% Mizar problem: t53_yellow_6,yellow_6,2670,63 fof(t53_yellow_6,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( k13_yellow_6(k14_yellow_6(A,B)) = B <=> v8_yellow_6(B,A) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_orders_2,abstractness_v1_pre_topc,abstractness_v6_waybel_0,antisymmetry_r2_hidden,cc1_classes2,cc1_fraenkel,cc1_funct_1,cc1_index_1,cc1_pboole,cc1_relat_1,cc1_relset_1,cc1_yellow_1,cc1_yellow_3,cc1_yellow_6,cc2_classes2,cc2_funct_1,cc2_index_1,cc2_pboole,cc2_yellow_3,cc2_yellow_6,cc3_classes2,cc3_pboole,cc3_yellow_6,cc4_yellow_6,cc5_yellow_6,cc6_yellow_6,cc7_yellow_6,cc8_yellow_6,cc9_yellow_6,commutativity_k2_tarski,d10_xboole_0,d10_yellow_6,d11_pralg_1,d12_yellow_6,d14_yellow_6,d15_yellow_6,d16_yellow_6,d18_pboole,d1_binop_1,d1_funct_2,d21_yellow_6,d22_yellow_6,d23_yellow_6,d24_yellow_6,d25_yellow_6,d26_yellow_6,d27_yellow_6,d28_yellow_6,d2_yellow_0,d2_yellow_3,d3_pboole,d3_relat_1,d3_tarski,d3_yellow_6,d4_yellow_1,d4_yellow_6,d5_funct_1,d5_tarski,d5_yellow_6,d6_yellow_6,d7_yellow_6,d8_waybel_0,d9_relat_1,dt_g1_orders_2,dt_g1_pre_topc,dt_g1_waybel_0,dt_k10_pralg_1,dt_k11_yellow_6,dt_k12_pralg_1,dt_k13_yellow_6,dt_k14_yellow_6,dt_k1_binop_1,dt_k1_classes1,dt_k1_domain_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_waybel_0,dt_k1_xboole_0,dt_k1_yellow_3,dt_k1_yellow_6,dt_k1_zfmisc_1,dt_k2_funcop_1,dt_k2_pre_circ,dt_k2_relat_1,dt_k2_tarski,dt_k2_yellow_3,dt_k2_yellow_6,dt_k2_zfmisc_1,dt_k3_waybel_0,dt_k3_waybel_3,dt_k3_yellow_3,dt_k3_yellow_6,dt_k4_card_3,dt_k4_relset_1,dt_k4_tarski,dt_k4_waybel_3,dt_k4_yellow_6,dt_k5_classes1,dt_k5_relat_1,dt_k5_yellow_1,dt_k5_yellow_6,dt_k6_pre_topc,dt_k7_funct_2,dt_k7_yellow_3,dt_k7_yellow_6,dt_k8_funct_2,dt_k8_yellow_6,dt_k9_yellow_6,dt_l1_orders_2,dt_l1_pre_topc,dt_l1_struct_0,dt_l1_waybel_0,dt_m1_pboole,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_m2_yellow_6,dt_m3_pboole,dt_m3_yellow_6,dt_m4_yellow_6,dt_u1_orders_2,dt_u1_pre_topc,dt_u1_struct_0,dt_u1_waybel_0,existence_l1_orders_2,existence_l1_pre_topc,existence_l1_struct_0,existence_l1_waybel_0,existence_m1_pboole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,existence_m2_yellow_6,existence_m3_pboole,existence_m3_yellow_6,existence_m4_yellow_6,fc10_relat_1,fc10_yellow_1,fc10_yellow_3,fc10_yellow_6,fc11_yellow_6,fc12_relat_1,fc12_yellow_6,fc13_yellow_3,fc13_yellow_6,fc14_yellow_6,fc15_yellow_6,fc16_yellow_6,fc18_yellow_6,fc19_yellow_6,fc1_classes2,fc1_funcop_1,fc1_funct_1,fc1_orders_2,fc1_struct_0,fc1_subset_1,fc1_yellow_0,fc1_yellow_6,fc23_yellow_6,fc24_yellow_6,fc25_yellow_6,fc2_complsp1,fc2_funcop_1,fc2_pboole,fc2_seqm_3,fc2_subset_1,fc2_yellow_6,fc3_ami_1,fc3_classes2,fc3_funcop_1,fc3_pralg_1,fc3_subset_1,fc3_yellow_6,fc4_ami_1,fc4_index_1,fc4_relat_1,fc4_subset_1,fc4_yellow_6,fc5_classes2,fc5_relat_1,fc5_yellow_6,fc6_classes2,fc6_funct_1,fc6_relat_1,fc6_waybel_0,fc7_funcop_1,fc7_relat_1,fc7_yellow_3,fc8_funcop_1,fc8_relat_1,fc9_funcop_1,fc9_relat_1,fc9_yellow_6,fraenkel_a_0_0_domain_1,fraenkel_a_2_3_yellow_6,fraenkel_a_3_1_yellow_6,fraenkel_a_4_1_yellow_6,fraenkel_a_4_2_yellow_6,fraenkel_a_5_0_yellow_6,free_g1_orders_2,free_g1_pre_topc,free_g1_waybel_0,l16_yellow_6,l17_yellow_6,l20_yellow_6,l53_yellow_6,rc10_yellow_6,rc11_yellow_6,rc1_classes2,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_index_1,rc1_orders_2,rc1_pboole,rc1_pre_topc,rc1_relat_1,rc1_subset_1,rc1_yellow_1,rc1_yellow_6,rc2_classes2,rc2_funct_1,rc2_pboole,rc2_pre_topc,rc2_relat_1,rc2_subset_1,rc2_yellow_6,rc3_funct_1,rc3_pboole,rc3_relat_1,rc3_struct_0,rc3_yellow_6,rc4_funct_1,rc4_pboole,rc4_pralg_1,rc4_waybel_0,rc4_yellow_6,rc5_funct_1,rc5_struct_0,rc5_yellow_6,rc8_yellow_6,rc9_yellow_6,redefinition_k10_pralg_1,redefinition_k1_domain_1,redefinition_k1_waybel_0,redefinition_k2_pre_circ,redefinition_k2_yellow_3,redefinition_k3_waybel_3,redefinition_k3_yellow_6,redefinition_k4_relset_1,redefinition_k4_waybel_3,redefinition_k7_funct_2,redefinition_k7_yellow_3,redefinition_k8_funct_2,redefinition_k8_yellow_6,redefinition_m2_relset_1,reflexivity_r1_tarski,s1_funct_7__e13_124_4_6__yellow_6,s1_mssubfam__e9_124_4_6__yellow_6,s3_funct_2__e10_124_4_6_2__yellow_6,s3_pboole__e30_124_4__yellow_6,s5_pboole__e1_124_4_6__yellow_6,s5_pboole__e6_124_4_6__yellow_6,s7_domain_1__e3_124_4_6_4__yellow_6,t106_zfmisc_1,t11_yellow_3,t12_relset_1,t13_yellow_6,t14_yellow_6,t18_card_3,t1_subset,t20_funct_1,t22_yellow_6,t2_subset,t2_tarski,t33_yellow_6,t35_yellow_6,t36_yellow_6,t3_subset,t41_yellow_6,t43_yellow_6,t49_yellow_6,t4_subset,t52_yellow_6,t5_subset,t6_boole,t7_boole,t7_funct_2,t8_boole,t9_domain_1,t9_funct_1,t9_yellow_6]), [file(yellow_6,t53_yellow_6)]). fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ), file(orders_2,v1_orders_2), []). fof(abstractness_v1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(A) => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ), file(pre_topc,v1_pre_topc), []). fof(abstractness_v6_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v6_waybel_0(B,A) => B = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),u1_waybel_0(A,B)) ) ) ), file(waybel_0,v6_waybel_0), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc1_classes2,axiom,( ! [A] : ( v2_classes1(A) => v1_classes1(A) ) ), file(classes2,cc1_classes2), []). fof(cc1_fraenkel,axiom,( ! [A] : ( v1_fraenkel(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ), file(fraenkel,cc1_fraenkel), []). fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), []). fof(cc1_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(index_1,cc1_index_1), []). fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). 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_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_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_struct_0(A) => v1_yellow_3(A) ) ) ), file(yellow_3,cc1_yellow_3), []). fof(cc1_yellow_6,axiom,( ! [A] : ( v1_classes2(A) => ( v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) ) ) ), file(yellow_6,cc1_yellow_6), []). fof(cc2_classes2,axiom,( ! [A] : ( v1_classes2(A) => ( v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A) ) ) ), file(classes2,cc2_classes2), []). 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_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ~ v1_xboole_0(B) ) ) ), file(index_1,cc2_index_1), []). fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v3_relat_1(B) => ~ v2_relat_1(B) ) ) ) ), file(pboole,cc2_pboole), []). fof(cc2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v1_yellow_3(A) => ~ v3_struct_0(A) ) ) ), file(yellow_3,cc2_yellow_3), []). fof(cc2_yellow_6,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_classes1(A) ) => ( v1_ordinal1(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) ) ) ), file(yellow_6,cc2_yellow_6), []). fof(cc3_classes2,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_classes1(A) ) => v1_classes2(A) ) ), file(classes2,cc3_classes2), []). fof(cc3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => v1_funcop_1(D) ) ) ), file(pboole,cc3_pboole), []). fof(cc3_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ! [C] : ( m3_yellow_6(C,A,B) => v1_yellow_1(C) ) ) ), file(yellow_6,cc3_yellow_6), []). fof(cc4_yellow_6,axiom,( ! [A,B] : ( ( l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => ( ~ v1_xboole_0(C) & v1_yellow_1(C) & v4_waybel_3(C) ) ) ) ), file(yellow_6,cc4_yellow_6), []). fof(cc5_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ! [C] : ( m3_yellow_6(C,A,B) => ( v1_yellow_1(C) & v4_waybel_3(C) ) ) ) ), file(yellow_6,cc5_yellow_6), []). fof(cc6_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( l1_waybel_0(B,A) => ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & v1_yellow_6(B,A) ) => ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & v3_yellow_6(B,A) ) ) ) ) ), file(yellow_6,cc6_yellow_6), []). fof(cc7_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => v1_relat_1(B) ) ) ), file(yellow_6,cc7_yellow_6), []). fof(cc8_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v8_yellow_6(B,A) => ( v1_relat_1(B) & v4_yellow_6(B,A) & v5_yellow_6(B,A) & v6_yellow_6(B,A) & v7_yellow_6(B,A) ) ) ) ) ), file(yellow_6,cc8_yellow_6), []). fof(cc9_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( ( v4_yellow_6(B,A) & v5_yellow_6(B,A) & v6_yellow_6(B,A) & v7_yellow_6(B,A) ) => ( v1_relat_1(B) & v8_yellow_6(B,A) ) ) ) ) ), file(yellow_6,cc9_yellow_6), []). 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(d10_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_waybel_0(B,A) => ( v1_yellow_6(B,A) => ( v3_struct_0(B) | k5_yellow_6(A,B) = k1_yellow_6(u1_waybel_0(A,B)) ) ) ) ) ), file(yellow_6,d10_yellow_6), []). fof(d11_pralg_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_pralg_1(A) <=> ! [B] : ( r2_hidden(B,k1_relat_1(A)) => l1_struct_0(k1_funct_1(A,B)) ) ) ) ), file(pralg_1,d11_pralg_1), []). fof(d12_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( m2_yellow_6(C,A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B)) & m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) & u1_waybel_0(A,C) = k7_funct_2(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,u1_waybel_0(A,B)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( r1_orders_2(C,F,G) => r1_orders_2(B,E,k3_yellow_6(u1_struct_0(C),B,D,G)) ) ) ) ) ) ) ) ) ) ), file(yellow_6,d12_yellow_6), []). fof(d14_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( B = k7_yellow_6(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( ~ v3_struct_0(D) & v3_orders_2(D) & v6_waybel_0(D,A) & v7_waybel_0(D) & l1_waybel_0(D,A) & D = C & r2_hidden(u1_struct_0(D),k2_yellow_6(u1_struct_0(A))) ) ) ) ) ), file(yellow_6,d14_yellow_6), []). fof(d15_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ! [C] : ( m1_pboole(C,A) => ( m3_yellow_6(C,A,B) <=> ! [D] : ( r2_hidden(D,k2_relat_1(C)) => ( ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,B) ) ) ) ) ) ), file(yellow_6,d15_yellow_6), []). fof(d16_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => ! [D] : ( ( ~ v3_struct_0(D) & v3_orders_2(D) & v6_waybel_0(D,A) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ( D = k9_yellow_6(A,B,C) <=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = k3_yellow_3(B,k5_yellow_1(u1_struct_0(B),C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( r2_hidden(E,u1_struct_0(B)) & r2_hidden(F,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) ) => k1_binop_1(u1_waybel_0(A,D),E,F) = k1_funct_1(u1_waybel_0(A,k8_yellow_6(u1_struct_0(B),A,C,E)),k1_funct_1(F,E)) ) ) ) ) ) ) ) ) ) ), file(yellow_6,d16_yellow_6), []). fof(d18_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ! [D] : ( m1_pboole(D,A) => ( m3_pboole(D,A,B,C) <=> ! [E] : ( r2_hidden(E,A) => ( v1_funct_1(k1_funct_1(D,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_funct_1(D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ), file(pboole,d18_pboole), []). fof(d1_binop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ), file(binop_1,d1_binop_1), []). 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(d21_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) <=> r1_tarski(B,k2_zfmisc_1(k7_yellow_6(A),u1_struct_0(A))) ) ) ), file(yellow_6,d21_yellow_6), []). fof(d22_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( B = k13_yellow_6(A) <=> ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ( r2_hidden(C,k7_yellow_6(A)) & r2_hidden(D,k11_yellow_6(A,C)) ) ) ) ) ) ) ) ), file(yellow_6,d22_yellow_6), []). fof(d23_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v4_yellow_6(B,A) <=> ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & v1_yellow_6(C,A) & l1_waybel_0(C,A) ) => ( r2_hidden(C,k7_yellow_6(A)) => r2_hidden(k4_tarski(C,k5_yellow_6(A,C)),B) ) ) ) ) ) ), file(yellow_6,d23_yellow_6), []). fof(d24_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v5_yellow_6(B,A) <=> ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m2_yellow_6(D,A,C) => ( r2_hidden(D,k7_yellow_6(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,E),B) => r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) ) ) ), file(yellow_6,d24_yellow_6), []). fof(d25_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v6_yellow_6(B,A) <=> ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,k7_yellow_6(A)) & ~ r2_hidden(k4_tarski(C,D),B) & ! [E] : ( m2_yellow_6(E,A,C) => ~ ( r2_hidden(E,k7_yellow_6(A)) & ! [F] : ( m2_yellow_6(F,A,E) => ~ r2_hidden(k4_tarski(F,D),B) ) ) ) ) ) ) ) ) ) ), file(yellow_6,d25_yellow_6), []). fof(d26_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v7_yellow_6(B,A) <=> ! [C] : ( ( ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) => ! [E] : ( m3_yellow_6(E,u1_struct_0(C),A) => ( ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => r2_hidden(k4_tarski(k8_yellow_6(u1_struct_0(C),A,E,F),k3_waybel_0(A,C,F)),B) ) => r2_hidden(k4_tarski(k9_yellow_6(A,C,E),D),B) ) ) ) ) ) ) ) ) ), file(yellow_6,d26_yellow_6), []). fof(d27_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ! [C] : ( ( v1_pre_topc(C) & l1_pre_topc(C) ) => ( C = k14_yellow_6(A,B) <=> ( u1_struct_0(C) = u1_struct_0(A) & u1_pre_topc(C) = a_2_3_yellow_6(A,B) ) ) ) ) ) ), file(yellow_6,d27_yellow_6), []). fof(d28_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v8_yellow_6(B,A) <=> ( v4_yellow_6(B,A) & v5_yellow_6(B,A) & v6_yellow_6(B,A) & v7_yellow_6(B,A) ) ) ) ) ), file(yellow_6,d28_yellow_6), []). fof(d2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,D) ) => r1_orders_2(A,B,D) ) ) ) ) ) ) ), file(yellow_0,d2_yellow_0), []). fof(d2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k3_yellow_3(A,B) <=> ( u1_struct_0(C) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) & u1_orders_2(C) = k2_yellow_3(u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_orders_2(A),u1_orders_2(B)) ) ) ) ) ) ), file(yellow_3,d2_yellow_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_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),A) => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ), file(relat_1,d3_relat_1), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_yellow_6,axiom,( ! [A] : k2_yellow_6(A) = k1_classes1(k5_classes1(A)) ), file(yellow_6,d3_yellow_6), []). 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_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) => ( v4_waybel_3(A) <=> ! [B] : ( r2_hidden(B,k2_relat_1(A)) => ( ~ v3_struct_0(B) & l1_struct_0(B) ) ) ) ) ), file(yellow_6,d4_yellow_6), []). fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d5_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v7_waybel_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,B,D) & r1_orders_2(A,C,D) ) ) ) ) ) ), file(yellow_6,d5_yellow_6), []). fof(d6_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ( v1_yellow_6(B,A) <=> v5_seqm_3(u1_waybel_0(A,B)) ) ) ) ), file(yellow_6,d6_yellow_6), []). fof(d7_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v6_waybel_0(D,B) & l1_waybel_0(D,B) ) => ( D = k4_yellow_6(A,B,C) <=> ( g1_orders_2(u1_struct_0(D),u1_orders_2(D)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) & u1_waybel_0(B,D) = k2_pre_circ(u1_struct_0(D),C) ) ) ) ) ) ) ), file(yellow_6,d7_yellow_6), []). 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(d9_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_relat_1(A) <=> ~ r2_hidden(k1_xboole_0,k2_relat_1(A)) ) ) ), file(relat_1,d9_relat_1), []). fof(dt_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ( v1_orders_2(g1_orders_2(A,B)) & l1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,g1_orders_2), []). fof(dt_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_pre_topc(g1_pre_topc(A,B)) & l1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(pre_topc,g1_pre_topc), []). fof(dt_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ( v6_waybel_0(g1_waybel_0(A,B,C,D),A) & l1_waybel_0(g1_waybel_0(A,B,C,D),A) ) ) ), file(waybel_0,g1_waybel_0), []). fof(dt_k10_pralg_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_pralg_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => l1_struct_0(k10_pralg_1(A,B,C)) ) ), file(pralg_1,k10_pralg_1), []). fof(dt_k11_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(k11_yellow_6(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(yellow_6,k11_yellow_6), []). fof(dt_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_k13_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m4_yellow_6(k13_yellow_6(A),A) ) ), file(yellow_6,k13_yellow_6), []). fof(dt_k14_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( v1_pre_topc(k14_yellow_6(A,B)) & l1_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,k14_yellow_6), []). fof(dt_k1_binop_1,axiom,( $true ), file(binop_1,k1_binop_1), []). fof(dt_k1_classes1,axiom,( $true ), file(classes1,k1_classes1), []). fof(dt_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => m1_subset_1(k1_domain_1(A,B,C,D),k2_zfmisc_1(A,B)) ) ), file(domain_1,k1_domain_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), []). fof(dt_k1_tarski,axiom,( $true ), file(tarski,k1_tarski), []). fof(dt_k1_waybel_0,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k1_waybel_0(A,B,C,D),u1_struct_0(B)) ) ), file(waybel_0,k1_waybel_0), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_yellow_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k1_yellow_3(A,B)) ) ), file(yellow_3,k1_yellow_3), []). fof(dt_k1_yellow_6,axiom,( $true ), file(yellow_6,k1_yellow_6), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k2_funcop_1,axiom,( $true ), file(funcop_1,k2_funcop_1), []). 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_yellow_3,axiom,( ! [A,B,C,D,E,F] : ( ( m1_relset_1(E,A,B) & m1_relset_1(F,C,D) ) => m2_relset_1(k2_yellow_3(A,B,C,D,E,F),k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ), file(yellow_3,k2_yellow_3), []). fof(dt_k2_yellow_6,axiom,( $true ), file(yellow_6,k2_yellow_6), []). 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_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ( ~ v3_struct_0(k3_waybel_3(A,B,C)) & l1_orders_2(k3_waybel_3(A,B,C)) ) ) ), file(waybel_3,k3_waybel_3), []). fof(dt_k3_yellow_3,axiom,( ! [A,B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k3_yellow_3(A,B)) & l1_orders_2(k3_yellow_3(A,B)) ) ) ), file(yellow_3,k3_yellow_3), []). fof(dt_k3_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(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(D,A) ) => m1_subset_1(k3_yellow_6(A,B,C,D),u1_struct_0(B)) ) ), file(yellow_6,k3_yellow_6), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_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_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_waybel_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => m1_subset_1(k4_waybel_3(A,B,C,D),u1_struct_0(k3_waybel_3(A,B,D))) ) ), file(waybel_3,k4_waybel_3), []). fof(dt_k4_yellow_6,axiom,( ! [A,B,C] : ( ( l1_orders_2(A) & ~ v3_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( v6_waybel_0(k4_yellow_6(A,B,C),B) & l1_waybel_0(k4_yellow_6(A,B,C),B) ) ) ), file(yellow_6,k4_yellow_6), []). fof(dt_k5_classes1,axiom,( $true ), file(classes1,k5_classes1), []). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), []). 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_k5_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & l1_waybel_0(B,A) ) => m1_subset_1(k5_yellow_6(A,B),u1_struct_0(A)) ) ), file(yellow_6,k5_yellow_6), []). fof(dt_k6_pre_topc,axiom,( ! [A,B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ), file(pre_topc,k6_pre_topc), []). fof(dt_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => ( v1_funct_1(k7_funct_2(A,B,C,D,E)) & v1_funct_2(k7_funct_2(A,B,C,D,E),A,C) & m2_relset_1(k7_funct_2(A,B,C,D,E),A,C) ) ) ), file(funct_2,k7_funct_2), []). fof(dt_k7_yellow_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => m1_subset_1(k7_yellow_3(A,B,C,D),u1_struct_0(k3_yellow_3(A,B))) ) ), file(yellow_3,k7_yellow_3), []). fof(dt_k7_yellow_6,axiom,( $true ), file(yellow_6,k7_yellow_6), []). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & l1_struct_0(B) & m3_yellow_6(C,A,B) & m1_subset_1(D,A) ) => ( ~ v3_struct_0(k8_yellow_6(A,B,C,D)) & v3_orders_2(k8_yellow_6(A,B,C,D)) & v7_waybel_0(k8_yellow_6(A,B,C,D)) & l1_waybel_0(k8_yellow_6(A,B,C,D),B) ) ) ), file(yellow_6,k8_yellow_6), []). fof(dt_k9_yellow_6,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) & m3_yellow_6(C,u1_struct_0(B),A) ) => ( ~ v3_struct_0(k9_yellow_6(A,B,C)) & v3_orders_2(k9_yellow_6(A,B,C)) & v6_waybel_0(k9_yellow_6(A,B,C),A) & v7_waybel_0(k9_yellow_6(A,B,C)) & l1_waybel_0(k9_yellow_6(A,B,C),A) ) ) ), file(yellow_6,k9_yellow_6), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) ), file(pre_topc,l1_pre_topc), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l1_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => l1_orders_2(B) ) ) ), file(waybel_0,l1_waybel_0), []). fof(dt_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_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_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m3_pboole(D,A,B,C) => m1_pboole(D,A) ) ) ), file(pboole,m3_pboole), []). fof(dt_m3_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ! [C] : ( m3_yellow_6(C,A,B) => m1_pboole(C,A) ) ) ), file(yellow_6,m3_yellow_6), []). fof(dt_m4_yellow_6,axiom,( $true ), file(yellow_6,m4_yellow_6), []). fof(dt_u1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ), file(orders_2,u1_orders_2), []). fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ), file(pre_topc,u1_pre_topc), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u1_waybel_0,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ( v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) & m2_relset_1(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(waybel_0,u1_waybel_0), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) ), file(pre_topc,l1_pre_topc), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l1_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_waybel_0(B,A) ) ), file(waybel_0,l1_waybel_0), []). fof(existence_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_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(existence_m3_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m3_pboole(D,A,B,C) ) ), file(pboole,m3_pboole), []). fof(existence_m3_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ? [C] : m3_yellow_6(C,A,B) ) ), file(yellow_6,m3_yellow_6), []). fof(existence_m4_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : m4_yellow_6(B,A) ) ), file(yellow_6,m4_yellow_6), []). fof(fc10_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), []). 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(fc10_yellow_3,axiom,( ! [A,B] : ( ( v3_orders_2(A) & l1_orders_2(A) & v3_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k3_yellow_3(A,B)) & v3_orders_2(k3_yellow_3(A,B)) ) ) ), file(yellow_3,fc10_yellow_3), []). fof(fc10_yellow_6,axiom,( ! [A,B] : ( ( v7_waybel_0(A) & l1_orders_2(A) & v7_waybel_0(B) & l1_orders_2(B) ) => ( v1_orders_2(k3_yellow_3(A,B)) & v7_waybel_0(k3_yellow_3(A,B)) ) ) ), file(yellow_6,fc10_yellow_6), []). fof(fc11_yellow_6,axiom,( ! [A,B,C] : ( ( l1_orders_2(A) & ~ v3_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( v6_waybel_0(k4_yellow_6(A,B,C),B) & v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ), file(yellow_6,fc11_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(fc12_yellow_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( ~ v3_struct_0(k4_yellow_6(A,B,C)) & v6_waybel_0(k4_yellow_6(A,B,C),B) & v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ), file(yellow_6,fc12_yellow_6), []). fof(fc13_yellow_3,axiom,( ! [A] : ( ( ~ v1_yellow_3(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(u1_orders_2(A)) & v1_relat_1(u1_orders_2(A)) ) ) ), file(yellow_3,fc13_yellow_3), []). fof(fc13_yellow_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v7_waybel_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( ~ v3_struct_0(k4_yellow_6(A,B,C)) & v6_waybel_0(k4_yellow_6(A,B,C),B) & v7_waybel_0(k4_yellow_6(A,B,C)) & v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ), file(yellow_6,fc13_yellow_6), []). fof(fc14_yellow_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( ~ v3_struct_0(k4_yellow_6(A,B,C)) & v3_orders_2(k4_yellow_6(A,B,C)) & v6_waybel_0(k4_yellow_6(A,B,C),B) & v1_yellow_6(k4_yellow_6(A,B,C),B) ) ) ), file(yellow_6,fc14_yellow_6), []). fof(fc15_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & l1_waybel_0(B,A) ) => ( ~ v1_xboole_0(u1_waybel_0(A,B)) & v1_relat_1(u1_waybel_0(A,B)) & v1_funct_1(u1_waybel_0(A,B)) & v1_funct_2(u1_waybel_0(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ), file(yellow_6,fc15_yellow_6), []). fof(fc16_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & v1_yellow_6(B,A) & l1_waybel_0(B,A) ) => ( 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)) & v5_seqm_3(u1_waybel_0(A,B)) ) ) ), file(yellow_6,fc16_yellow_6), []). fof(fc18_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k7_yellow_6(A)) ) ), file(yellow_6,fc18_yellow_6), []). fof(fc19_yellow_6,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) & m3_yellow_6(C,u1_struct_0(B),A) ) => ( ~ v3_struct_0(k5_yellow_1(u1_struct_0(B),C)) & v1_orders_2(k5_yellow_1(u1_struct_0(B),C)) & v3_orders_2(k5_yellow_1(u1_struct_0(B),C)) & v7_waybel_0(k5_yellow_1(u1_struct_0(B),C)) ) ) ), file(yellow_6,fc19_yellow_6), []). fof(fc1_classes2,axiom,( ! [A] : ( ~ v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) ) ), file(classes2,fc1_classes2), []). 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_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), []). fof(fc1_orders_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,A) ) => ( ~ v3_struct_0(g1_orders_2(A,B)) & v1_orders_2(g1_orders_2(A,B)) ) ) ), file(orders_2,fc1_orders_2), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_yellow_0,axiom,( ! [A,B] : ( m1_relset_1(B,k1_tarski(A),k1_tarski(A)) => ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B)) & v1_orders_2(g1_orders_2(k1_tarski(A),B)) & v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ), file(yellow_0,fc1_yellow_0), []). fof(fc1_yellow_6,axiom,( ! [A] : ( v1_ordinal1(k2_yellow_6(A)) & v1_classes1(k2_yellow_6(A)) & v2_classes1(k2_yellow_6(A)) & v1_classes2(k2_yellow_6(A)) ) ), file(yellow_6,fc1_yellow_6), []). fof(fc23_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_relat_1(k13_yellow_6(A)) & v4_yellow_6(k13_yellow_6(A),A) & v5_yellow_6(k13_yellow_6(A),A) & v6_yellow_6(k13_yellow_6(A),A) & v7_yellow_6(k13_yellow_6(A),A) ) ) ), file(yellow_6,fc23_yellow_6), []). fof(fc24_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( ~ v3_struct_0(k14_yellow_6(A,B)) & v1_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,fc24_yellow_6), []). fof(fc25_yellow_6,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) ) => ( ~ v3_struct_0(k14_yellow_6(A,B)) & v1_pre_topc(k14_yellow_6(A,B)) & v2_pre_topc(k14_yellow_6(A,B)) ) ) ), file(yellow_6,fc25_yellow_6), []). fof(fc2_complsp1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ~ v3_struct_0(g1_pre_topc(A,B)) & v1_pre_topc(g1_pre_topc(A,B)) ) ) ), file(complsp1,fc2_complsp1), []). 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_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc2_seqm_3,axiom,( ! [A,B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v5_seqm_3(k2_funcop_1(A,B)) ) ), file(seqm_3,fc2_seqm_3), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_yellow_6,axiom,( ! [A] : ( ~ v1_xboole_0(k2_yellow_6(A)) & v1_ordinal1(k2_yellow_6(A)) & v1_classes1(k2_yellow_6(A)) & v2_classes1(k2_yellow_6(A)) & v1_classes2(k2_yellow_6(A)) ) ), file(yellow_6,fc2_yellow_6), []). fof(fc3_ami_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(ami_1,fc3_ami_1), []). fof(fc3_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( v1_ordinal1(k1_classes1(A)) & ~ v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) ) ) ), file(classes2,fc3_classes2), []). 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_pralg_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ( ~ v1_xboole_0(k4_card_3(B)) & v1_fraenkel(k4_card_3(B)) ) ) ), file(pralg_1,fc3_pralg_1), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) & v5_seqm_3(k2_funcop_1(A,B)) & v2_pralg_1(k2_funcop_1(A,B)) ) ) ), file(yellow_6,fc3_yellow_6), []). fof(fc4_ami_1,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(ami_1,fc4_ami_1), []). fof(fc4_index_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => v1_fraenkel(k2_relat_1(A)) ) ), file(index_1,fc4_index_1), []). 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_yellow_6,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & m1_pboole(B,A) ) => v1_fraenkel(u1_struct_0(k5_yellow_1(A,B))) ) ), file(yellow_6,fc4_yellow_6), []). fof(fc5_classes2,axiom,( ! [A] : v1_ordinal1(k5_classes1(A)) ), file(classes2,fc5_classes2), []). fof(fc5_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), []). fof(fc5_yellow_6,axiom,( ! [A,B] : ( ( v2_pralg_1(B) & v4_waybel_3(B) & m1_pboole(B,A) ) => ( v1_relat_1(k12_pralg_1(A,B)) & v2_relat_1(k12_pralg_1(A,B)) & v1_funct_1(k12_pralg_1(A,B)) ) ) ), file(yellow_6,fc5_yellow_6), []). fof(fc6_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => ( v1_ordinal1(k1_classes1(A)) & ~ v1_xboole_0(k1_classes1(A)) & v1_classes1(k1_classes1(A)) & v2_classes1(k1_classes1(A)) & v1_classes2(k1_classes1(A)) ) ) ), file(classes2,fc6_classes2), []). 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_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), []). 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(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), []). fof(fc7_yellow_3,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) ) => ( ~ v3_struct_0(k3_yellow_3(A,B)) & v1_orders_2(k3_yellow_3(A,B)) ) ) ), file(yellow_3,fc7_yellow_3), []). fof(fc8_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) ) ) ), file(funcop_1,fc8_funcop_1), []). fof(fc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_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_relat_1,axiom,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), []). fof(fc9_yellow_6,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & 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(yellow_6,fc9_yellow_6), []). fof(fraenkel_a_0_0_domain_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_domain_1) <=> ? [B] : ( m1_subset_1(B,f1_s7_domain_1) & A = B & p1_s7_domain_1(B) ) ) ), file(domain_1,a_0_0_domain_1), []). fof(fraenkel_a_2_3_yellow_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & m4_yellow_6(C,B) ) => ( r2_hidden(A,a_2_3_yellow_6(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) => ! [F] : ( ( ~ v3_struct_0(F) & v3_orders_2(F) & v7_waybel_0(F) & l1_waybel_0(F,B) ) => ( r2_hidden(k4_tarski(F,E),C) => r1_waybel_0(B,F,D) ) ) ) ) ) ) ) ), file(yellow_6,a_2_3_yellow_6), []). fof(fraenkel_a_3_1_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_1_yellow_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k3_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) ), file(yellow_6,a_3_1_yellow_6), []). fof(fraenkel_a_4_1_yellow_6,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m2_yellow_6(D,B,C) & m1_subset_1(E,u1_struct_0(D)) ) => ( r2_hidden(A,a_4_1_yellow_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = k3_waybel_0(B,D,F) & r1_orders_2(D,E,F) ) ) ) ), file(yellow_6,a_4_1_yellow_6), []). fof(fraenkel_a_4_2_yellow_6,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & ~ v3_struct_0(C) & v3_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m2_yellow_6(D,B,C) & m1_subset_1(E,u1_struct_0(D)) ) => ( r2_hidden(A,a_4_2_yellow_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = F & r1_orders_2(D,E,F) ) ) ) ), file(yellow_6,a_4_2_yellow_6), []). fof(fraenkel_a_5_0_yellow_6,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) & m4_yellow_6(C,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,k14_yellow_6(B,C)) & m2_yellow_6(E,k14_yellow_6(B,C),D) & m1_subset_1(F,u1_struct_0(E)) ) => ( r2_hidden(A,a_5_0_yellow_6(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(E)) & A = k3_waybel_0(k14_yellow_6(B,C),E,G) & r1_orders_2(E,F,G) ) ) ) ), file(yellow_6,a_5_0_yellow_6), []). fof(free_g1_orders_2,axiom,( ! [A,B] : ( m1_relset_1(B,A,A) => ! [C,D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) ), file(orders_2,g1_orders_2), []). fof(free_g1_pre_topc,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C,D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) ), file(pre_topc,g1_pre_topc), []). fof(free_g1_waybel_0,axiom,( ! [A,B,C,D] : ( ( l1_struct_0(A) & m1_relset_1(C,B,B) & v1_funct_1(D) & v1_funct_2(D,B,u1_struct_0(A)) & m1_relset_1(D,B,u1_struct_0(A)) ) => ! [E,F,G,H] : ( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(waybel_0,g1_waybel_0), []). fof(l16_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v7_waybel_0(A) <=> v7_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(yellow_6,l16_yellow_6), []). fof(l17_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ( v3_orders_2(A) <=> v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ), file(yellow_6,l17_yellow_6), []). fof(l20_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F & g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) & r1_orders_2(A,C,D) ) => r1_orders_2(B,E,F) ) ) ) ) ) ) ) ), file(yellow_6,l20_yellow_6), []). fof(l53_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => k7_yellow_6(A) = k7_yellow_6(B) ) ) ) ), file(yellow_6,l53_yellow_6), []). fof(rc10_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v3_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v3_yellow_6(B,A) ) ) ), file(yellow_6,rc10_yellow_6), []). fof(rc11_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m4_yellow_6(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v8_yellow_6(B,A) ) ) ), file(yellow_6,rc11_yellow_6), []). fof(rc1_classes2,axiom,( ? [A] : ( v1_ordinal1(A) & ~ v1_xboole_0(A) & v1_classes1(A) & v2_classes1(A) & v1_classes2(A) ) ), file(classes2,rc1_classes2), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & ~ v3_relat_1(B) & v1_funct_1(B) ) ) ), file(index_1,rc1_index_1), []). fof(rc1_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) ) ), file(orders_2,rc1_orders_2), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) ), file(pre_topc,rc1_pre_topc), []). 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_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(rc1_yellow_6,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) ) ), file(yellow_6,rc1_yellow_6), []). fof(rc2_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & ~ v1_xboole_0(B) ) ) ), file(classes2,rc2_classes2), []). 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_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v3_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc2_pboole), []). 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_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_yellow_6,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v5_seqm_3(A) & v2_pralg_1(A) ) ), file(yellow_6,rc2_yellow_6), []). 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_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) ), file(pboole,rc3_pboole), []). 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_yellow_6,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v4_waybel_3(B) ) ), file(yellow_6,rc3_yellow_6), []). 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_pboole,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ), file(pboole,rc4_pboole), []). fof(rc4_pralg_1,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) ) ), file(pralg_1,rc4_pralg_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_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_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(rc5_yellow_6,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_pralg_1(B) & v1_yellow_1(B) & v4_waybel_3(B) ) ), file(yellow_6,rc5_yellow_6), []). fof(rc8_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v3_struct_0(B) & v3_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v1_yellow_6(B,A) ) ) ), file(yellow_6,rc8_yellow_6), []). fof(rc9_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ? [C] : ( m3_yellow_6(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v2_pralg_1(C) & v1_yellow_1(C) & v4_waybel_3(C) ) ) ), file(yellow_6,rc9_yellow_6), []). fof(redefinition_k10_pralg_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_pralg_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k10_pralg_1(A,B,C) = k1_funct_1(B,C) ) ), file(pralg_1,k10_pralg_1), []). fof(redefinition_k1_domain_1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,A) & m1_subset_1(D,B) ) => k1_domain_1(A,B,C,D) = k4_tarski(C,D) ) ), file(domain_1,k1_domain_1), []). 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_pre_circ,axiom,( ! [A,B] : k2_pre_circ(A,B) = k2_funcop_1(A,B) ), file(pre_circ,k2_pre_circ), []). fof(redefinition_k2_yellow_3,axiom,( ! [A,B,C,D,E,F] : ( ( m1_relset_1(E,A,B) & m1_relset_1(F,C,D) ) => k2_yellow_3(A,B,C,D,E,F) = k1_yellow_3(E,F) ) ), file(yellow_3,k2_yellow_3), []). fof(redefinition_k3_waybel_3,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => k3_waybel_3(A,B,C) = k1_funct_1(B,C) ) ), file(waybel_3,k3_waybel_3), []). fof(redefinition_k3_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v3_struct_0(B) & l1_orders_2(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(D,A) ) => k3_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_6,k3_yellow_6), []). 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_waybel_3,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_yellow_1(B) & v4_waybel_3(B) & m1_pboole(B,A) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => k4_waybel_3(A,B,C,D) = k1_funct_1(C,D) ) ), file(waybel_3,k4_waybel_3), []). fof(redefinition_k7_funct_2,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) & v1_funct_1(E) & v1_funct_2(E,B,C) & m1_relset_1(E,B,C) ) => k7_funct_2(A,B,C,D,E) = k5_relat_1(D,E) ) ), file(funct_2,k7_funct_2), []). fof(redefinition_k7_yellow_3,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) & ~ v3_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => k7_yellow_3(A,B,C,D) = k4_tarski(C,D) ) ), file(yellow_3,k7_yellow_3), []). fof(redefinition_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_yellow_6,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & l1_struct_0(B) & m3_yellow_6(C,A,B) & m1_subset_1(D,A) ) => k8_yellow_6(A,B,C,D) = k1_funct_1(C,D) ) ), file(yellow_6,k8_yellow_6), []). 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(s1_funct_7__e13_124_4_6__yellow_6,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( ~ 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) & m2_yellow_6(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v6_waybel_0(D,A) & v7_waybel_0(D) & v1_yellow_6(D,A) & l1_waybel_0(D,A) & v4_waybel_3(E) & m3_yellow_6(E,u1_struct_0(D),A) & v2_relat_1(F) & m1_pboole(F,u1_struct_0(D)) & m1_pboole(G,u1_struct_0(D)) & m3_pboole(H,u1_struct_0(D),G,F) ) => ( ! [I] : ( m1_subset_1(I,u1_struct_0(D)) => ! [J] : ( m1_subset_1(J,u1_struct_0(k5_yellow_1(u1_struct_0(D),E))) => r2_hidden(k1_funct_1(k1_funct_1(H,I),k4_waybel_3(u1_struct_0(D),E,J,I)),u1_struct_0(C)) ) ) => ? [I] : ( v1_funct_1(I) & v1_funct_2(I,k2_zfmisc_1(u1_struct_0(D),u1_struct_0(k5_yellow_1(u1_struct_0(D),E))),u1_struct_0(C)) & m2_relset_1(I,k2_zfmisc_1(u1_struct_0(D),u1_struct_0(k5_yellow_1(u1_struct_0(D),E))),u1_struct_0(C)) & ! [J] : ( m1_subset_1(J,u1_struct_0(D)) => ! [K] : ( m1_subset_1(K,u1_struct_0(k5_yellow_1(u1_struct_0(D),E))) => k8_funct_2(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(k5_yellow_1(u1_struct_0(D),E))),u1_struct_0(C),I,k1_domain_1(u1_struct_0(D),u1_struct_0(k5_yellow_1(u1_struct_0(D),E)),J,K)) = k1_funct_1(k1_funct_1(H,J),k4_waybel_3(u1_struct_0(D),E,K,J)) ) ) ) ) ) ), file(yellow_6,s1_funct_7__e13_124_4_6__yellow_6), []). fof(s1_mssubfam__e9_124_4_6__yellow_6,axiom,( ! [A,B,C,D,E,F,G] : ( ( ~ 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) & m2_yellow_6(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v6_waybel_0(D,A) & v7_waybel_0(D) & v1_yellow_6(D,A) & l1_waybel_0(D,A) & v4_waybel_3(E) & m3_yellow_6(E,u1_struct_0(D),A) & v2_relat_1(F) & m1_pboole(F,u1_struct_0(D)) & m1_pboole(G,u1_struct_0(D)) ) => ( ! [H] : ( r2_hidden(H,u1_struct_0(D)) => ! [I] : ~ ( r2_hidden(I,k1_funct_1(G,H)) & ! [J] : ~ ( r2_hidden(J,k1_funct_1(F,H)) & ? [K] : ( v1_relat_1(K) & v1_funct_1(K) & ? [L] : ( m1_subset_1(L,u1_struct_0(D)) & k1_funct_1(K,I) = J & L = H & k1_funct_1(u1_waybel_0(A,k8_yellow_6(u1_struct_0(D),A,E,L)),I) = k1_funct_1(u1_waybel_0(A,C),J) ) ) ) ) ) => ? [H] : ( m3_pboole(H,u1_struct_0(D),G,F) & ! [I] : ~ ( r2_hidden(I,u1_struct_0(D)) & ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k1_funct_1(G,I),k1_funct_1(F,I)) & m2_relset_1(J,k1_funct_1(G,I),k1_funct_1(F,I)) ) => ~ ( J = k1_funct_1(H,I) & ! [M] : ( r2_hidden(M,k1_funct_1(G,I)) => ? [N] : ( v1_relat_1(N) & v1_funct_1(N) & ? [O] : ( m1_subset_1(O,u1_struct_0(D)) & k1_funct_1(N,M) = k1_funct_1(J,M) & O = I & k1_funct_1(u1_waybel_0(A,k8_yellow_6(u1_struct_0(D),A,E,O)),M) = k1_funct_1(u1_waybel_0(A,C),k1_funct_1(J,M)) ) ) ) ) ) ) ) ) ) ), file(yellow_6,s1_mssubfam__e9_124_4_6__yellow_6), []). fof(s3_funct_2__e10_124_4_6_2__yellow_6,axiom,( ! [A,B,C,D,E,F,G] : ( ( ~ 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) & m2_yellow_6(C,A,B) & ~ v3_struct_0(D) & v3_orders_2(D) & v6_waybel_0(D,A) & v7_waybel_0(D) & v1_yellow_6(D,A) & l1_waybel_0(D,A) & v2_relat_1(E) & m1_pboole(E,u1_struct_0(D)) & ~ v3_struct_0(F) & v3_orders_2(F) & v7_waybel_0(F) & l1_waybel_0(F,A) & m1_subset_1(G,u1_struct_0(D)) ) => ( ! [H] : ( m1_subset_1(H,u1_struct_0(F)) => ? [I] : ( m1_subset_1(I,k1_funct_1(E,G)) & k1_funct_1(u1_waybel_0(A,F),H) = k1_funct_1(u1_waybel_0(A,C),I) ) ) => ? [H] : ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(F),k1_funct_1(E,G)) & m2_relset_1(H,u1_struct_0(F),k1_funct_1(E,G)) & ! [I] : ( m1_subset_1(I,u1_struct_0(F)) => k1_funct_1(u1_waybel_0(A,F),I) = k1_funct_1(u1_waybel_0(A,C),k8_funct_2(u1_struct_0(F),k1_funct_1(E,G),H,I)) ) ) ) ) ), file(yellow_6,s3_funct_2__e10_124_4_6_2__yellow_6), []). fof(s3_pboole__e30_124_4__yellow_6,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & m4_yellow_6(B,A) & m1_subset_1(C,u1_struct_0(k14_yellow_6(A,B))) & ~ v3_struct_0(D) & v3_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) & m2_yellow_6(E,A,D) & ~ v3_struct_0(F) & v3_orders_2(F) & v6_waybel_0(F,A) & v7_waybel_0(F) & v1_yellow_6(F,A) & l1_waybel_0(F,A) ) => ( ! [G] : ~ ( r2_hidden(G,u1_struct_0(F)) & ! [H] : ~ ? [I] : ( m1_subset_1(I,u1_struct_0(E)) & ? [J] : ( ~ v3_struct_0(J) & v3_orders_2(J) & v7_waybel_0(J) & l1_waybel_0(J,A) & G = I & J = H & r2_hidden(k4_tarski(J,C),B) & r1_tarski(k2_relat_1(u1_waybel_0(A,J)),a_4_1_yellow_6(A,D,E,I)) ) ) ) => ? [G] : ( m1_pboole(G,u1_struct_0(F)) & ! [H] : ( r2_hidden(H,u1_struct_0(F)) => ? [K] : ( m1_subset_1(K,u1_struct_0(E)) & ? [L] : ( ~ v3_struct_0(L) & v3_orders_2(L) & v7_waybel_0(L) & l1_waybel_0(L,A) & H = K & L = k1_funct_1(G,H) & r2_hidden(k4_tarski(L,C),B) & r1_tarski(k2_relat_1(u1_waybel_0(A,L)),a_4_1_yellow_6(A,D,E,K)) ) ) ) ) ) ) ), file(yellow_6,s3_pboole__e30_124_4__yellow_6), []). fof(s5_pboole__e1_124_4_6__yellow_6,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) & m2_yellow_6(C,A,B) ) => ? [D] : ( m1_pboole(D,u1_struct_0(C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => k1_funct_1(D,E) = a_4_2_yellow_6(A,B,C,E) ) ) ) ), file(yellow_6,s5_pboole__e1_124_4_6__yellow_6), []). fof(s5_pboole__e6_124_4_6__yellow_6,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) & ~ v3_struct_0(B) & v3_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v1_yellow_6(B,A) & l1_waybel_0(B,A) & v4_waybel_3(C) & m3_yellow_6(C,u1_struct_0(B),A) ) => ? [D] : ( m1_pboole(D,u1_struct_0(B)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k1_funct_1(D,E) = u1_struct_0(k8_yellow_6(u1_struct_0(B),A,C,E)) ) ) ) ), file(yellow_6,s5_pboole__e6_124_4_6__yellow_6), []). fof(s7_domain_1__e3_124_4_6_4__yellow_6,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) & m2_yellow_6(C,A,B) ) => m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(u1_struct_0(C))) ) ), file(yellow_6,s7_domain_1__e3_124_4_6_4__yellow_6), []). fof(t106_zfmisc_1,axiom,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) ), file(zfmisc_1,t106_zfmisc_1), []). fof(t11_yellow_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_orders_2(A,C,D) & r1_orders_2(B,E,F) ) <=> r1_orders_2(k3_yellow_3(A,B),k7_yellow_3(A,B,C,E),k7_yellow_3(A,B,D,F)) ) ) ) ) ) ) ) ), file(yellow_3,t11_yellow_3), []). fof(t12_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( r1_tarski(k1_relat_1(C),A) & r1_tarski(k2_relat_1(C),B) ) ) ), file(relset_1,t12_relset_1), []). fof(t13_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => u1_struct_0(k4_yellow_6(A,B,C)) = u1_struct_0(A) ) ) ) ), file(yellow_6,t13_yellow_6), []). fof(t14_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_yellow_6(A,B,C))) => k3_waybel_0(B,k4_yellow_6(A,B,C),D) = C ) ) ) ) ), file(yellow_6,t14_yellow_6), []). fof(t18_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k4_card_3(B)) <=> ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(B)) => r2_hidden(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) ), file(card_3,t18_card_3), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( ! [D] : ( r2_hidden(D,k1_relat_1(C)) <=> ( r2_hidden(D,k1_relat_1(A)) & r2_hidden(k1_funct_1(A,D),k1_relat_1(B)) ) ) & ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k1_funct_1(C,D) = k1_funct_1(B,k1_funct_1(A,D)) ) ) => C = k5_relat_1(A,B) ) ) ) ) ), file(funct_1,t20_funct_1), []). fof(t22_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k5_yellow_6(B,k4_yellow_6(A,B,C)) = C ) ) ) ), file(yellow_6,t22_yellow_6), []). 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(t33_yellow_6,axiom,( ! [A,B] : ( l1_struct_0(B) => ! [C] : ( m1_pboole(C,A) => ( m3_yellow_6(C,A,B) <=> ! [D] : ( r2_hidden(D,A) => ( ~ v3_struct_0(k1_funct_1(C,D)) & v3_orders_2(k1_funct_1(C,D)) & v7_waybel_0(k1_funct_1(C,D)) & l1_waybel_0(k1_funct_1(C,D),B) ) ) ) ) ) ), file(yellow_6,t33_yellow_6), []). fof(t35_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => u1_struct_0(k9_yellow_6(A,B,C)) = k2_zfmisc_1(u1_struct_0(B),k4_card_3(k12_pralg_1(u1_struct_0(B),C))) ) ) ) ), file(yellow_6,t35_yellow_6), []). fof(t36_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_yellow_6(A,B,C))) => ( F = k7_yellow_3(B,k5_yellow_1(u1_struct_0(B),C),D,E) => k3_waybel_0(A,k9_yellow_6(A,B,C),F) = k1_waybel_0(k3_waybel_3(u1_struct_0(B),C,D),A,u1_waybel_0(A,k8_yellow_6(u1_struct_0(B),A,C,D)),k4_waybel_3(u1_struct_0(B),C,E,D)) ) ) ) ) ) ) ) ), file(yellow_6,t36_yellow_6), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t41_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => r1_tarski(k11_yellow_6(A,B),k11_yellow_6(A,C)) ) ) ) ), file(yellow_6,t41_yellow_6), []). fof(t43_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v3_struct_0(B) & v3_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k11_yellow_6(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & E = a_3_1_yellow_6(A,B,D) & r2_hidden(C,k6_pre_topc(A,E)) ) ) ) ) ) ) ), file(yellow_6,t43_yellow_6), []). fof(t49_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => r1_tarski(B,k13_yellow_6(k14_yellow_6(A,B))) ) ) ), file(yellow_6,t49_yellow_6), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t52_yellow_6,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v8_yellow_6(B,A) & m4_yellow_6(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_yellow_6(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_yellow_6(A,B))) => ~ ( r2_hidden(D,k6_pre_topc(k14_yellow_6(A,B),C)) & ! [E] : ( ( ~ v3_struct_0(E) & v3_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,k14_yellow_6(A,B)) ) => ~ ( r2_hidden(k4_tarski(E,D),B) & r1_tarski(k2_relat_1(u1_waybel_0(k14_yellow_6(A,B),E)),C) & r2_hidden(D,k11_yellow_6(k14_yellow_6(A,B),E)) ) ) ) ) ) ) ) ), file(yellow_6,t52_yellow_6), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_funct_2,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m2_relset_1(D,A,B) ) => ( r2_hidden(C,A) => ( B = k1_xboole_0 | r2_hidden(k1_funct_1(D,C),B) ) ) ) ), file(funct_2,t7_funct_2), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t9_domain_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,k2_zfmisc_1(B,C)) & ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,C) => A != k4_tarski(D,E) ) ) ) ) ) ), file(domain_1,t9_domain_1), []). 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_yellow_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v2_pralg_1(B) & m1_pboole(B,A) ) => ! [C] : ( m1_subset_1(C,A) => k1_funct_1(k12_pralg_1(A,B),C) = u1_struct_0(k10_pralg_1(A,B,C)) ) ) ) ), file(yellow_6,t9_yellow_6), []).