% Mizar problem: t7_circuit1,circuit1,422,68 fof(t7_circuit1,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) & v6_trees_3(G) ) => ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( ( r2_hidden(C,k6_subset_1(u1_struct_0(A),k4_msafree2(A),k1_msafree2(A))) & E = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),G) & r2_hidden(k1_nat_1(H,1),k4_finseq_1(G)) & r2_hidden(k1_funct_1(G,k1_nat_1(H,1)),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D)) ) => r2_hidden(k8_trees_2(E,k3_lang1(k5_numbers,H),F),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v4_msualg_1,antisymmetry_r2_hidden,cc10_membered,cc10_trees_3,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_circuit1,cc1_dtconstr,cc1_finseq_1,cc1_finset_1,cc1_fraenkel,cc1_funct_1,cc1_membered,cc1_msafree2,cc1_msualg_1,cc1_nat_1,cc1_pboole,cc1_pre_circ,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_circuit1,cc2_dtconstr,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_msafree2,cc2_msualg_1,cc2_nat_1,cc2_pboole,cc2_xreal_0,cc3_membered,cc3_msafree2,cc3_nat_1,cc3_pboole,cc3_xreal_0,cc4_membered,cc4_msafree2,cc4_trees_3,cc4_xreal_0,cc5_trees_3,cc5_xreal_0,cc6_membered,cc6_trees_3,cc6_xreal_0,cc7_trees_3,cc7_xreal_0,cc8_xreal_0,cc9_membered,commutativity_k1_nat_1,commutativity_k2_tarski,commutativity_k2_xboole_0,commutativity_k2_xcmplx_0,commutativity_k3_xboole_0,connectedness_r1_xreal_0,d10_msafree,d11_finseq_1,d11_msafree,d12_msafree,d12_trees_2,d13_msafree,d16_msafree,d18_trees_3,d1_lang1,d1_tarski,d2_msafree,d2_xboole_0,d3_tarski,d3_xboole_0,d4_finseq_1,d4_finseq_4,d4_trees_4,d4_xboole_0,d5_funct_1,d5_tarski,d6_trees_3,d7_msafree2,d7_xboole_0,d8_msafree2,d9_dtconstr,dt_g1_lang1,dt_g3_msualg_1,dt_k10_msafree,dt_k11_msafree,dt_k12_finseq_1,dt_k12_trees_4,dt_k13_finseq_1,dt_k13_trees_3,dt_k16_trees_3,dt_k1_card_1,dt_k1_dtconstr,dt_k1_funct_1,dt_k1_msafree2,dt_k1_msualg_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_card_3,dt_k2_funct_6,dt_k2_msafree,dt_k2_msualg_1,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_1,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_lang1,dt_k3_msafree,dt_k3_msafree2,dt_k3_xboole_0,dt_k4_dtconstr,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_msafree,dt_k4_msafree2,dt_k4_relset_1,dt_k4_tarski,dt_k4_trees_4,dt_k4_xboole_0,dt_k5_finseq_1,dt_k5_lang1,dt_k5_msafree,dt_k5_msafree2,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_trees_1,dt_k5_trees_2,dt_k5_trees_3,dt_k6_dtconstr,dt_k6_finseq_1,dt_k6_lang1,dt_k6_msafree,dt_k6_msafree2,dt_k6_pboole,dt_k6_subset_1,dt_k7_dtconstr,dt_k7_finseq_1,dt_k7_msafree,dt_k7_pboole,dt_k8_dtconstr,dt_k8_finseq_1,dt_k8_msafree,dt_k8_pboole,dt_k8_trees_2,dt_k9_dtconstr,dt_l1_lang1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_pboole,dt_m1_relset_1,dt_m1_struct_0,dt_m1_subset_1,dt_m1_trees_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_struct_0,existence_l2_msualg_1,existence_l3_msualg_1,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_pboole,existence_m1_relset_1,existence_m1_struct_0,existence_m1_subset_1,existence_m1_trees_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_finset_1,fc10_membered,fc10_trees_3,fc10_xreal_0,fc11_finseq_1,fc11_finset_1,fc11_membered,fc11_xreal_0,fc12_finseq_1,fc12_finset_1,fc12_membered,fc12_xreal_0,fc13_finseq_1,fc13_membered,fc13_trees_3,fc14_finseq_1,fc14_finset_1,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc16_trees_3,fc17_finseq_1,fc19_trees_3,fc1_dtconstr,fc1_finset_1,fc1_funct_1,fc1_msafree,fc1_msualg_1,fc1_nat_1,fc1_ordinal2,fc1_pboole,fc1_struct_0,fc1_xboole_0,fc22_membered,fc22_trees_3,fc23_membered,fc23_trees_3,fc24_membered,fc25_membered,fc26_membered,fc26_trees_3,fc27_membered,fc28_membered,fc29_membered,fc2_dtconstr,fc2_finseq_1,fc2_finset_1,fc2_membered,fc2_msafree,fc2_pboole,fc2_trees_1,fc2_trees_2,fc2_xboole_0,fc30_membered,fc31_membered,fc32_membered,fc33_membered,fc34_membered,fc35_membered,fc36_membered,fc37_membered,fc38_membered,fc39_membered,fc3_dtconstr,fc3_finseq_1,fc3_msafree,fc3_nat_1,fc3_pre_circ,fc3_xboole_0,fc3_xreal_0,fc40_membered,fc41_membered,fc4_finseq_1,fc4_msafree,fc4_nat_1,fc4_pre_circ,fc5_membered,fc5_msafree,fc5_pre_circ,fc5_trees_2,fc6_funct_1,fc6_membered,fc6_msafree,fc6_pre_circ,fc6_trees_3,fc7_membered,fc7_msafree,fc7_trees_3,fc7_xreal_0,fc8_membered,fc8_msafree,fc8_trees_3,fc8_xreal_0,fc9_finseq_1,fc9_finset_1,fc9_membered,fc9_trees_3,fc9_xreal_0,fraenkel_a_3_0_circuit1,fraenkel_a_3_0_msafree,free_g1_lang1,free_g3_msualg_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,irreflexivity_r1_subset_1,rc1_dtconstr,rc1_finseq_1,rc1_finset_1,rc1_fraenkel,rc1_funct_1,rc1_membered,rc1_msafree,rc1_nat_1,rc1_pboole,rc1_pralg_1,rc1_pre_circ,rc1_trees_1,rc1_xboole_0,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_funct_1,rc2_nat_1,rc2_pboole,rc2_pralg_1,rc2_trees_1,rc2_trees_3,rc2_xboole_0,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_msafree2,rc3_nat_1,rc3_pboole,rc3_struct_0,rc3_xreal_0,rc4_finseq_1,rc4_finset_1,rc4_funct_1,rc4_pboole,rc4_trees_3,rc4_xreal_0,rc5_funct_1,rc5_msafree2,rc5_msualg_1,rc5_struct_0,rc5_trees_2,rc5_trees_3,rc6_finseq_1,rc6_msafree2,rc6_msualg_1,rc6_trees_2,rc6_trees_3,rc7_finseq_1,rc7_trees_2,rc7_trees_3,rc8_finseq_1,rc8_trees_2,rc8_trees_3,rc9_trees_2,redefinition_k12_finseq_1,redefinition_k12_trees_4,redefinition_k1_dtconstr,redefinition_k1_nat_1,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k3_lang1,redefinition_k3_msafree,redefinition_k4_finseq_1,redefinition_k4_msafree2,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k6_dtconstr,redefinition_k6_subset_1,redefinition_k7_dtconstr,redefinition_k7_pboole,redefinition_k8_dtconstr,redefinition_k8_finseq_1,redefinition_k8_pboole,redefinition_k9_dtconstr,redefinition_m1_dtconstr,redefinition_m1_struct_0,redefinition_m1_trees_1,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_r1_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc0_boole,spc1_boole,spc1_numerals,symmetry_r1_subset_1,symmetry_r1_xboole_0,t106_zfmisc_1,t10_dtconstr,t10_msafree,t13_finseq_2,t13_msafree,t13_msafree2,t14_msafree2,t15_trees_4,t17_pre_circ,t19_pre_circ,t1_arithm,t1_boole,t1_numerals,t1_real,t1_subset,t29_finseq_1,t2_boole,t2_real,t2_subset,t2_tarski,t31_finseq_3,t33_zfmisc_1,t3_boole,t3_msafree1,t3_real,t3_subset,t3_trees_4,t47_trees_1,t48_finseq_1,t4_boole,t4_real,t4_subset,t5_msafree,t5_real,t5_subset,t6_boole,t6_circuit1,t6_msafree,t6_real,t7_boole,t7_msafree,t7_real,t8_boole,t8_real,t9_dtconstr,t9_msafree]), [file(circuit1,t7_circuit1)]). 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_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), []). 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(cc11_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), []). fof(cc12_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), []). fof(cc13_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), []). fof(cc14_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), []). fof(cc15_membered,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), []). fof(cc16_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), []). fof(cc17_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), []). fof(cc18_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), []). fof(cc19_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), []). fof(cc1_circuit1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) => ( ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) ), file(circuit1,cc1_circuit1), []). fof(cc1_dtconstr,axiom,( ! [A,B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) ), file(dtconstr,cc1_dtconstr), []). fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), []). fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), []). 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_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), []). fof(cc1_msafree2,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v3_struct_0(A) & v2_msualg_1(A) ) => ( ~ v3_struct_0(A) & v2_msafree2(A) ) ) ) ), file(msafree2,cc1_msafree2), []). 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_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_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_pre_circ,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_trees_3(A)) => v1_finset_1(B) ) ) ), file(pre_circ,cc1_pre_circ), []). 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_xreal_0,axiom,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), []). fof(cc20_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), []). fof(cc2_circuit1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) => ( ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) ) ) ) ), file(circuit1,cc2_circuit1), []). 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_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), []). fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). fof(cc2_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) ) => ( v5_msualg_1(B,A) & v3_msafree2(B,A) ) ) ) ) ), file(msafree2,cc2_msafree2), []). 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(cc2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). fof(cc3_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) => ( ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) ), file(msafree2,cc3_msafree2), []). 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(cc3_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). fof(cc4_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) => ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) ) ) ) ) ), file(msafree2,cc4_msafree2), []). 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(cc4_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), []). 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(cc5_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), []). fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), []). 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(cc6_xreal_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), []). 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(cc7_xreal_0,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), []). fof(cc8_xreal_0,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), []). fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), []). 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(commutativity_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_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_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => k5_msafree(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))),k4_msafree(A,B)) ) ) ), file(msafree,d10_msafree), []). fof(d11_finseq_1,axiom,( ! [A,B] : ( B = k13_finseq_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m2_finseq_1(C,A) ) ) ), file(finseq_1,d11_finseq_1), []). fof(d11_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => k6_msafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) ), file(msafree,d11_msafree), []). fof(d12_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_msafree(A,B,C) = a_3_0_msafree(A,B,C) ) ) ) ), file(msafree,d12_msafree), []). fof(d12_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m2_finseq_1(B,k5_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(B,k1_relat_1(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ( D = k8_trees_2(A,B,C) <=> ( k1_relat_1(D) = k5_trees_1(k1_relat_1(A),B,k1_relat_1(C)) & ! [E] : ( m2_finseq_1(E,k5_numbers) => ~ ( r2_hidden(E,k5_trees_1(k1_relat_1(A),B,k1_relat_1(C))) & ~ ( ~ r1_tarski(B,E) & k1_funct_1(D,E) = k1_funct_1(A,E) ) & ! [F] : ( m2_finseq_1(F,k5_numbers) => ~ ( r2_hidden(F,k1_relat_1(C)) & E = k8_finseq_1(k5_numbers,B,F) & k1_funct_1(D,E) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) ) ) ), file(trees_2,d12_trees_2), []). fof(d13_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_pboole(C,u1_struct_0(A)) => ( C = k8_msafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k7_msafree(A,B,D) ) ) ) ) ) ), file(msafree,d13_msafree), []). fof(d16_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => k11_msafree(A,B) = g3_msualg_1(A,k8_msafree(A,B),k10_msafree(A,B)) ) ) ), file(msafree,d16_msafree), []). fof(d18_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v6_trees_3(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k16_trees_3(A) <=> ( k4_finseq_1(B) = k4_finseq_1(A) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k1_funct_1(D,k1_xboole_0) ) ) ) ) ) ) ) ) ) ), file(trees_3,d18_trees_3), []). 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(d2_msafree,axiom,( ! [A,B] : ( m1_pboole(B,A) => ! [C] : ( r2_hidden(C,A) => ! [D] : ( D = k2_msafree(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,k1_funct_1(B,C)) & E = k4_tarski(F,C) ) ) ) ) ) ), file(msafree,d2_msafree), []). fof(d2_xboole_0,axiom,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), []). fof(d3_tarski,axiom,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), []). fof(d3_xboole_0,axiom,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), []). 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_finseq_4,axiom,( ! [A,B,C] : ( ( v1_funct_1(C) & m2_relset_1(C,A,B) ) => ! [D] : ( r2_hidden(D,k1_relat_1(C)) => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ), file(finseq_4,d4_finseq_4), []). 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(d4_xboole_0,axiom,( ! [A,B,C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) ), file(xboole_0,d4_xboole_0), []). 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(d6_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_trees_3(B,A) <=> ! [C] : ( r2_hidden(C,B) => ( v1_funct_1(C) & v3_trees_2(C) & m3_trees_2(C,A) ) ) ) ) ), file(trees_3,d6_trees_3), []). fof(d7_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k4_msafree2(A)) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ( C = k5_msafree2(A,B) <=> k2_msualg_1(A,C) = B ) ) ) ) ) ), file(msafree2,d7_msafree2), []). fof(d7_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) ), file(xboole_0,d7_xboole_0), []). fof(d8_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => k6_msafree2(A,B) = k11_msafree(A,u4_msualg_1(A,B)) ) ) ), file(msafree2,d8_msafree2), []). 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(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_k10_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m3_pboole(k10_msafree(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),k8_msafree(A,B))),k8_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k8_msafree(A,B))) ) ), file(msafree,k10_msafree), []). fof(dt_k11_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => l3_msualg_1(k11_msafree(A,B),A) ) ), file(msafree,k11_msafree), []). 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_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_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_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k1_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(msafree2,k1_msafree2), []). 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_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_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_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_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), []). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), []). fof(dt_k2_trees_1,axiom,( ! [A] : ( m1_subset_1(A,k5_numbers) => ( ~ v1_xboole_0(k2_trees_1(A)) & v1_finset_1(k2_trees_1(A)) & v1_trees_1(k2_trees_1(A)) ) ) ), file(trees_1,k2_trees_1), []). 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_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k3_lang1(A,B),A,k3_finseq_2(A)) ) ), file(lang1,k3_lang1), []). 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_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k3_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(msafree2,k3_msafree2), []). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), []). 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_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => m2_relset_1(k4_msafree(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(msafree,k4_msafree), []). fof(dt_k4_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ( ~ v1_xboole_0(k4_msafree2(A)) & m1_subset_1(k4_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ) ), file(msafree2,k4_msafree2), []). 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_k4_xboole_0,axiom,( $true ), file(xboole_0,k4_xboole_0), []). 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_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => l1_lang1(k5_msafree(A,B)) ) ), file(msafree,k5_msafree), []). fof(dt_k5_msafree2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k5_msafree2(A,B),u1_msualg_1(A)) ) ), file(msafree2,k5_msafree2), []). 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_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_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k5_numbers) & ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( ~ v1_xboole_0(k5_trees_1(A,B,C)) & v1_trees_1(k5_trees_1(A,B,C)) ) ) ), file(trees_1,k5_trees_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_finseq_1,axiom,( ! [A] : ( v1_xboole_0(k6_finseq_1(A)) & m2_finseq_1(k6_finseq_1(A),A) ) ), file(finseq_1,k6_finseq_1), []). fof(dt_k6_lang1,axiom,( $true ), file(lang1,k6_lang1), []). fof(dt_k6_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_msualg_1(A)) ) => m1_subset_1(k6_msafree(A,B,C),u1_struct_0(k5_msafree(A,B))) ) ), file(msafree,k6_msafree), []). fof(dt_k6_msafree2,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(k6_msafree2(A,B),A) & v5_msualg_1(k6_msafree2(A,B),A) & v2_msafree(k6_msafree2(A,B),A) & l3_msualg_1(k6_msafree2(A,B),A) ) ) ), file(msafree2,k6_msafree2), []). 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_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_subset_1(k6_subset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(subset_1,k6_subset_1), []). 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_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,k7_finseq_1), []). fof(dt_k7_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k7_msafree(A,B,C),k1_zfmisc_1(k4_dtconstr(k5_msafree(A,B)))) ) ), file(msafree,k7_msafree), []). 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_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ), file(finseq_1,k8_finseq_1), []). fof(dt_k8_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => m1_pboole(k8_msafree(A,B),u1_struct_0(A)) ) ), file(msafree,k8_msafree), []). 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_k8_trees_2,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & m1_finseq_1(B,k5_numbers) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( v1_relat_1(k8_trees_2(A,B,C)) & v1_funct_1(k8_trees_2(A,B,C)) & v3_trees_2(k8_trees_2(A,B,C)) ) ) ), file(trees_2,k8_trees_2), []). 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_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_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_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_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_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_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k5_numbers) ) ) ), file(trees_1,m1_trees_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_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_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_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_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_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_1(B,A) ) ), file(trees_1,m1_trees_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_finset_1,axiom,( ! [A,B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc10_finset_1), []). fof(fc10_membered,axiom,( ! [A] : ( v1_int_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) ) ) ), file(membered,fc10_membered), []). fof(fc10_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(fc10_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), []). fof(fc11_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), []). fof(fc11_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) ), file(finset_1,fc11_finset_1), []). fof(fc11_membered,axiom,( ! [A] : ( v4_ordinal2(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) & v4_membered(k1_tarski(A)) & v5_membered(k1_tarski(A)) ) ) ), file(membered,fc11_membered), []). fof(fc11_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), []). fof(fc12_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finseq_1(A)) & v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc12_finseq_1), []). fof(fc12_finset_1,axiom,( ! [A,B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) ), file(finset_1,fc12_finset_1), []). fof(fc12_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). fof(fc12_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), []). fof(fc13_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(A,B)) & v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) ) ) ), file(finseq_1,fc13_finseq_1), []). fof(fc13_membered,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), []). 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(fc14_finseq_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ v1_xboole_0(k7_finseq_1(B,A)) & v1_relat_1(k7_finseq_1(B,A)) & v1_funct_1(k7_finseq_1(B,A)) & v1_finset_1(k7_finseq_1(B,A)) & v1_finseq_1(k7_finseq_1(B,A)) ) ) ), file(finseq_1,fc14_finseq_1), []). fof(fc14_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), []). fof(fc14_membered,axiom,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), []). fof(fc15_membered,axiom,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), []). fof(fc16_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(k13_finseq_1(A)) & v1_fraenkel(k13_finseq_1(A)) ) ), file(finseq_1,fc16_finseq_1), []). fof(fc16_membered,axiom,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), []). 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(fc17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), []). 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_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) ) ), file(finset_1,fc1_finset_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_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_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_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc22_membered,axiom,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), []). 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_membered,axiom,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), []). fof(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(fc24_membered,axiom,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), []). fof(fc25_membered,axiom,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), []). fof(fc26_membered,axiom,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), []). fof(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(fc27_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) ), file(membered,fc27_membered), []). fof(fc28_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) ), file(membered,fc28_membered), []). fof(fc29_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc29_membered), []). 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_finseq_1,axiom, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), []). fof(fc2_finset_1,axiom,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). 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_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_trees_1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & m1_subset_1(B,A) & ~ v1_xboole_0(C) & v1_finset_1(C) & v1_trees_1(C) ) => ( ~ v1_xboole_0(k5_trees_1(A,B,C)) & v1_finset_1(k5_trees_1(A,B,C)) & v1_trees_1(k5_trees_1(A,B,C)) ) ) ), file(trees_1,fc2_trees_1), []). fof(fc2_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) ) ) ), file(trees_2,fc2_trees_2), []). 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(fc30_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc30_membered), []). fof(fc31_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc31_membered), []). fof(fc32_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc32_membered), []). fof(fc33_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc33_membered), []). fof(fc34_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc34_membered), []). fof(fc35_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(A,B)) & v2_membered(k3_xboole_0(A,B)) & v3_membered(k3_xboole_0(A,B)) & v4_membered(k3_xboole_0(A,B)) & v5_membered(k3_xboole_0(A,B)) ) ) ), file(membered,fc35_membered), []). fof(fc36_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k3_xboole_0(B,A)) & v2_membered(k3_xboole_0(B,A)) & v3_membered(k3_xboole_0(B,A)) & v4_membered(k3_xboole_0(B,A)) & v5_membered(k3_xboole_0(B,A)) ) ) ), file(membered,fc36_membered), []). fof(fc37_membered,axiom,( ! [A,B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) ), file(membered,fc37_membered), []). fof(fc38_membered,axiom,( ! [A,B] : ( v2_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc38_membered), []). fof(fc39_membered,axiom,( ! [A,B] : ( v3_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc39_membered), []). 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_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) ), file(finseq_1,fc3_finseq_1), []). 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_pre_circ,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v2_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) ) ) ), file(pre_circ,fc3_pre_circ), []). fof(fc3_xboole_0,axiom,( ! [A,B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) ), file(xboole_0,fc3_xboole_0), []). fof(fc3_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), []). fof(fc40_membered,axiom,( ! [A,B] : ( v4_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc40_membered), []). fof(fc41_membered,axiom,( ! [A,B] : ( v5_membered(A) => ( v1_membered(k4_xboole_0(A,B)) & v2_membered(k4_xboole_0(A,B)) & v3_membered(k4_xboole_0(A,B)) & v4_membered(k4_xboole_0(A,B)) & v5_membered(k4_xboole_0(A,B)) ) ) ), file(membered,fc41_membered), []). fof(fc4_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & v1_finset_1(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) ) ), file(finseq_1,fc4_finseq_1), []). fof(fc4_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_msafree(A,B)) & v1_lang1(k5_msafree(A,B)) ) ) ), file(msafree,fc4_msafree), []). 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_pre_circ,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & m1_subset_1(B,k1_relat_1(A)) ) => ( v1_relat_1(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v1_finset_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) ) ) ), file(pre_circ,fc4_pre_circ), []). fof(fc5_membered,axiom, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), []). fof(fc5_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( ~ v3_struct_0(k5_msafree(A,B)) & v1_lang1(k5_msafree(A,B)) & v1_dtconstr(k5_msafree(A,B)) & v2_dtconstr(k5_msafree(A,B)) & v3_dtconstr(k5_msafree(A,B)) ) ) ), file(msafree,fc5_msafree), []). fof(fc5_pre_circ,axiom,( ! [A,B,C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & m1_subset_1(B,k1_relat_1(A)) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) & v3_trees_2(C) ) => ( v1_relat_1(k8_trees_2(A,B,C)) & v1_funct_1(k8_trees_2(A,B,C)) & v1_finset_1(k8_trees_2(A,B,C)) & v3_trees_2(k8_trees_2(A,B,C)) ) ) ), file(pre_circ,fc5_pre_circ), []). fof(fc5_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(trees_2,fc5_trees_2), []). 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_membered,axiom, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), []). fof(fc6_msafree,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ( ~ v1_xboole_0(k7_msafree(A,B,C)) & v3_trees_3(k7_msafree(A,B,C)) ) ) ), file(msafree,fc6_msafree), []). fof(fc6_pre_circ,axiom,( ! [A] : ( v1_relat_1(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)) & v1_finset_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) ) ), file(pre_circ,fc6_pre_circ), []). 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_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). fof(fc7_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v1_relat_1(k8_msafree(A,B)) & v2_relat_1(k8_msafree(A,B)) & ~ v3_relat_1(k8_msafree(A,B)) & v1_funct_1(k8_msafree(A,B)) ) ) ), file(msafree,fc7_msafree), []). fof(fc7_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc7_trees_3), []). fof(fc7_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). fof(fc8_msafree,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( v4_msualg_1(k11_msafree(A,B),A) & v5_msualg_1(k11_msafree(A,B),A) ) ) ), file(msafree,fc8_msafree), []). fof(fc8_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v5_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v4_trees_3(k7_finseq_1(A,B)) & v5_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc8_trees_3), []). fof(fc8_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_1), []). fof(fc9_finset_1,axiom,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), []). fof(fc9_membered,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) & v3_membered(k1_tarski(A)) ) ) ), file(membered,fc9_membered), []). fof(fc9_trees_3,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & v1_funct_1(k7_finseq_1(A,B)) & v1_finset_1(k7_finseq_1(A,B)) & v1_finseq_1(k7_finseq_1(A,B)) & v6_trees_3(k7_finseq_1(A,B)) ) ) ), file(trees_3,fc9_trees_3), []). fof(fc9_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), []). fof(fraenkel_a_3_0_circuit1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v5_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_circuit1(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,u4_msualg_1(B,C))),k5_trees_3(u1_struct_0(k5_msafree(B,u4_msualg_1(B,C)))),k4_dtconstr(k5_msafree(B,u4_msualg_1(B,C)))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(u4_msualg_1(B,C),D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u1_msualg_1(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) ), file(circuit1,a_3_0_circuit1), []). fof(fraenkel_a_3_0_msafree,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(B) & ~ v2_msualg_1(B) & l1_msualg_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_msafree(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u1_msualg_1(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) ), file(msafree,a_3_0_msafree), []). 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(idempotence_k3_xboole_0,axiom,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), []). fof(irreflexivity_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r1_subset_1(A,A) ) ), file(subset_1,r1_subset_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_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), []). fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), []). fof(rc1_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), []). fof(rc1_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v5_msualg_1(B,A) & v2_msafree(B,A) ) ) ), file(msafree,rc1_msafree), []). 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_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(pralg_1,rc1_pralg_1), []). fof(rc1_pre_circ,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(pre_circ,rc1_pre_circ), []). fof(rc1_trees_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_trees_1(A) ) ), file(trees_1,rc1_trees_1), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), []). fof(rc1_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), []). fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), []). fof(rc2_finset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), []). fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_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_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_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k3_finseq_2(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(pralg_1,rc2_pralg_1), []). fof(rc2_trees_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) ), file(trees_1,rc2_trees_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(rc2_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), []). fof(rc3_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), []). fof(rc3_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), []). fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_msafree2,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) & v3_msafree2(B,A) & v4_msafree2(B,A) ) ) ), file(msafree2,rc3_msafree2), []). 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_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(rc3_xreal_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), []). fof(rc4_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), []). fof(rc4_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), []). fof(rc4_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), []). fof(rc4_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(rc4_xreal_0,axiom,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), []). 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_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ? [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) & ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ), file(msafree2,rc5_msafree2), []). 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_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_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ), file(trees_2,rc5_trees_2), []). 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_finseq_1,axiom,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), []). fof(rc6_msafree2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ? [D] : ( m1_subset_1(D,k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),C)) & ~ v1_xboole_0(D) & v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) ) ) ), file(msafree2,rc6_msafree2), []). 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_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) ) ), file(trees_2,rc6_trees_2), []). 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_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), []). fof(rc7_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ), file(trees_2,rc7_trees_2), []). 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_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), []). fof(rc8_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m3_trees_2(B,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) ) ), file(trees_2,rc8_trees_2), []). 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(rc9_trees_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_relset_1(C,A,B) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) ), file(trees_2,rc9_trees_2), []). 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_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_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_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_lang1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_lang1(A,B) = k5_finseq_1(B) ) ), file(lang1,k3_lang1), []). 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_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => k4_msafree2(A) = k3_msafree2(A) ) ), file(msafree2,k4_msafree2), []). 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_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_k6_subset_1,axiom,( ! [A,B,C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k6_subset_1(A,B,C) = k4_xboole_0(B,C) ) ), file(subset_1,k6_subset_1), []). 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_finseq_1,axiom,( ! [A,B,C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) ), file(finseq_1,k8_finseq_1), []). 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_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_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) <=> m1_subset_1(B,A) ) ) ), file(trees_1,m1_trees_1), []). 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_r1_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) ), file(subset_1,r1_subset_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(spc0_boole,axiom,( v1_xboole_0(0) ), file(boole,spc0_boole), []). 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_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) => r1_subset_1(B,A) ) ) ), file(subset_1,r1_subset_1), []). fof(symmetry_r1_xboole_0,axiom,( ! [A,B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) ), file(xboole_0,r1_xboole_0), []). 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_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & v2_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ! [C] : ( m1_struct_0(C,A,k7_dtconstr(A)) => ~ ( k1_funct_1(B,k1_xboole_0) = C & ! [D] : ( m1_trees_4(D,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ~ ( B = k12_trees_4(u1_struct_0(A),C,D) & r1_lang1(A,C,k1_dtconstr(u1_struct_0(A),k5_trees_3(u1_struct_0(A)),D)) ) ) ) ) ) ) ), file(dtconstr,t10_dtconstr), []). fof(t10_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B))) => ( r1_lang1(k5_msafree(A,B),k6_msafree(A,B,C),k1_dtconstr(u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),D)) <=> r2_hidden(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),k8_msafree(A,B))),C)) ) ) ) ) ) ), file(msafree,t10_msafree), []). fof(t13_finseq_2,axiom,( ! [A] : ( m2_subset_1(A,k1_numbers,k5_numbers) => ! [B,C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r2_hidden(k1_funct_1(C,A),B) ) ) ) ), file(finseq_2,t13_finseq_2), []). fof(t13_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_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)) => ( C != D => r1_subset_1(k1_funct_1(k8_msafree(A,B),C),k1_funct_1(k8_msafree(A,B),D)) ) ) ) ) ) ), file(msafree,t13_msafree), []). fof(t13_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_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) & v6_trees_3(D) ) => ( r2_hidden(k4_trees_4(k4_tarski(C,u1_struct_0(A)),D),k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),k2_msualg_1(A,C))) => k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C)) ) ) ) ) ) ), file(msafree2,t13_msafree2), []). fof(t14_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_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) & v6_trees_3(D) ) => ( r2_hidden(k4_trees_4(k4_tarski(C,u1_struct_0(A)),D),k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),k2_msualg_1(A,C))) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_relset_1(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C))) => r2_hidden(k1_funct_1(D,E),k1_funct_1(u4_msualg_1(A,k11_msafree(A,B)),k1_funct_1(k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ), file(msafree2,t14_msafree2), []). 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_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) => r2_hidden(k12_finseq_1(k5_numbers,B),k13_trees_3(k2_funct_6(A))) ) ) ) ), file(pre_circ,t17_pre_circ), []). fof(t19_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ! [C,D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & v6_trees_3(E) ) => ~ ( r2_hidden(k12_finseq_1(k5_numbers,D),k1_relat_1(A)) & A = k4_trees_4(C,E) & ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & v6_trees_3(F) ) => ~ ( k8_trees_2(A,k12_finseq_1(k5_numbers,D),B) = k4_trees_4(C,F) & k3_finseq_1(F) = k3_finseq_1(E) & k1_funct_1(F,k1_nat_1(D,1)) = B & ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( r2_hidden(G,k4_finseq_1(E)) => ( G = k1_nat_1(D,1) | k1_funct_1(F,G) = k1_funct_1(E,G) ) ) ) ) ) ) ) ) ) ) ), file(pre_circ,t19_pre_circ), []). fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,0) = A ) ), file(arithm,t1_arithm), []). fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t29_finseq_1,axiom,( ! [A] : m2_finseq_1(k1_xboole_0,A) ), file(finseq_1,t29_finseq_1), []). fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), []). fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), []). 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_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_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). fof(t3_msafree1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [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(k4_tarski(k4_tarski(C,u1_struct_0(A)),D),k4_msafree(A,B)) => ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( r2_hidden(E,k4_finseq_1(D)) => ( ( r2_hidden(k1_funct_1(D,E),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)) = k1_funct_1(D,E) => k2_msualg_1(A,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) & ( r2_hidden(k1_funct_1(D,E),k3_card_3(k3_msafree(u1_struct_0(A),B))) => r2_hidden(k1_funct_1(D,E),k2_msafree(u1_struct_0(A),B,k1_funct_1(k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ) ), file(msafree1,t3_msafree1), []). fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), []). fof(t3_subset,axiom,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), []). fof(t3_trees_4,axiom,( ! [A] : ( k1_relat_1(k1_trees_4(A)) = k2_trees_1(0) & k1_funct_1(k1_trees_4(A),k1_xboole_0) = A ) ), file(trees_4,t3_trees_4), []). fof(t47_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( r2_hidden(k1_xboole_0,A) & r2_hidden(k6_finseq_1(k5_numbers),A) ) ) ), file(trees_1,t47_trees_1), []). fof(t48_finseq_1,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) ) => ( k7_finseq_1(A,B) = k1_xboole_0 => ( A = k1_xboole_0 & B = k1_xboole_0 ) ) ) ) ), file(finseq_1,t48_finseq_1), []). fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), []). 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_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_pboole(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m2_finseq_2(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))),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(k4_tarski(C,u1_struct_0(A)),D),k4_msafree(A,B)) <=> ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( r2_hidden(E,k4_finseq_1(D)) => ( ( r2_hidden(k1_funct_1(D,E),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)) = k1_funct_1(D,E) => k2_msualg_1(A,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) & ( r2_hidden(k1_funct_1(D,E),k3_card_3(k3_msafree(u1_struct_0(A),B))) => r2_hidden(k1_funct_1(D,E),k2_msafree(u1_struct_0(A),B,k1_funct_1(k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ) ), file(msafree,t5_msafree), []). fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), []). 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_circuit1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),C)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & v6_trees_3(F) ) => ( ( r2_hidden(C,k4_msafree2(A)) & E = k4_trees_4(k4_tarski(k5_msafree2(A,C),u1_struct_0(A)),F) ) => ! [G] : ( m2_subset_1(G,k1_numbers,k5_numbers) => ( ( r2_hidden(G,k4_finseq_1(F)) & r2_hidden(k1_funct_1(F,G),k1_funct_1(u4_msualg_1(A,k6_msafree2(A,B)),D)) ) => D = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,k5_msafree2(A,C)),G) ) ) ) ) ) ) ) ) ) ), file(circuit1,t6_circuit1), []). fof(t6_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ( k6_lang1(k5_msafree(A,B)) = k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A))) & k5_lang1(k5_msafree(A,B)) = k3_card_3(k3_msafree(u1_struct_0(A),B)) ) ) ) ), file(msafree,t6_msafree), []). fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t7_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( r2_hidden(C,k6_dtconstr(k5_msafree(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(msafree,t7_msafree), []). fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), []). fof(t9_dtconstr,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ! [C] : ( m1_struct_0(C,A,k6_dtconstr(A)) => ( k1_funct_1(B,k1_xboole_0) = C => B = k8_dtconstr(A,C) ) ) ) ) ), file(dtconstr,t9_dtconstr), []). fof(t9_msafree,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_msualg_1(A)) => ! [D] : ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B))) => ( r2_hidden(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),k8_msafree(A,B))),C)) <=> ( k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_finseq_1(D)) => r2_hidden(k1_funct_1(D,E),k7_msafree(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) ), file(msafree,t9_msafree), []).