19,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(B)) & v13_waybel_0(C,k3_yellow_1(B)) & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(B)))) ) => ( ~ v3_struct_0(k3_yellow19(A,B,C)) & v2_orders_2(k3_yellow19(A,B,C)) & v3_orders_2(k3_yellow19(A,B,C)) & v6_waybel_0(k3_yellow19(A,B,C),A) & v7_waybel_0(k3_yellow19(A,B,C)) ) ) ), file(yellow19,fc5_yellow19), []). 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(fc8_yellow_6,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)) & v7_waybel_0(k3_yellow_1(A)) & v24_waybel_0(k3_yellow_1(A)) & v25_waybel_0(k3_yellow_1(A)) & ~ v1_yellow_3(k3_yellow_1(A)) & v1_lattice3(k3_yellow_1(A)) & v2_lattice3(k3_yellow_1(A)) & v3_lattice3(k3_yellow_1(A)) ) ), file(yellow_6,fc8_yellow_6), []). fof(fraenkel_a_2_2_waybel33,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_2_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_9(B,k6_waybel_9(B,C,D)) ) ) ) ), file(waybel33,a_2_2_waybel33), []). fof(fraenkel_a_2_4_waybel33,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) ) => ( r2_hidden(A,a_2_4_waybel33(B,C)) <=> ? [D,E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_struct_0(E,k3_yellow_1(k2_pre_topc(B)),C) & A = k4_tarski(D,E) & r2_hidden(D,E) ) ) ) ), file(waybel33,a_2_4_waybel33), []). fof(fraenkel_a_2_5_waybel33,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) ) => ( r2_hidden(A,a_2_5_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow19(B,k2_pre_topc(B),C))) & A = k2_waybel_9(B,k6_waybel_9(B,k3_yellow19(B,k2_pre_topc(B),C),D)) ) ) ) ), file(waybel33,a_2_5_waybel33), []). fof(fraenkel_a_2_6_waybel33,axiom,( ! [A,B,C] : ( ( v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v13_waybel_0(C,k3_yellow_1(k2_pre_topc(B))) & v1_tex_2(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(B))))) ) => ( r2_hidden(A,a_2_6_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(D,C) ) ) ) ), file(waybel33,a_2_6_waybel33), []). fof(fraenkel_a_3_0_waybel33,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v2_orders_2(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k3_yellow_1(C)) & v13_waybel_0(D,k3_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) ) => ( r2_hidden(A,a_3_0_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,E) & r2_hidden(E,D) ) ) ) ), file(waybel33,a_3_0_waybel33), []). fof(fraenkel_a_3_1_yellow19,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k3_yellow_1(C)) & v13_waybel_0(D,k3_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_1(C)))) ) => ( r2_hidden(A,a_3_1_yellow19(B,C,D)) <=> ? [E,F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_struct_0(F,k3_yellow_1(C),D) & A = k4_tarski(E,F) & r2_hidden(E,F) ) ) ) ), file(yellow19,a_3_1_yellow19), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(free_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ! [E,F,G,H] : ( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(waybel_0,g1_waybel_0), []). fof(rc10_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc10_waybel_0), []). fof(rc11_waybel_0,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_0,rc11_waybel_0), []). fof(rc12_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v16_waybel_0(A) ) ), file(waybel_0,rc12_waybel_0), []). fof(rc13_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ), file(waybel_0,rc13_waybel_0), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_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_relat_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ), file(waybel_0,rc1_waybel_0), []). fof(rc1_waybel_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) ) ), file(waybel_3,rc1_waybel_3), []). fof(rc1_waybel_7,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & ~ v3_realset2(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & ~ v1_yellow_3(A) & v2_waybel_1(A) & v9_waybel_1(A) & v10_waybel_1(A) & v11_waybel_1(A) & v1_lattice3(A) & v2_lattice3(A) ) ), file(waybel_7,rc1_waybel_7), []). fof(rc1_yellow11,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v6_group_1(A) ) ), file(yellow11,rc1_yellow11), []). fof(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_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), []). fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_waybel_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ), file(waybel_0,rc2_waybel_0), []). fof(rc2_waybel_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) ), file(waybel_3,rc2_waybel_3), []). fof(rc2_waybel_7,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ), file(waybel_7,rc2_waybel_7), []). fof(rc2_yellow13,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v1_orders_2(A) & v6_group_1(A) & v3_realset2(A) ) ), file(yellow13,rc2_yellow13), []). fof(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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), []). fof(rc3_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). fof(rc3_waybel28,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m2_yellow_6(C,A,B) & ~ v3_struct_0(C) & v3_orders_2(C) & v6_waybel_0(C,A) & v7_waybel_0(C) ) ) ), file(waybel28,rc3_waybel28), []). fof(rc3_waybel_7,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(waybel_7,rc3_waybel_7), []). 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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) ) ) ), file(waybel_0,rc4_waybel_0), []). fof(rc4_waybel_7,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v3_realset2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ), file(waybel_7,rc4_waybel_7), []). 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(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_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_waybel_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => k6_waybel_9(A,B,C) = k5_waybel_9(A,B,C) ) ), file(waybel_9,k6_waybel_9), []). fof(redefinition_m1_struct_0,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_struct_0(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(struct_0,m1_struct_0), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(t10_subset_1,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ r2_hidden(C,B) ) ) ) ), file(subset_1,t10_subset_1), []). fof(t11_waybel33,axiom,( ! [A] : ( ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => k1_waybel11(A,B) = k1_yellow_0(A,a_2_2_waybel33(A,B)) ) ) ), file(waybel33,t11_waybel33), []). fof(t12_waybel33,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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v13_waybel_0(B,k3_yellow_1(k2_pre_topc(A))) & v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_1(k2_pre_topc(A))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow19(A,k2_pre_topc(A),B))) => ( k2_mcart_1(D) = C => k2_yellow_0(A,C) = k2_waybel_9(A,k6_waybel_9(A,k3_yellow19(A,k2_pre_topc(A),B),D)) ) ) ) ) ) ) ), file(waybel33,t12_waybel33), []). fof(t18_yellow_1,axiom,( ! [A] : k3_yellow_0(k3_yellow_1(A)) = k1_xboole_0 ), file(yellow_1,t18_yellow_1), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). 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(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). 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(t4_waybel_7,axiom,( ! [A] : u1_struct_0(k3_yellow_1(A)) = k1_zfmisc_1(A) ), file(waybel_7,t4_waybel_7), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_waybel_7,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_tex_2(B,k1_zfmisc_1(u1_struct_0(A))) <=> ~ r2_hidden(k3_yellow_0(A),B) ) ) ) ), file(waybel_7,t8_waybel_7), []).