% Mizar problem: t27_osafree,osafree,3333,30 fof(t27_osafree,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B))) => ( r6_pboole(u1_struct_0(A),C,k20_osafree(A,B)) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( r2_hidden(F,k1_funct_1(B,D)) => ( ( r3_orders_2(A,D,E) => r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F,D)),k1_trees_4(k4_tarski(F,D))),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) ) & ! [G] : ( ( r2_hidden(k4_tarski(k1_trees_4(k4_tarski(F,D)),G),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) | r2_hidden(k4_tarski(G,k1_trees_4(k4_tarski(F,D))),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,E)) ) => ( r3_orders_2(A,D,E) & G = k1_trees_4(k4_tarski(F,D)) ) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ! [E] : ( m1_subset_1(E,u1_msualg_1(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,k8_osafree(A,B))) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,E,k8_osafree(A,B))) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( r2_hidden(k4_tarski(k8_funct_2(k3_msualg_1(A,D,k8_osafree(A,B)),k4_msualg_1(A,D,k8_osafree(A,B)),k5_msualg_1(A,D,k8_osafree(A,B)),F),k8_funct_2(k3_msualg_1(A,E,k8_osafree(A,B)),k4_msualg_1(A,E,k8_osafree(A,B)),k5_msualg_1(A,E,k8_osafree(A,B)),G)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,H)) <=> ( r1_osalg_1(A,D,E) & k3_finseq_1(k1_msualg_1(A,D)) = k3_finseq_1(k1_msualg_1(A,E)) & r3_orders_2(A,k1_osalg_1(A,D),H) & r3_orders_2(A,k1_osalg_1(A,E),H) & ? [I] : ( m2_finseq_2(I,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) & k4_finseq_1(I) = k4_finseq_1(F) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( r2_hidden(J,k4_finseq_1(I)) => r2_hidden(k4_tarski(k1_funct_1(F,J),k1_funct_1(G,J)),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,k4_finseq_4(k5_numbers,u1_struct_0(A),I,J))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc10_trees_3,cc1_dtconstr,cc1_msualg_1,cc1_msualg_4,cc1_msualg_9,cc1_nat_1,cc1_osalg_1,cc1_partfun1,cc1_pboole,cc1_relset_1,cc1_trees_4,cc2_dtconstr,cc2_msualg_1,cc2_nat_1,cc2_pboole,cc3_nat_1,cc3_pboole,cc4_trees_3,cc5_trees_3,cc6_trees_3,cc7_trees_3,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d10_osafree,d11_msualg_1,d11_osafree,d11_relat_2,d1_funct_2,d1_lang1,d1_tarski,d20_osafree,d21_osafree,d22_osafree,d23_osafree,d2_relat_1,d3_lang1,d3_relat_2,d4_finseq_1,d4_osafree,d4_trees_4,d5_osafree,d5_tarski,d6_osafree,d7_osafree,d8_osafree,d9_dtconstr,d9_osafree,dt_g1_lang1,dt_g3_msualg_1,dt_k12_finseq_1,dt_k12_trees_4,dt_k13_finseq_1,dt_k13_trees_3,dt_k15_lang1,dt_k16_trees_3,dt_k17_osafree,dt_k18_osafree,dt_k19_osafree,dt_k1_card_1,dt_k1_dtconstr,dt_k1_funct_1,dt_k1_msualg_1,dt_k1_msualg_4,dt_k1_nat_1,dt_k1_numbers,dt_k1_osafree,dt_k1_osalg_1,dt_k1_relat_1,dt_k1_tarski,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k20_osafree,dt_k2_card_3,dt_k2_funct_6,dt_k2_msafree,dt_k2_msualg_1,dt_k2_msualg_4,dt_k2_osafree,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_4,dt_k2_xboole_0,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_card_3,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_msafree,dt_k3_msualg_1,dt_k3_osafree,dt_k3_relat_1,dt_k4_dtconstr,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_msualg_1,dt_k4_osafree,dt_k4_relset_1,dt_k4_tarski,dt_k4_trees_4,dt_k5_finseq_1,dt_k5_lang1,dt_k5_msualg_1,dt_k5_msualg_4,dt_k5_numbers,dt_k5_ordinal2,dt_k5_osafree,dt_k5_relat_1,dt_k5_trees_2,dt_k5_trees_3,dt_k6_dtconstr,dt_k6_lang1,dt_k6_osafree,dt_k6_pboole,dt_k7_dtconstr,dt_k7_osafree,dt_k7_pboole,dt_k8_dtconstr,dt_k8_funct_2,dt_k8_osafree,dt_k8_pboole,dt_k9_dtconstr,dt_k9_osafree,dt_l1_lang1,dt_l1_msualg_1,dt_l1_orders_2,dt_l1_osalg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l2_osalg_1,dt_l3_msualg_1,dt_l3_osalg_1,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_msualg_4,dt_m1_osalg_4,dt_m1_pboole,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m1_trees_4,dt_m2_dtconstr,dt_m2_finseq_1,dt_m2_finseq_2,dt_m2_relset_1,dt_m2_subset_1,dt_m3_pboole,dt_m3_trees_2,dt_m4_trees_3,dt_m5_trees_3,dt_u1_lang1,dt_u1_msualg_1,dt_u1_struct_0,dt_u2_msualg_1,dt_u3_msualg_1,dt_u4_msualg_1,dt_u5_msualg_1,existence_l1_lang1,existence_l1_msualg_1,existence_l1_orders_2,existence_l1_osalg_1,existence_l1_struct_0,existence_l2_msualg_1,existence_l2_osalg_1,existence_l3_msualg_1,existence_l3_osalg_1,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_msualg_4,existence_m1_osalg_4,existence_m1_pboole,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m1_trees_4,existence_m2_dtconstr,existence_m2_finseq_1,existence_m2_finseq_2,existence_m2_relset_1,existence_m2_subset_1,existence_m3_pboole,existence_m3_trees_2,existence_m4_trees_3,existence_m5_trees_3,fc10_trees_3,fc13_trees_3,fc16_trees_3,fc19_trees_3,fc1_dtconstr,fc1_msafree,fc1_msualg_1,fc1_nat_1,fc1_ordinal2,fc1_osafree,fc1_osalg_1,fc1_pboole,fc1_struct_0,fc1_subset_1,fc1_xboole_0,fc22_trees_3,fc23_trees_3,fc26_trees_3,fc2_dtconstr,fc2_msafree,fc2_osafree,fc2_pboole,fc2_subset_1,fc2_xboole_0,fc3_dtconstr,fc3_msafree,fc3_nat_1,fc3_osafree,fc3_subset_1,fc3_xboole_0,fc4_nat_1,fc4_osafree,fc4_subset_1,fc5_osafree,fc6_osafree,fc6_trees_3,fc7_funcop_1,fc8_funcop_1,fraenkel_a_1_1_lang1,fraenkel_a_2_1_osafree,fraenkel_a_3_0_osafree,fraenkel_a_3_10_osafree,fraenkel_a_3_5_osafree,fraenkel_a_3_6_osafree,fraenkel_a_3_8_osafree,fraenkel_a_3_9_osafree,fraenkel_a_4_2_osafree,fraenkel_a_4_4_osafree,fraenkel_a_4_5_osafree,free_g1_lang1,free_g3_msualg_1,idempotence_k2_xboole_0,rc10_osalg_1,rc11_osalg_1,rc12_osalg_1,rc1_dtconstr,rc1_funcop_1,rc1_msualg_4,rc1_nat_1,rc1_osalg_4,rc1_pboole,rc1_subset_1,rc1_xboole_0,rc2_msualg_4,rc2_nat_1,rc2_partfun1,rc2_pboole,rc2_subset_1,rc2_trees_3,rc2_xboole_0,rc3_nat_1,rc3_osalg_4,rc3_pboole,rc3_struct_0,rc4_pboole,rc4_trees_3,rc5_msualg_1,rc5_osalg_1,rc5_osalg_4,rc5_struct_0,rc5_trees_3,rc6_msualg_1,rc6_osalg_4,rc6_trees_3,rc7_trees_3,rc8_trees_3,redefinition_k12_finseq_1,redefinition_k12_trees_4,redefinition_k15_lang1,redefinition_k1_dtconstr,redefinition_k1_msualg_4,redefinition_k1_nat_1,redefinition_k1_osalg_1,redefinition_k2_msualg_4,redefinition_k2_trees_4,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_msafree,redefinition_k4_finseq_1,redefinition_k4_relset_1,redefinition_k5_msualg_4,redefinition_k5_numbers,redefinition_k6_dtconstr,redefinition_k7_dtconstr,redefinition_k7_pboole,redefinition_k8_dtconstr,redefinition_k8_funct_2,redefinition_k8_pboole,redefinition_k9_dtconstr,redefinition_k9_osafree,redefinition_m1_dtconstr,redefinition_m1_struct_0,redefinition_m1_trees_4,redefinition_m2_finseq_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,redefinition_m2_subset_1,redefinition_m5_trees_3,redefinition_r3_orders_2,redefinition_r6_pboole,reflexivity_r1_osalg_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,reflexivity_r3_orders_2,reflexivity_r6_pboole,s7_dtconstr__e5_58_1__osafree,spc1_boole,spc1_numerals,symmetry_r1_osalg_1,symmetry_r6_pboole,t106_zfmisc_1,t10_osafree,t11_osafree,t12_funct_1,t12_osafree,t13_osafree,t15_trees_4,t17_trees_4,t1_boole,t1_subset,t20_osafree,t22_funct_1,t22_osafree,t2_subset,t2_tarski,t31_finseq_3,t33_finseq_2,t33_zfmisc_1,t3_pboole,t3_subset,t4_osafree,t4_subset,t5_subset,t6_boole,t6_msualg_3,t7_boole,t8_boole,t97_orders_1,t9_domain_1]), [file(osafree,t27_osafree)]). fof(abstractness_v1_lang1,axiom,( ! [A] : ( l1_lang1(A) => ( v1_lang1(A) => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) ), file(lang1,v1_lang1), []). fof(abstractness_v4_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(B,A) => B = g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)) ) ) ), file(msualg_1,v4_msualg_1), []). fof(antisymmetry_r2_hidden,axiom,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), []). fof(cc10_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v6_trees_3(B) ) ) ), file(trees_3,cc10_trees_3), []). fof(cc1_dtconstr,axiom,( ! [A,B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) ), file(dtconstr,cc1_dtconstr), []). fof(cc1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(u4_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc1_msualg_1), []). fof(cc1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => v1_msualg_4(D) ) ) ), file(msualg_4,cc1_msualg_4), []). fof(cc1_msualg_9,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_msualg_1(A)) ) => ! [D] : ( m1_subset_1(D,k3_msualg_1(A,C,B)) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) ) ) ), file(msualg_9,cc1_msualg_9), []). fof(cc1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(nat_1,cc1_nat_1), []). fof(cc1_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( v4_osalg_1(A) => ( v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) ) ) ) ), file(osalg_1,cc1_osalg_1), []). fof(cc1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) ), file(partfun1,cc1_partfun1), []). 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_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_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_finseq_1(C,B) => v6_trees_3(C) ) ) ), file(trees_4,cc1_trees_4), []). fof(cc2_dtconstr,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m4_trees_3(B,A) ) => ! [C] : ( m1_finseq_1(C,B) => v6_trees_3(C) ) ) ), file(dtconstr,cc2_dtconstr), []). fof(cc2_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,B)))) => ~ v1_xboole_0(C) ) ) ), file(msualg_1,cc2_msualg_1), []). fof(cc2_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc2_nat_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(cc3_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ( v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(nat_1,cc3_nat_1), []). 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(cc4_trees_3,axiom,( ! [A] : ( v3_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_trees_3(B) ) ) ), file(trees_3,cc4_trees_3), []). fof(cc5_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_trees_3(B,A) => v3_trees_3(B) ) ) ), file(trees_3,cc5_trees_3), []). fof(cc6_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_relset_1(C,A,B) => ( ( v1_funct_1(C) & v1_funct_2(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,A,B) & v3_trees_2(C) ) ) ) ) ), file(trees_3,cc6_trees_3), []). fof(cc7_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_trees_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v4_trees_3(A) ) ) ), file(trees_3,cc7_trees_3), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d10_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m3_pboole(C,u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B))) => ( C = k7_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => k5_msualg_4(A,k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C,D) = k6_osafree(A,B,D) ) ) ) ) ) ), file(osafree,d10_osafree), []). fof(d11_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ), file(msualg_1,d11_msualg_1), []). fof(d11_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => k8_osafree(A,B) = g3_msualg_1(A,k5_osafree(A,B),k7_osafree(A,B)) ) ) ), file(osafree,d11_osafree), []). fof(d11_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_relat_2(A) <=> r3_relat_2(A,k3_relat_1(A)) ) ) ), file(relat_2,d11_relat_2), []). fof(d1_funct_2,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), []). fof(d1_lang1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_lang1(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_lang1(A)) ) ) ) ) ), file(lang1,d1_lang1), []). fof(d1_tarski,axiom,( ! [A,B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) ), file(tarski,d1_tarski), []). fof(d20_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) => k17_osafree(A,B,C) = a_3_5_osafree(A,B,C) ) ) ) ), file(osafree,d20_osafree), []). fof(d21_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) => ! [D] : ( m2_finseq_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) => k18_osafree(A,B,C,D) = a_4_2_osafree(A,B,C,D) ) ) ) ) ), file(osafree,d21_osafree), []). fof(d22_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) & m2_relset_1(C,k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) => ( C = k19_osafree(A,B) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B))) => ( r2_hidden(D,k6_dtconstr(k2_osafree(A,B))) => k1_funct_1(C,k2_trees_4(u1_struct_0(k2_osafree(A,B)),D)) = k17_osafree(A,B,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B))) => ! [E] : ( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( r1_lang1(k2_osafree(A,B),D,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E)) => k1_funct_1(C,k12_trees_4(u1_struct_0(k2_osafree(A,B)),D,E)) = k18_osafree(A,B,D,k15_lang1(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),E,C)) ) ) ) ) ) ) ) ) ), file(osafree,d22_osafree), []). fof(d23_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( ( v3_msualg_4(C,A,k8_osafree(A,B)) & m1_osalg_4(C,A,k8_osafree(A,B)) ) => ( C = k20_osafree(A,B) <=> ! [D] : ( r2_hidden(D,u1_struct_0(A)) => k1_funct_1(C,D) = a_3_8_osafree(A,B,D) ) ) ) ) ) ), file(osafree,d23_osafree), []). fof(d2_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( A = B <=> ! [C,D] : ( r2_hidden(k4_tarski(C,D),A) <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ), file(relat_1,d2_relat_1), []). fof(d3_lang1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_lang1(A) ) => k6_lang1(A) = a_1_1_lang1(A) ) ), file(lang1,d3_lang1), []). fof(d3_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_relat_2(A,B) <=> ! [C,D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) ) => r2_hidden(k4_tarski(D,C),A) ) ) ) ), file(relat_2,d3_relat_2), []). fof(d4_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k2_relat_1(B),A) ) ) ), file(finseq_1,d4_finseq_1), []). fof(d4_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => ! [C] : ( m2_relset_1(C,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) => ( C = k1_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B)))) => ! [E] : ( m2_finseq_2(E,k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) => ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(D,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) & ! [F] : ( m1_subset_1(F,u1_msualg_1(A)) => ( k4_tarski(F,u1_struct_0(A)) = D => ( k3_finseq_1(E) = k3_finseq_1(k1_msualg_1(A,F)) & ! [G] : ( r2_hidden(G,k4_finseq_1(E)) => ( ( r2_hidden(k1_funct_1(E,G),k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))) => ! [H] : ( m1_subset_1(H,u1_msualg_1(A)) => ( k4_tarski(H,u1_struct_0(A)) = k1_funct_1(E,G) => r3_orders_2(A,k1_osalg_1(A,H),k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G)) ) ) ) & ~ ( r2_hidden(k1_funct_1(E,G),k3_card_3(k3_msafree(u1_struct_0(A),B))) & ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r3_orders_2(A,H,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,F),G)) & r2_hidden(k1_funct_1(E,G),k2_msafree(u1_struct_0(A),B,H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ), file(osafree,d4_osafree), []). fof(d4_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v6_trees_3(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( C = k4_trees_4(A,B) <=> ( ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) & B = D & k1_relat_1(C) = k13_trees_3(k2_funct_6(D)) ) & k1_funct_1(C,k1_xboole_0) = A & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(B),D) => k5_trees_2(C,k12_finseq_1(k5_numbers,D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ) ), file(trees_4,d4_trees_4), []). fof(d5_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => k2_osafree(A,B) = g1_lang1(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k1_osafree(A,B)) ) ) ), file(osafree,d5_osafree), []). fof(d5_tarski,axiom,( ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ), file(tarski,d5_tarski), []). fof(d6_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => k3_osafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) ), file(osafree,d6_osafree), []). fof(d7_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_osafree(A,B,C) = a_3_0_osafree(A,B,C) ) ) ) ), file(osafree,d7_osafree), []). fof(d8_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( ( v11_osalg_1(C,A) & m1_pboole(C,u1_struct_0(A)) ) => ( C = k5_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k4_osafree(A,B,D) ) ) ) ) ) ), file(osafree,d8_osafree), []). fof(d9_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m1_struct_0(B,A,k7_dtconstr(A)) => ! [C] : ( m1_trees_4(C,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ( m2_dtconstr(C,A,B) <=> r1_lang1(A,B,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),C)) ) ) ) ) ), file(dtconstr,d9_dtconstr), []). fof(d9_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) & m2_relset_1(D,k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) ) => ( D = k6_osafree(A,B,C) <=> ! [E] : ( m1_trees_4(E,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( r1_lang1(k2_osafree(A,B),k3_osafree(A,B,C),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E)) => k1_funct_1(D,E) = k12_trees_4(u1_struct_0(k2_osafree(A,B)),k3_osafree(A,B,C),E) ) ) ) ) ) ) ) ), file(osafree,d9_osafree), []). fof(dt_g1_lang1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k3_finseq_2(A)) => ( v1_lang1(g1_lang1(A,B)) & l1_lang1(g1_lang1(A,B)) ) ) ), file(lang1,g1_lang1), []). fof(dt_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ( v4_msualg_1(g3_msualg_1(A,B,C),A) & l3_msualg_1(g3_msualg_1(A,B,C),A) ) ) ), file(msualg_1,g3_msualg_1), []). fof(dt_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) ), file(finseq_1,k12_finseq_1), []). fof(dt_k12_trees_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_finseq_1(C,k5_trees_3(A)) ) => m5_trees_3(k12_trees_4(A,B,C),A,k5_trees_3(A)) ) ), file(trees_4,k12_trees_4), []). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), []). fof(dt_k13_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ~ v1_xboole_0(k13_trees_3(A)) & v1_trees_1(k13_trees_3(A)) ) ) ), file(trees_3,k13_trees_3), []). fof(dt_k15_lang1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) ) => m2_finseq_2(k15_lang1(A,B,C,D),B,k3_finseq_2(B)) ) ), file(lang1,k15_lang1), []). fof(dt_k16_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k16_trees_3(A)) & v1_funct_1(k16_trees_3(A)) & v1_finseq_1(k16_trees_3(A)) ) ) ), file(trees_3,k16_trees_3), []). fof(dt_k17_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) ) => m1_subset_1(k17_osafree(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ), file(osafree,k17_osafree), []). fof(dt_k18_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) & m1_finseq_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) => m1_subset_1(k18_osafree(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ), file(osafree,k18_osafree), []). fof(dt_k19_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_funct_1(k19_osafree(A,B)) & v1_funct_2(k19_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) & m2_relset_1(k19_osafree(A,B),k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A)))) ) ) ), file(osafree,k19_osafree), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m4_trees_3(B,A) & m1_finseq_1(C,B) ) => m2_finseq_1(k1_dtconstr(A,B,C),A) ) ), file(dtconstr,k1_dtconstr), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(msualg_1,k1_msualg_1), []). fof(dt_k1_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m1_msualg_4(D,A,B,C) & m1_subset_1(E,A) ) => m2_relset_1(k1_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ), file(msualg_4,k1_msualg_4), []). fof(dt_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ), file(nat_1,k1_nat_1), []). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), []). fof(dt_k1_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => m2_relset_1(k1_osafree(A,B),k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))),k3_finseq_2(k2_xboole_0(k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))),k3_card_3(k3_msafree(u1_struct_0(A),B))))) ) ), file(osafree,k1_osafree), []). fof(dt_k1_osalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m1_subset_1(k1_osalg_1(A,B),u1_struct_0(A)) ) ), file(osalg_1,k1_osalg_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_trees_4,axiom,( ! [A] : ( v1_relat_1(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) ) ), file(trees_4,k1_trees_4), []). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), []). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), []). fof(dt_k20_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v3_msualg_4(k20_osafree(A,B),A,k8_osafree(A,B)) & m1_osalg_4(k20_osafree(A,B),A,k8_osafree(A,B)) ) ) ), file(osafree,k20_osafree), []). fof(dt_k2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A)) ) ) ), file(card_3,k2_card_3), []). fof(dt_k2_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)) ) ) ), file(funct_6,k2_funct_6), []). fof(dt_k2_msafree,axiom,( $true ), file(msafree,k2_msafree), []). fof(dt_k2_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m1_subset_1(k2_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,k2_msualg_1), []). fof(dt_k2_msualg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) ) => ( v3_relat_2(k2_msualg_4(A,B,C,D)) & v8_relat_2(k2_msualg_4(A,B,C,D)) & v1_partfun1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D)) & m2_relset_1(k2_msualg_4(A,B,C,D),k1_funct_1(u4_msualg_1(A,B),D),k1_funct_1(u4_msualg_1(A,B),D)) ) ) ), file(msualg_4,k2_msualg_4), []). fof(dt_k2_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => l1_lang1(k2_osafree(A,B)) ) ), file(osafree,k2_osafree), []). 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_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m5_trees_3(k2_trees_4(A,B),A,k5_trees_3(A)) ) ), file(trees_4,k2_trees_4), []). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), []). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), []). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), []). fof(dt_k3_card_3,axiom,( $true ), file(card_3,k3_card_3), []). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), []). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), []). fof(dt_k3_msafree,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k3_msafree(A,B),A) ) ), file(msafree,k3_msafree), []). fof(dt_k3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) ), file(msualg_1,k3_msualg_1), []). fof(dt_k3_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => m1_subset_1(k3_osafree(A,B,C),u1_struct_0(k2_osafree(A,B))) ) ), file(osafree,k3_osafree), []). fof(dt_k3_relat_1,axiom,( $true ), file(relat_1,k3_relat_1), []). fof(dt_k4_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_lang1(A) ) => m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) ), file(dtconstr,k4_dtconstr), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) ), file(msualg_1,k4_msualg_1), []). fof(dt_k4_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k4_osafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k2_osafree(A,B)))) ) ), file(osafree,k4_osafree), []). 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_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k4_trees_4(A,B)) & v1_funct_1(k4_trees_4(A,B)) & v3_trees_2(k4_trees_4(A,B)) ) ) ), file(trees_4,k4_trees_4), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). fof(dt_k5_lang1,axiom,( $true ), file(lang1,k5_lang1), []). fof(dt_k5_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => ( v1_funct_1(k5_msualg_1(A,B,C)) & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) ), file(msualg_1,k5_msualg_1), []). fof(dt_k5_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_msualg_1(A)) & m1_pboole(C,u1_msualg_1(A)) & m3_pboole(D,u1_msualg_1(A),B,C) & m1_subset_1(E,u1_msualg_1(A)) ) => ( v1_funct_1(k5_msualg_4(A,B,C,D,E)) & v1_funct_2(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k5_msualg_4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ), file(msualg_4,k5_msualg_4), []). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), []). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), []). fof(dt_k5_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v11_osalg_1(k5_osafree(A,B),A) & m1_pboole(k5_osafree(A,B),u1_struct_0(A)) ) ) ), file(osafree,k5_osafree), []). 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_trees_2,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & m1_finseq_1(B,k5_numbers) ) => ( v1_relat_1(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) ) ) ), file(trees_2,k5_trees_2), []). fof(dt_k5_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m4_trees_3(k5_trees_3(A),A) ) ), file(trees_3,k5_trees_3), []). fof(dt_k6_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k6_dtconstr(A)) & m1_subset_1(k6_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(dtconstr,k6_dtconstr), []). fof(dt_k6_lang1,axiom,( $true ), file(lang1,k6_lang1), []). fof(dt_k6_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => ( v1_funct_1(k6_osafree(A,B,C)) & v1_funct_2(k6_osafree(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) & m2_relset_1(k6_osafree(A,B,C),k1_funct_1(k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),C),k1_funct_1(k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B)),C)) ) ) ), file(osafree,k6_osafree), []). fof(dt_k6_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => m1_pboole(k6_pboole(A,B),k3_finseq_2(A)) ) ), file(pboole,k6_pboole), []). fof(dt_k7_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k7_dtconstr(A)) & m1_subset_1(k7_dtconstr(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(dtconstr,k7_dtconstr), []). fof(dt_k7_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m3_pboole(k7_osafree(A,B),u1_msualg_1(A),k8_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k5_osafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k5_osafree(A,B))) ) ), file(osafree,k7_osafree), []). fof(dt_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => m1_pboole(k7_pboole(A,B,C,D),A) ) ), file(pboole,k7_pboole), []). fof(dt_k8_dtconstr,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k6_dtconstr(A)) ) => m1_dtconstr(k8_dtconstr(A,B),u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ), file(dtconstr,k8_dtconstr), []). 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_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v12_osalg_1(k8_osafree(A,B),A) & l3_msualg_1(k8_osafree(A,B),A) ) ) ), file(osafree,k8_osafree), []). fof(dt_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => ( v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ), file(pboole,k8_pboole), []). fof(dt_k9_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k7_dtconstr(A)) & m2_dtconstr(C,A,B) ) => m1_dtconstr(k9_dtconstr(A,B,C),u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ), file(dtconstr,k9_dtconstr), []). fof(dt_k9_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => m1_struct_0(k9_osafree(A,B,C),k2_osafree(A,B),k7_dtconstr(k2_osafree(A,B))) ) ), file(osafree,k9_osafree), []). fof(dt_l1_lang1,axiom,( ! [A] : ( l1_lang1(A) => l1_struct_0(A) ) ), file(lang1,l1_lang1), []). fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l1_struct_0(A) ) ), file(msualg_1,l1_msualg_1), []). fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) ), file(orders_2,l1_orders_2), []). fof(dt_l1_osalg_1,axiom,( ! [A] : ( l1_osalg_1(A) => l1_msualg_1(A) ) ), file(osalg_1,l1_osalg_1), []). fof(dt_l1_struct_0,axiom,( $true ), file(struct_0,l1_struct_0), []). fof(dt_l2_msualg_1,axiom,( $true ), file(msualg_1,l2_msualg_1), []). fof(dt_l2_osalg_1,axiom,( ! [A] : ( l2_osalg_1(A) => ( l1_msualg_1(A) & l1_orders_2(A) ) ) ), file(osalg_1,l2_osalg_1), []). fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) ), file(msualg_1,l3_msualg_1), []). fof(dt_l3_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( l1_osalg_1(A) & l2_osalg_1(A) ) ) ), file(osalg_1,l3_osalg_1), []). fof(dt_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_dtconstr(D,A,B,C) => m5_trees_3(D,A,B) ) ) ), file(dtconstr,m1_dtconstr), []). fof(dt_m1_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), []). fof(dt_m1_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), []). fof(dt_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ! [D] : ( m1_msualg_4(D,A,B,C) => m1_pboole(D,A) ) ) ), file(msualg_4,m1_msualg_4), []). fof(dt_m1_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_osalg_4(C,A,B) => m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ), file(osalg_4,m1_osalg_4), []). 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_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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) => m2_finseq_1(C,A) ) ) ), file(trees_4,m1_trees_4), []). fof(dt_m2_dtconstr,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k7_dtconstr(A)) ) => ! [C] : ( m2_dtconstr(C,A,B) => m1_trees_4(C,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ) ), file(dtconstr,m2_dtconstr), []). fof(dt_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), []). fof(dt_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), []). 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_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), []). 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_trees_2,axiom,( ! [A,B] : ( m3_trees_2(B,A) => v1_relat_1(B) ) ), file(trees_2,m3_trees_2), []). fof(dt_m4_trees_3,axiom,( $true ), file(trees_3,m4_trees_3), []). fof(dt_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ! [C] : ( m5_trees_3(C,A,B) => ( v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) ) ) ) ), file(trees_3,m5_trees_3), []). fof(dt_u1_lang1,axiom,( ! [A] : ( l1_lang1(A) => m2_relset_1(u1_lang1(A),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(lang1,u1_lang1), []). fof(dt_u1_msualg_1,axiom,( $true ), file(msualg_1,u1_msualg_1), []). fof(dt_u1_struct_0,axiom,( $true ), file(struct_0,u1_struct_0), []). fof(dt_u2_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u2_msualg_1(A)) & v1_funct_2(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) & m2_relset_1(u2_msualg_1(A),u1_msualg_1(A),k3_finseq_2(u1_struct_0(A))) ) ) ), file(msualg_1,u2_msualg_1), []). fof(dt_u3_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_funct_1(u3_msualg_1(A)) & v1_funct_2(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) & m2_relset_1(u3_msualg_1(A),u1_msualg_1(A),u1_struct_0(A)) ) ) ), file(msualg_1,u3_msualg_1), []). fof(dt_u4_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & l2_msualg_1(B,A) ) => m1_pboole(u4_msualg_1(A,B),u1_struct_0(A)) ) ), file(msualg_1,u4_msualg_1), []). fof(dt_u5_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m3_pboole(u5_msualg_1(A,B),u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),u4_msualg_1(A,B))),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,B))) ) ), file(msualg_1,u5_msualg_1), []). fof(existence_l1_lang1,axiom,( ? [A] : l1_lang1(A) ), file(lang1,l1_lang1), []). fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) ), file(msualg_1,l1_msualg_1), []). fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) ), file(orders_2,l1_orders_2), []). fof(existence_l1_osalg_1,axiom,( ? [A] : l1_osalg_1(A) ), file(osalg_1,l1_osalg_1), []). fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) ), file(struct_0,l1_struct_0), []). fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) ), file(msualg_1,l2_msualg_1), []). fof(existence_l2_osalg_1,axiom,( ? [A] : l2_osalg_1(A) ), file(osalg_1,l2_osalg_1), []). fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) ), file(msualg_1,l3_msualg_1), []). fof(existence_l3_osalg_1,axiom,( ? [A] : l3_osalg_1(A) ), file(osalg_1,l3_osalg_1), []). fof(existence_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : m1_dtconstr(D,A,B,C) ) ), file(dtconstr,m1_dtconstr), []). fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), []). fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), []). fof(existence_m1_msualg_4,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ? [D] : m1_msualg_4(D,A,B,C) ) ), file(msualg_4,m1_msualg_4), []). fof(existence_m1_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : m1_osalg_4(C,A,B) ) ), file(osalg_4,m1_osalg_4), []). 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_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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m1_trees_4(C,A,B) ) ), file(trees_4,m1_trees_4), []). fof(existence_m2_dtconstr,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k7_dtconstr(A)) ) => ? [C] : m2_dtconstr(C,A,B) ) ), file(dtconstr,m2_dtconstr), []). fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), []). fof(existence_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), []). fof(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), []). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), []). 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_trees_2,axiom,( ! [A] : ? [B] : m3_trees_2(B,A) ), file(trees_2,m3_trees_2), []). fof(existence_m4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m4_trees_3(B,A) ) ), file(trees_3,m4_trees_3), []). fof(existence_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ? [C] : m5_trees_3(C,A,B) ) ), file(trees_3,m5_trees_3), []). fof(fc10_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc10_trees_3), []). fof(fc13_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) & v5_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc13_trees_3), []). fof(fc16_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v6_trees_3(k5_finseq_1(A)) ) ) ), file(trees_3,fc16_trees_3), []). fof(fc19_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ( v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)) & v1_finset_1(k2_funct_6(A)) & v1_finseq_1(k2_funct_6(A)) & v4_trees_3(k2_funct_6(A)) ) ) ), file(trees_3,fc19_trees_3), []). fof(fc1_dtconstr,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_relset_1(B,A,k3_finseq_2(A)) ) => ( ~ v3_struct_0(g1_lang1(A,B)) & v1_lang1(g1_lang1(A,B)) ) ) ), file(dtconstr,fc1_dtconstr), []). fof(fc1_msafree,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k2_card_3(B)) & v2_relat_1(k2_card_3(B)) & v1_funct_1(k2_card_3(B)) ) ) ), file(msafree,fc1_msafree), []). fof(fc1_msualg_1,axiom,( ! [A,B] : ( ( l1_struct_0(A) & v5_msualg_1(B,A) & l2_msualg_1(B,A) ) => ( v1_relat_1(u4_msualg_1(A,B)) & v2_relat_1(u4_msualg_1(A,B)) & v1_funct_1(u4_msualg_1(A,B)) ) ) ), file(msualg_1,fc1_msualg_1), []). fof(fc1_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc1_nat_1), []). fof(fc1_ordinal2,axiom, ( v1_ordinal1(k5_ordinal2) & v2_ordinal1(k5_ordinal2) & v3_ordinal1(k5_ordinal2) & ~ v1_xboole_0(k5_ordinal2) ), file(ordinal2,fc1_ordinal2), []). fof(fc1_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_osafree(A,B)) & v1_lang1(k2_osafree(A,B)) ) ) ), file(osafree,fc1_osafree), []). fof(fc1_osalg_1,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_finseq_1(C,A) ) => ( v1_relat_1(k5_relat_1(C,B)) & v1_funct_1(k5_relat_1(C,B)) & v1_finseq_1(k5_relat_1(C,B)) ) ) ), file(osalg_1,fc1_osalg_1), []). fof(fc1_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & ~ v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) ) ) ), file(pboole,fc1_pboole), []). 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_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc22_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ~ v1_xboole_0(k2_xboole_0(A,B)) & v1_trees_1(k2_xboole_0(A,B)) ) ) ), file(trees_3,fc22_trees_3), []). fof(fc23_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ( ~ v1_xboole_0(k13_trees_3(A)) & v1_finset_1(k13_trees_3(A)) & v1_trees_1(k13_trees_3(A)) ) ) ), file(trees_3,fc23_trees_3), []). fof(fc26_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_trees_3(A)) ) => ( ~ v1_xboole_0(k1_relat_1(B)) & v1_finset_1(k1_relat_1(B)) & v1_trees_1(k1_relat_1(B)) ) ) ), file(trees_3,fc26_trees_3), []). fof(fc2_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k4_dtconstr(A)) & v3_trees_3(k4_dtconstr(A)) ) ) ), file(dtconstr,fc2_dtconstr), []). fof(fc2_msafree,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) ) => ~ v1_xboole_0(k3_card_3(B)) ) ), file(msafree,fc2_msafree), []). fof(fc2_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k2_osafree(A,B)) & v1_lang1(k2_osafree(A,B)) & v1_dtconstr(k2_osafree(A,B)) & v2_dtconstr(k2_osafree(A,B)) & v3_dtconstr(k2_osafree(A,B)) ) ) ), file(osafree,fc2_osafree), []). 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_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) ), file(xboole_0,fc2_xboole_0), []). fof(fc3_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v3_dtconstr(A) & l1_lang1(A) ) => ( ~ v1_xboole_0(k4_dtconstr(A)) & v3_trees_3(k4_dtconstr(A)) ) ) ), file(dtconstr,fc3_dtconstr), []). fof(fc3_msafree,axiom,( ! [A] : ( ( ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(u1_msualg_1(A)) ) ), file(msafree,fc3_msafree), []). fof(fc3_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v4_ordinal2(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(nat_1,fc3_nat_1), []). fof(fc3_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k4_osafree(A,B,C)) & v3_trees_3(k4_osafree(A,B,C)) ) ) ), file(osafree,fc3_osafree), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc4_nat_1,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & ~ v1_xboole_0(B) & v4_ordinal2(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v4_ordinal2(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(nat_1,fc4_nat_1), []). fof(fc4_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_relat_1(k5_osafree(A,B)) & v2_relat_1(k5_osafree(A,B)) & ~ v3_relat_1(k5_osafree(A,B)) & v1_funct_1(k5_osafree(A,B)) & v11_osalg_1(k5_osafree(A,B),A) ) ) ), file(osafree,fc4_osafree), []). 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(fc5_osafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k8_osafree(A,B),A) & v5_msualg_1(k8_osafree(A,B),A) & v12_osalg_1(k8_osafree(A,B),A) ) ) ), file(osafree,fc5_osafree), []). fof(fc6_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => ~ v1_xboole_0(k3_msualg_1(A,C,k8_osafree(A,B))) ) ), file(osafree,fc6_osafree), []). fof(fc6_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k5_trees_3(A)) & v3_trees_3(k5_trees_3(A)) ) ) ), file(trees_3,fc6_trees_3), []). 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(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(fraenkel_a_1_1_lang1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(B) & l1_lang1(B) ) => ( r2_hidden(A,a_1_1_lang1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & r1_lang1(B,C,D) ) ) ) ) ), file(lang1,a_1_1_lang1), []). fof(fraenkel_a_2_1_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_osafree(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k2_osafree(B,C))) & A = D & ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & r1_lang1(k2_osafree(B,C),D,E) ) ) ) ) ), file(osafree,a_2_1_osafree), []). fof(fraenkel_a_3_0_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_osafree(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = E & ~ ( ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ~ ( r3_orders_2(B,F,D) & r2_hidden(G,k1_funct_1(C,F)) & E = k1_trees_4(k4_tarski(G,F)) ) ) & ! [F] : ( m1_subset_1(F,u1_msualg_1(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & r3_orders_2(B,k1_osalg_1(B,F),D) ) ) ) ) ) ) ), file(osafree,a_3_0_osafree), []). fof(fraenkel_a_3_10_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_struct_0(D,k2_osafree(B,C),k6_dtconstr(k2_osafree(B,C))) ) => ( r2_hidden(A,a_3_10_osafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_tarski(k8_dtconstr(k2_osafree(B,C),D),E) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( r2_hidden(G,k1_funct_1(C,F)) & D = k4_tarski(G,F) & r3_orders_2(B,F,E) ) ) ) ) ) ), file(osafree,a_3_10_osafree), []). fof(fraenkel_a_3_5_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(k2_osafree(B,C))) ) => ( r2_hidden(A,a_3_5_osafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(B,C)),D),E) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( r2_hidden(G,k1_funct_1(C,F)) & D = k4_tarski(G,F) & r3_orders_2(B,F,E) ) ) ) ) ) ), file(osafree,a_3_5_osafree), []). fof(fraenkel_a_3_6_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_osafree(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = E & ~ ( ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ~ ( r3_orders_2(B,F,D) & r2_hidden(G,k1_funct_1(C,F)) & E = k1_trees_4(k4_tarski(G,F)) ) ) & ! [F] : ( m1_subset_1(F,u1_msualg_1(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & r3_orders_2(B,k1_osalg_1(B,F),D) ) ) ) ) ) ) ), file(osafree,a_3_6_osafree), []). fof(fraenkel_a_3_8_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_8_osafree(B,C,D)) <=> ? [E,F] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = k4_tarski(E,F) & r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),F)) ) ) ) ), file(osafree,a_3_8_osafree), []). fof(fraenkel_a_3_9_osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_9_osafree(B,C,D)) <=> ? [E,F] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = k4_tarski(E,F) & r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),F)) ) ) ) ), file(osafree,a_3_9_osafree), []). fof(fraenkel_a_4_2_osafree,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(k2_osafree(B,C))) & m2_finseq_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_2_osafree(B,C,D,E)) <=> ? [F,G,H] : ( m1_subset_1(F,u1_msualg_1(B)) & m1_subset_1(G,k3_msualg_1(B,F,k8_osafree(B,C))) & m1_subset_1(H,u1_struct_0(B)) & A = k4_tarski(k8_funct_2(k3_msualg_1(B,F,k8_osafree(B,C)),k4_msualg_1(B,F,k8_osafree(B,C)),k5_msualg_1(B,F,k8_osafree(B,C)),G),H) & ? [I] : ( m1_subset_1(I,u1_msualg_1(B)) & D = k4_tarski(I,u1_struct_0(B)) & r1_osalg_1(B,I,F) & k3_finseq_1(k1_msualg_1(B,I)) = k3_finseq_1(k1_msualg_1(B,F)) & r3_orders_2(B,k1_osalg_1(B,I),H) & r3_orders_2(B,k1_osalg_1(B,F),H) ) & ? [I] : ( m2_finseq_2(I,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & k4_finseq_1(I) = k4_finseq_1(E) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( r2_hidden(J,k4_finseq_1(E)) => r2_hidden(k4_tarski(k1_funct_1(G,J),k4_finseq_4(k5_numbers,u1_struct_0(B),I,J)),k1_funct_1(E,J)) ) ) ) ) ) ) ), file(osafree,a_4_2_osafree), []). fof(fraenkel_a_4_4_osafree,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m1_subset_1(D,u1_msualg_1(B)) & m2_finseq_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_4_osafree(B,C,D,E)) <=> ? [F,G,H] : ( m1_subset_1(F,u1_msualg_1(B)) & m1_subset_1(G,k3_msualg_1(B,F,k8_osafree(B,C))) & m1_subset_1(H,u1_struct_0(B)) & A = k4_tarski(k8_funct_2(k3_msualg_1(B,F,k8_osafree(B,C)),k4_msualg_1(B,F,k8_osafree(B,C)),k5_msualg_1(B,F,k8_osafree(B,C)),G),H) & ? [I] : ( m1_subset_1(I,u1_msualg_1(B)) & k9_osafree(B,C,D) = k4_tarski(I,u1_struct_0(B)) & r1_osalg_1(B,I,F) & k3_finseq_1(k1_msualg_1(B,I)) = k3_finseq_1(k1_msualg_1(B,F)) & r3_orders_2(B,k1_osalg_1(B,I),H) & r3_orders_2(B,k1_osalg_1(B,F),H) ) & ? [I] : ( m2_finseq_2(I,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & k4_finseq_1(I) = k4_finseq_1(E) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( r2_hidden(J,k4_finseq_1(E)) => r2_hidden(k4_tarski(k1_funct_1(G,J),k4_finseq_4(k5_numbers,u1_struct_0(B),I,J)),k1_funct_1(E,J)) ) ) ) ) ) ) ), file(osafree,a_4_4_osafree), []). fof(fraenkel_a_4_5_osafree,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_1(B) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(B)) & m2_finseq_2(D,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & m2_subset_1(E,k1_numbers,k5_numbers) ) => ( r2_hidden(A,a_4_5_osafree(B,C,D,E)) <=> ? [F,G] : ( m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & m1_dtconstr(G,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = k4_tarski(F,G) & r2_hidden(k4_tarski(F,k4_finseq_4(k5_numbers,u1_struct_0(B),D,E)),k8_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),G)) ) ) ) ), file(osafree,a_4_5_osafree), []). fof(free_g1_lang1,axiom,( ! [A,B] : ( m1_relset_1(B,A,k3_finseq_2(A)) => ! [C,D] : ( g1_lang1(A,B) = g1_lang1(C,D) => ( A = C & B = D ) ) ) ), file(lang1,g1_lang1), []). fof(free_g3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) & m3_pboole(C,u1_msualg_1(A),k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),B)),k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),B)) ) => ! [D,E,F] : ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) ), file(msualg_1,g3_msualg_1), []). fof(idempotence_k2_xboole_0,axiom,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), []). fof(rc10_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) ) ) ), file(osalg_1,rc10_osalg_1), []). fof(rc11_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) ) ) ), file(osalg_1,rc11_osalg_1), []). fof(rc12_osalg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v12_osalg_1(B,A) ) ) ), file(osalg_1,rc12_osalg_1), []). fof(rc1_dtconstr,axiom,( ? [A] : ( l1_lang1(A) & ~ v3_struct_0(A) & v1_lang1(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_dtconstr(A) ) ), file(dtconstr,rc1_dtconstr), []). 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_msualg_4,axiom,( ! [A] : ? [B] : ( m1_pboole(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_msualg_4(B) ) ), file(msualg_4,rc1_msualg_4), []). fof(rc1_nat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc1_nat_1), []). fof(rc1_osalg_4,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_pboole(B,u1_struct_0(A)) & v1_relat_1(B) & v1_funct_1(B) & v11_osalg_1(B,A) & v1_msualg_4(B) ) ) ), file(osalg_4,rc1_osalg_4), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). 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_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc2_msualg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) ) ) ), file(msualg_4,rc2_msualg_4), []). fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) ), file(nat_1,rc2_nat_1), []). fof(rc2_partfun1,axiom,( ! [A,B] : ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & v1_funct_1(C) ) ), file(partfun1,rc2_partfun1), []). 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_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_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) ), file(trees_3,rc2_trees_3), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), []). fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k5_numbers) & ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(nat_1,rc3_nat_1), []). fof(rc3_osalg_4,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v1_funct_1(C) & v1_msualg_4(C) & v3_msualg_4(C,A,B) ) ) ), file(osalg_4,rc3_osalg_4), []). 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_struct_0,axiom,( ? [A] : ( l1_struct_0(A) & ~ v3_struct_0(A) ) ), file(struct_0,rc3_struct_0), []). 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_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m4_trees_3(B,A) & ~ v1_xboole_0(B) & v1_finset_1(B) & v3_trees_3(B) ) ) ), file(trees_3,rc4_trees_3), []). fof(rc5_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) ), file(msualg_1,rc5_msualg_1), []). fof(rc5_osalg_1,axiom,( ? [A] : ( l1_osalg_1(A) & ~ v3_struct_0(A) & ~ v2_msualg_1(A) ) ), file(osalg_1,rc5_osalg_1), []). fof(rc5_osalg_4,axiom,( ? [A] : ( l1_orders_2(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v2_osalg_4(A) ) ), file(osalg_4,rc5_osalg_4), []). 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_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc5_trees_3), []). fof(rc6_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) ) ) ), file(msualg_1,rc6_msualg_1), []). fof(rc6_osalg_4,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v3_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) ) ), file(osalg_4,rc6_osalg_4), []). fof(rc6_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) ), file(trees_3,rc6_trees_3), []). fof(rc7_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v4_trees_3(A) & v5_trees_3(A) ) ), file(trees_3,rc7_trees_3), []). fof(rc8_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v6_trees_3(A) ) ), file(trees_3,rc8_trees_3), []). fof(redefinition_k12_finseq_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) ), file(finseq_1,k12_finseq_1), []). fof(redefinition_k12_trees_4,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_finseq_1(C,k5_trees_3(A)) ) => k12_trees_4(A,B,C) = k4_trees_4(B,C) ) ), file(trees_4,k12_trees_4), []). fof(redefinition_k15_lang1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) ) => k15_lang1(A,B,C,D) = k5_relat_1(C,D) ) ), file(lang1,k15_lang1), []). fof(redefinition_k1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & m4_trees_3(B,A) & m1_finseq_1(C,B) ) => k1_dtconstr(A,B,C) = k16_trees_3(C) ) ), file(dtconstr,k1_dtconstr), []). fof(redefinition_k1_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m1_msualg_4(D,A,B,C) & m1_subset_1(E,A) ) => k1_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_4,k1_msualg_4), []). fof(redefinition_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ), file(nat_1,k1_nat_1), []). fof(redefinition_k1_osalg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => k1_osalg_1(A,B) = k2_msualg_1(A,B) ) ), file(osalg_1,k1_osalg_1), []). fof(redefinition_k2_msualg_4,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v3_msualg_4(C,A,B) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,B),u4_msualg_1(A,B)) & m1_subset_1(D,u1_struct_0(A)) ) => k2_msualg_4(A,B,C,D) = k1_funct_1(C,D) ) ), file(msualg_4,k2_msualg_4), []). fof(redefinition_k2_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k2_trees_4(A,B) = k1_trees_4(B) ) ), file(trees_4,k2_trees_4), []). fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), []). fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), []). fof(redefinition_k3_msafree,axiom,( ! [A,B] : ( m1_pboole(B,A) => k3_msafree(A,B) = k2_card_3(B) ) ), file(msafree,k3_msafree), []). fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), []). 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_k5_msualg_4,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_msualg_1(A)) & m1_pboole(C,u1_msualg_1(A)) & m3_pboole(D,u1_msualg_1(A),B,C) & m1_subset_1(E,u1_msualg_1(A)) ) => k5_msualg_4(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_4,k5_msualg_4), []). fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k6_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => k6_dtconstr(A) = k5_lang1(A) ) ), file(dtconstr,k6_dtconstr), []). fof(redefinition_k7_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & l1_lang1(A) ) => k7_dtconstr(A) = k6_lang1(A) ) ), file(dtconstr,k7_dtconstr), []). fof(redefinition_k7_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_pboole(D,B) ) => k7_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k7_pboole), []). fof(redefinition_k8_dtconstr,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k6_dtconstr(A)) ) => k8_dtconstr(A,B) = k1_trees_4(B) ) ), file(dtconstr,k8_dtconstr), []). 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_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k8_pboole), []). fof(redefinition_k9_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k7_dtconstr(A)) & m2_dtconstr(C,A,B) ) => k9_dtconstr(A,B,C) = k4_trees_4(B,C) ) ), file(dtconstr,k9_dtconstr), []). fof(redefinition_k9_osafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => k9_osafree(A,B,C) = k3_osafree(A,B,C) ) ), file(osafree,k9_osafree), []). fof(redefinition_m1_dtconstr,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_dtconstr(D,A,B,C) <=> m1_subset_1(D,C) ) ) ), file(dtconstr,m1_dtconstr), []). 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_m1_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) <=> m1_finseq_1(C,B) ) ) ), file(trees_4,m1_trees_4), []). fof(redefinition_m2_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), []). fof(redefinition_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), []). fof(redefinition_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), []). fof(redefinition_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), []). fof(redefinition_m5_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m4_trees_3(B,A) ) => ! [C] : ( m5_trees_3(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(trees_3,m5_trees_3), []). fof(redefinition_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( r3_orders_2(A,B,C) <=> r1_orders_2(A,B,C) ) ) ), file(orders_2,r3_orders_2), []). fof(redefinition_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) <=> B = C ) ) ), file(pboole,r6_pboole), []). fof(reflexivity_r1_osalg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_osalg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => r1_osalg_1(A,B,B) ) ), file(osalg_1,r1_osalg_1), []). fof(reflexivity_r1_tarski,axiom,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), []). fof(reflexivity_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), []). fof(reflexivity_r3_orders_2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & v2_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => r3_orders_2(A,B,B) ) ), file(orders_2,r3_orders_2), []). fof(reflexivity_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => r6_pboole(A,B,B) ) ), file(pboole,r6_pboole), []). fof(s7_dtconstr__e5_58_1__osafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_msualg_4(C,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B))) & m1_msualg_4(D,u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B))) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(k2_osafree(A,B))) => ( r2_hidden(E,k5_lang1(k2_osafree(A,B))) => ! [F,G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_hidden(k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(A,B)),E),F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,G)) <=> r2_hidden(k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(A,B)),E),F),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),D,G)) ) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(k2_osafree(A,B))) => ! [H] : ( m1_trees_4(H,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( ( r1_lang1(k2_osafree(A,B),E,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),H)) & ! [I] : ( ( v1_funct_1(I) & v3_trees_2(I) & m3_trees_2(I,u1_struct_0(k2_osafree(A,B))) ) => ( r2_hidden(I,k2_relat_1(H)) => ! [J,K] : ( m1_subset_1(K,u1_struct_0(A)) => ( r2_hidden(k4_tarski(I,J),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,K)) <=> r2_hidden(k4_tarski(I,J),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),D,K)) ) ) ) ) ) => ! [L,M] : ( m1_subset_1(M,u1_struct_0(A)) => ( r2_hidden(k4_tarski(k12_trees_4(u1_struct_0(k2_osafree(A,B)),E,H),L),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,M)) <=> r2_hidden(k4_tarski(k12_trees_4(u1_struct_0(k2_osafree(A,B)),E,H),L),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),D,M)) ) ) ) ) ) ) => ! [E] : ( ( v1_funct_1(E) & v3_trees_2(E) & m3_trees_2(E,u1_struct_0(k2_osafree(A,B))) ) => ( r2_hidden(E,k4_dtconstr(k2_osafree(A,B))) => ! [N,O] : ( m1_subset_1(O,u1_struct_0(A)) => ( r2_hidden(k4_tarski(E,N),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),C,O)) <=> r2_hidden(k4_tarski(E,N),k1_msualg_4(u1_struct_0(A),u4_msualg_1(A,k8_osafree(A,B)),u4_msualg_1(A,k8_osafree(A,B)),D,O)) ) ) ) ) ) ) ), file(osafree,s7_dtconstr__e5_58_1__osafree), []). fof(spc1_boole,axiom,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), []). fof(spc1_numerals,axiom, ( v2_xreal_0(1) & m1_subset_1(1,k5_numbers) ), file(numerals,spc1_numerals), []). fof(symmetry_r1_osalg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_osalg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => ( r1_osalg_1(A,B,C) => r1_osalg_1(A,C,B) ) ) ), file(osalg_1,r1_osalg_1), []). fof(symmetry_r6_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => ( r6_pboole(A,B,C) => r6_pboole(A,C,B) ) ) ), file(pboole,r6_pboole), []). fof(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(t10_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k1_funct_1(B,C)) => ( m1_dtconstr(k1_trees_4(k4_tarski(E,C)),u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) & ! [F] : k4_tarski(F,u1_struct_0(A)) != k1_funct_1(k1_trees_4(k4_tarski(E,C)),k1_xboole_0) & ( r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) => r3_orders_2(A,C,D) ) & ( r3_orders_2(A,C,D) => r2_hidden(k1_trees_4(k4_tarski(E,C)),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) ) ) ) ) ) ) ) ), file(osafree,t10_osafree), []). fof(t11_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A)) => ( ? [E] : ( m2_dtconstr(E,k2_osafree(A,B),k9_osafree(A,B,D)) & C = k9_dtconstr(k2_osafree(A,B),k9_osafree(A,B,D),E) & r1_lang1(k2_osafree(A,B),k9_osafree(A,B,D),k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),E)) & r2_hidden(E,k3_msualg_1(A,D,k8_osafree(A,B))) & C = k1_funct_1(k5_msualg_1(A,D,k8_osafree(A,B)),E) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : C != k1_trees_4(k4_tarski(F,E)) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E)) <=> r3_orders_2(A,k1_osalg_1(A,D),E) ) ) ) ) ) ) ) ) ), file(osafree,t11_osafree), []). fof(t12_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k1_relat_1(B)) => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ), file(funct_1,t12_funct_1), []). fof(t12_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) => ! [D] : ( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( r1_lang1(k2_osafree(A,B),C,k1_dtconstr(u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),D)) => ( r2_hidden(C,k7_dtconstr(k2_osafree(A,B))) & r2_hidden(k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D),k4_dtconstr(k2_osafree(A,B))) & ? [E] : ( m1_subset_1(E,u1_msualg_1(A)) & C = k4_tarski(E,u1_struct_0(A)) & r2_hidden(D,k3_msualg_1(A,E,k8_osafree(A,B))) & k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D) = k1_funct_1(k5_msualg_1(A,E,k8_osafree(A,B)),D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_hidden(k12_trees_4(u1_struct_0(k2_osafree(A,B)),C,D),k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),F)) <=> r3_orders_2(A,k1_osalg_1(A,E),F) ) ) ) ) ) ) ) ) ) ), file(osafree,t12_osafree), []). fof(t13_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,C,k8_osafree(A,B))) <=> ( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) & r1_lang1(k2_osafree(A,B),k9_osafree(A,B,C),k16_trees_3(D)) ) ) ) ) ) ) ), file(osafree,t13_osafree), []). fof(t15_trees_4,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) ) => ( k4_trees_4(A,C) = k4_trees_4(B,D) => ( A = B & C = D ) ) ) ) ), file(trees_4,t15_trees_4), []). fof(t17_trees_4,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k1_trees_4(A) = k4_trees_4(B,C) & v6_trees_3(C) ) => ( A = B & C = k1_xboole_0 ) ) ) ), file(trees_4,t17_trees_4), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),D)) <=> r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( r2_hidden(k4_tarski(E,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) => r2_hidden(k4_tarski(C,D),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),E)) ) ) ) ) ) ) ) ), file(osafree,t20_osafree), []). fof(t22_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(k5_relat_1(C,B))) => k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(B,k1_funct_1(C,A)) ) ) ) ), file(funct_1,t22_funct_1), []). fof(t22_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k2_osafree(A,B)),k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r3_orders_2(A,E,F) & r2_hidden(C,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E)) & r2_hidden(D,k1_funct_1(u4_msualg_1(A,k8_osafree(A,B)),E)) ) => ( r2_hidden(k4_tarski(D,E),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) <=> r2_hidden(k4_tarski(D,F),k8_funct_2(k4_dtconstr(k2_osafree(A,B)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(A,B)),u1_struct_0(A))),k19_osafree(A,B),C)) ) ) ) ) ) ) ) ) ), file(osafree,t22_osafree), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t2_tarski,axiom,( ! [A,B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) ), file(tarski,t2_tarski), []). fof(t31_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) <=> k4_finseq_1(A) = k4_finseq_1(B) ) ) ) ), file(finseq_3,t31_finseq_3), []). fof(t33_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(k2_relat_1(A),k1_relat_1(C)) & B = k5_relat_1(A,C) ) => k3_finseq_1(B) = k3_finseq_1(A) ) ) ) ) ), file(finseq_2,t33_finseq_2), []). fof(t33_zfmisc_1,axiom,( ! [A,B,C,D] : ( k4_tarski(A,B) = k4_tarski(C,D) => ( A = C & B = D ) ) ), file(zfmisc_1,t33_zfmisc_1), []). fof(t3_pboole,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( m1_pboole(C,A) => ( ! [D] : ( r2_hidden(D,A) => k1_funct_1(B,D) = k1_funct_1(C,D) ) => B = C ) ) ) ), file(pboole,t3_pboole), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t4_osafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( r2_hidden(C,k6_dtconstr(k2_osafree(A,B))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( r2_hidden(E,k1_funct_1(B,D)) & C = k4_tarski(E,D) ) ) ) ) ) ), file(osafree,t4_osafree), []). 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(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(t6_msualg_3,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,B,C)) => ( k1_relat_1(D) = k4_finseq_1(k1_msualg_1(A,B)) & ! [E] : ( r2_hidden(E,k1_relat_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)))) => r2_hidden(k1_funct_1(D,E),k1_funct_1(k5_relat_1(k1_msualg_1(A,B),u4_msualg_1(A,C)),E)) ) ) ) ) ) ) ) ), file(msualg_3,t6_msualg_3), []). 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(t97_orders_1,axiom,( ! [A,B] : ( ( v1_partfun1(B,A,A) & m2_relset_1(B,A,A) ) => k3_relat_1(B) = A ) ), file(orders_1,t97_orders_1), []). 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), []).