% Mizar problem: t23_circtrm1,circtrm1,1187,36 fof(t23_circtrm1,conjecture,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ( ! [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => ! [F] : ( m1_subset_1(F,u1_msualg_1(A)) => ~ ( r2_hidden(E,k9_trees_9(D)) & k1_funct_1(E,k1_xboole_0) = k4_tarski(F,u1_struct_0(A)) & k1_msualg_1(A,F) = k1_xboole_0 ) ) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u4_msualg_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B)))) => ! [F] : ( m1_circtrm1(F,A,C,D,B,E) => ! [G] : ( m1_dtconstr(G,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => ( r2_hidden(G,k9_trees_9(D)) => ( r1_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(G))),G) & k1_funct_1(k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(G))),G) = k7_circtrm1(A,B,C,G,F) ) ) ) ) ) ) ) ) ) ) ), inference(mizar_bg_added,[status(thm)],[abstractness_v1_lang1,abstractness_v1_msualg_1,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_arytm_3,cc1_circtrm1,cc1_finseq_1,cc1_fraenkel,cc1_funct_1,cc1_membered,cc1_msaterm,cc1_msualg_1,cc1_pboole,cc1_relset_1,cc1_trees_3,cc1_trees_9,cc20_membered,cc2_arytm_3,cc2_circcomb,cc2_circtrm1,cc2_funct_1,cc2_instalg1,cc2_membered,cc2_msualg_1,cc2_pboole,cc2_trees_3,cc2_trees_9,cc3_arytm_3,cc3_circtrm1,cc3_instalg1,cc3_membered,cc3_pboole,cc3_trees_3,cc3_trees_9,cc4_circtrm1,cc4_instalg1,cc4_membered,cc4_trees_3,cc4_trees_9,cc5_instalg1,cc5_trees_3,cc5_trees_9,cc6_membered,cc6_trees_3,cc6_trees_9,cc7_trees_3,cc8_trees_3,cc9_membered,cc9_trees_3,commutativity_k1_nat_1,commutativity_k2_pboole,commutativity_k2_tarski,commutativity_k2_xcmplx_0,connectedness_r1_xreal_0,d10_msualg_1,d11_msafree,d11_msualg_1,d11_trees_2,d1_circtrm1,d2_msafree2,d3_finseq_1,d4_finseq_1,d4_msaterm,d4_trees_4,d5_funct_1,d5_tarski,d6_circtrm1,d6_msualg_1,d7_circtrm1,d7_msualg_1,d8_circtrm1,d9_facirc_1,d9_msualg_1,dt_g1_lang1,dt_g1_msualg_1,dt_g3_msualg_1,dt_k11_trees_4,dt_k12_finseq_1,dt_k12_trees_9,dt_k13_finseq_1,dt_k13_trees_3,dt_k13_trees_9,dt_k1_card_1,dt_k1_circtrm1,dt_k1_finseq_1,dt_k1_funct_1,dt_k1_msaterm,dt_k1_msualg_1,dt_k1_msualg_3,dt_k1_nat_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_tarski,dt_k1_trees_3,dt_k1_trees_4,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_finseq_1,dt_k2_funct_6,dt_k2_msafree2,dt_k2_msaterm,dt_k2_msualg_1,dt_k2_pboole,dt_k2_relat_1,dt_k2_tarski,dt_k2_trees_1,dt_k2_trees_3,dt_k2_xcmplx_0,dt_k2_zfmisc_1,dt_k3_finseq_1,dt_k3_finseq_2,dt_k3_funct_6,dt_k3_msualg_1,dt_k3_trees_1,dt_k4_card_3,dt_k4_circtrm1,dt_k4_finseq_1,dt_k4_finseq_4,dt_k4_msualg_1,dt_k4_tarski,dt_k4_trees_1,dt_k4_trees_4,dt_k4_xboole_0,dt_k5_circtrm1,dt_k5_finseq_1,dt_k5_msafree,dt_k5_msaterm,dt_k5_msualg_1,dt_k5_numbers,dt_k5_ordinal2,dt_k5_relat_1,dt_k5_relset_1,dt_k5_trees_2,dt_k5_trees_3,dt_k6_circtrm1,dt_k6_circuit2,dt_k6_finseq_1,dt_k6_funct_3,dt_k6_lang1,dt_k6_msafree,dt_k6_msaterm,dt_k6_partfun1,dt_k6_pboole,dt_k6_relat_1,dt_k6_trees_1,dt_k7_circtrm1,dt_k7_dtconstr,dt_k7_finseq_1,dt_k7_msaterm,dt_k7_pboole,dt_k8_finseq_1,dt_k8_funct_2,dt_k8_pboole,dt_k9_facirc_1,dt_k9_msaterm,dt_k9_trees_9,dt_l1_lang1,dt_l1_msualg_1,dt_l1_struct_0,dt_l2_msualg_1,dt_l3_msualg_1,dt_m1_circtrm1,dt_m1_dtconstr,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_msaterm,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_finseq_1,dt_m2_finseq_2,dt_m2_msaterm,dt_m2_relset_1,dt_m2_subset_1,dt_m3_msaterm,dt_m3_pboole,dt_m3_trees_2,dt_m3_trees_3,dt_m4_msaterm,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_circtrm1,existence_m1_dtconstr,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_msaterm,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_finseq_1,existence_m2_finseq_2,existence_m2_msaterm,existence_m2_relset_1,existence_m2_subset_1,existence_m3_msaterm,existence_m3_pboole,existence_m3_trees_2,existence_m3_trees_3,existence_m4_msaterm,existence_m4_trees_3,existence_m5_trees_3,fc10_membered,fc10_trees_3,fc11_finseq_1,fc11_membered,fc12_finseq_1,fc12_membered,fc13_finseq_1,fc13_membered,fc13_trees_3,fc14_finseq_1,fc14_membered,fc15_membered,fc16_finseq_1,fc16_membered,fc16_trees_3,fc17_finseq_1,fc19_trees_3,fc1_circtrm1,fc1_finseq_1,fc1_funct_1,fc1_instalg1,fc1_msaterm,fc1_msualg_1,fc1_msualg_2,fc1_pboole,fc1_struct_0,fc1_subset_1,fc1_trees_3,fc1_trees_9,fc1_xboole_0,fc21_trees_3,fc23_trees_3,fc26_trees_3,fc2_circtrm1,fc2_finseq_1,fc2_funct_1,fc2_membered,fc2_msaterm,fc2_msualg_2,fc2_pboole,fc2_subset_1,fc2_trees_2,fc2_trees_3,fc2_trees_9,fc37_membered,fc38_membered,fc39_membered,fc3_card_3,fc3_circtrm1,fc3_finseq_1,fc3_msafree,fc3_msualg_2,fc3_subset_1,fc3_trees_3,fc3_trees_9,fc40_membered,fc41_membered,fc4_card_3,fc4_finseq_1,fc4_msafree,fc4_subset_1,fc4_trees_3,fc5_card_3,fc5_membered,fc5_msafree,fc5_trees_2,fc5_trees_9,fc6_circtrm1,fc6_funct_1,fc6_membered,fc6_msualg_2,fc6_trees_3,fc7_circtrm1,fc7_funcop_1,fc7_membered,fc7_trees_3,fc8_circtrm1,fc8_funcop_1,fc8_membered,fc8_trees_3,fc8_trees_9,fc9_finseq_1,fc9_membered,fc9_trees_3,fc9_trees_9,free_g1_lang1,free_g1_msualg_1,free_g3_msualg_1,idempotence_k2_pboole,rc1_arytm_3,rc1_circcomb,rc1_finseq_1,rc1_fraenkel,rc1_funcop_1,rc1_funct_1,rc1_instalg1,rc1_membered,rc1_msualg_1,rc1_pboole,rc1_subset_1,rc1_trees_2,rc1_trees_3,rc1_trees_9,rc1_xboole_0,rc2_finseq_1,rc2_funct_1,rc2_msualg_1,rc2_pboole,rc2_subset_1,rc2_trees_3,rc2_trees_9,rc2_xboole_0,rc3_finseq_1,rc3_funct_1,rc3_msualg_1,rc3_pboole,rc3_struct_0,rc3_trees_3,rc3_trees_9,rc4_finseq_1,rc4_funct_1,rc4_pboole,rc4_trees_3,rc4_trees_9,rc5_funct_1,rc5_msualg_1,rc5_struct_0,rc5_trees_2,rc5_trees_3,rc5_trees_9,rc6_finseq_1,rc6_msualg_1,rc6_trees_2,rc6_trees_3,rc6_trees_9,rc7_finseq_1,rc7_trees_2,rc7_trees_3,rc8_finseq_1,rc8_trees_2,rc8_trees_3,rc9_trees_2,redefinition_k11_trees_4,redefinition_k12_finseq_1,redefinition_k1_msualg_3,redefinition_k1_nat_1,redefinition_k2_finseq_1,redefinition_k2_msaterm,redefinition_k3_finseq_1,redefinition_k3_finseq_2,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_k5_relset_1,redefinition_k6_funct_3,redefinition_k6_msaterm,redefinition_k6_partfun1,redefinition_k7_dtconstr,redefinition_k7_pboole,redefinition_k8_finseq_1,redefinition_k8_funct_2,redefinition_k8_pboole,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_m3_trees_3,redefinition_m5_trees_3,reflexivity_r1_tarski,reflexivity_r1_xreal_0,s1_msaterm__e5_41__circtrm1,s2_finseq_1__e24_41_2__circtrm1,spc0_boole,spc1_boole,spc1_numerals,t10_facirc_1,t10_trees_4,t11_facirc_1,t129_zfmisc_1,t12_circtrm1,t12_facirc_1,t13_circtrm1,t13_facirc_1,t15_trees_4,t17_circtrm1,t17_facirc_1,t17_trees_4,t18_facirc_1,t19_facirc_1,t1_circtrm1,t1_numerals,t1_subset,t20_trees_9,t22_msaterm,t22_nat_1,t23_funct_1,t23_msaterm,t24_msaterm,t25_finseq_1,t25_trees_9,t27_msaterm,t28_nat_1,t2_subset,t31_funct_6,t34_funct_1,t38_nat_1,t3_boole,t3_subset,t3_trees_4,t42_msaterm,t43_msaterm,t46_relat_1,t47_finseq_1,t47_trees_1,t4_boole,t4_circtrm1,t4_circuit1,t4_msaterm,t4_subset,t5_subset,t5_trees_4,t6_boole,t79_trees_1,t7_boole,t80_trees_1,t81_trees_3,t8_boole,t8_msaterm,t9_funct_1]), [file(circtrm1,t23_circtrm1)]). 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_v1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_msualg_1(A) => A = g1_msualg_1(u1_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u3_msualg_1(A)) ) ) ), file(msualg_1,v1_msualg_1), []). 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_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), []). fof(cc1_circtrm1,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)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_circtrm1(A,B,C))) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) ), file(circtrm1,cc1_circtrm1), []). 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_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_msaterm,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)) ) => ! [C] : ( m1_subset_1(C,k1_msaterm(A,B)) => v1_finset_1(C) ) ) ), file(msaterm,cc1_msaterm), []). 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_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_pboole(B,A) => ( v2_relat_1(B) => ~ v3_relat_1(B) ) ) ) ), file(pboole,cc1_pboole), []). fof(cc1_relset_1,axiom,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), []). fof(cc1_trees_3,axiom,( ! [A] : ( v2_trees_3(A) => v1_trees_3(A) ) ), file(trees_3,cc1_trees_3), []). fof(cc1_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ) ), file(trees_9,cc1_trees_9), []). 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_arytm_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), []). fof(cc2_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v3_struct_0(A) & v1_circcomb(A) ) => ( ~ v3_struct_0(A) & v2_msafree2(A) ) ) ) ), file(circcomb,cc2_circcomb), []). fof(cc2_circtrm1,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)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_circtrm1(A,B,C))) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) & v3_trees_9(D) & v4_trees_9(D) ) ) ) ), file(circtrm1,cc2_circtrm1), []). 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_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ~ v3_struct_0(A) => v1_instalg1(A) ) ) ), file(instalg1,cc2_instalg1), []). fof(cc2_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), []). 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_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_trees_3,axiom,( ! [A] : ( v1_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_trees_3(B) ) ) ), file(trees_3,cc2_trees_3), []). fof(cc2_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v1_trees_9(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) ) ), file(trees_9,cc2_trees_9), []). fof(cc3_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), []). fof(cc3_circtrm1,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)) & m3_msaterm(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_msualg_1(k1_circtrm1(A,B,C))) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) ), file(circtrm1,cc3_circtrm1), []). fof(cc3_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v2_msualg_1(A) => v1_instalg1(A) ) ) ), file(instalg1,cc3_instalg1), []). fof(cc3_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), []). 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_trees_3,axiom,( ! [A] : ( v2_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_trees_3(B) & v2_trees_3(B) ) ) ) ), file(trees_3,cc3_trees_3), []). fof(cc3_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v2_trees_9(A) ) ) ), file(trees_9,cc3_trees_9), []). fof(cc4_circtrm1,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)) & m3_msaterm(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_msualg_1(k1_circtrm1(A,B,C))) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) & v3_trees_2(D) & v3_trees_9(D) & v4_trees_9(D) ) ) ) ), file(circtrm1,cc4_circtrm1), []). fof(cc4_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( v3_struct_0(A) & v1_instalg1(A) ) => v2_msualg_1(A) ) ) ), file(instalg1,cc4_instalg1), []). fof(cc4_membered,axiom,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), []). 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_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) ) ), file(trees_9,cc4_trees_9), []). fof(cc5_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v2_msualg_1(A) & v1_instalg1(A) ) => ~ v3_struct_0(A) ) ) ), file(instalg1,cc5_instalg1), []). 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_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v4_trees_9(A) ) ) ), file(trees_9,cc5_trees_9), []). 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_trees_9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A))) ) => ! [C] : ( m1_subset_1(C,B) => v1_finset_1(C) ) ) ), file(trees_9,cc6_trees_9), []). 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(cc8_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v4_trees_3(B) ) ) ), file(trees_3,cc8_trees_3), []). 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(cc9_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => ( v4_trees_3(B) & v5_trees_3(B) ) ) ) ), file(trees_3,cc9_trees_3), []). fof(commutativity_k1_nat_1,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) ), file(nat_1,k1_nat_1), []). fof(commutativity_k2_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => k2_pboole(A,B,C) = k2_pboole(A,C,B) ) ), file(pboole,k2_pboole), []). fof(commutativity_k2_tarski,axiom,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), []). fof(commutativity_k2_xcmplx_0,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), []). fof(connectedness_r1_xreal_0,axiom,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), []). fof(d10_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k4_msualg_1(A,B,C) = k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),u4_msualg_1(A,C)),B) ) ) ) ), file(msualg_1,d10_msualg_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(d11_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k5_msualg_1(A,B,C) = k1_funct_1(u5_msualg_1(A,C),B) ) ) ) ), file(msualg_1,d11_msualg_1), []). fof(d11_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) ) => ( C = k5_trees_2(A,B) <=> ( k1_relat_1(C) = k4_trees_1(k1_relat_1(A),B) & ! [D] : ( m2_finseq_1(D,k5_numbers) => ( r2_hidden(D,k4_trees_1(k1_relat_1(A),B)) => k1_funct_1(C,D) = k1_funct_1(A,k8_finseq_1(k5_numbers,B,D)) ) ) ) ) ) ) ) ), file(trees_2,d11_trees_2), []). fof(d1_circtrm1,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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => k1_circtrm1(A,B,C) = g1_msualg_1(k9_trees_9(C),k12_trees_9(C,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))),k13_trees_9(C,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))),k6_funct_3(k9_trees_9(C),k12_trees_9(C,k2_zfmisc_1(u1_msualg_1(A),k1_tarski(u1_struct_0(A)))))) ) ) ) ), file(circtrm1,d1_circtrm1), []). fof(d2_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => k2_msafree2(A) = k4_xboole_0(u1_struct_0(A),k5_relset_1(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A))) ) ), file(msafree2,d2_msafree2), []). fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), []). 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_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( v2_relat_1(C) & m1_pboole(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(C,D)) => k5_msaterm(A,B,C,D,E) = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) ), file(msaterm,d4_msaterm), []). fof(d4_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v6_trees_3(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( C = k4_trees_4(A,B) <=> ( ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) & B = D & k1_relat_1(C) = k13_trees_3(k2_funct_6(D)) ) & k1_funct_1(C,k1_xboole_0) = A & ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ( ~ r1_xreal_0(k3_finseq_1(B),D) => k5_trees_2(C,k12_finseq_1(k5_numbers,D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ) ), file(trees_4,d4_trees_4), []). fof(d5_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_circtrm1,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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( ( v5_msualg_1(D,A) & l3_msualg_1(D,A) ) => k6_circtrm1(A,B,C,D) = g3_msualg_1(k1_circtrm1(A,B,C),k4_circtrm1(A,B,C,D),k5_circtrm1(A,B,C,D)) ) ) ) ) ), file(circtrm1,d6_circtrm1), []). fof(d6_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => k1_msualg_1(A,B) = k1_funct_1(u2_msualg_1(A),B) ) ) ), file(msualg_1,d6_msualg_1), []). fof(d7_circtrm1,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) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B)) => ! [F] : ( F = k7_circtrm1(A,B,C,D,E) <=> ? [G] : ( m1_dtconstr(G,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) & G = D & F = k9_msaterm(A,B,C,G,E) ) ) ) ) ) ) ) ) ), file(circtrm1,d7_circtrm1), []). fof(d7_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => k2_msualg_1(A,B) = k1_funct_1(u3_msualg_1(A),B) ) ) ), file(msualg_1,d7_msualg_1), []). fof(d8_circtrm1,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] : ( m3_msaterm(C,A,B) => ! [D] : ( ( v5_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u4_msualg_1(k1_circtrm1(A,B,C),k6_circtrm1(A,B,C,D)))) => ! [F] : ( m3_pboole(F,u1_struct_0(A),B,u4_msualg_1(A,D)) => ( m1_circtrm1(F,A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_funct_1(B,G)) => ( r2_hidden(k1_trees_4(k4_tarski(H,G)),k9_trees_9(C)) => k1_funct_1(k1_funct_1(F,G),H) = k1_funct_1(E,k1_trees_4(k4_tarski(H,G))) ) ) ) ) ) ) ) ) ) ) ), file(circtrm1,d8_circtrm1), []). fof(d9_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( r1_facirc_1(A,B,C,D) <=> ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k1_funct_1(k9_facirc_1(A,B,C,E),D) = k1_funct_1(C,D) ) ) ) ) ) ), file(facirc_1,d9_facirc_1), []). fof(d9_msualg_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_msualg_1(A)) => ! [C] : ( l3_msualg_1(C,A) => k3_msualg_1(A,B,C) = k1_funct_1(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,C))),B) ) ) ) ), file(msualg_1,d9_msualg_1), []). 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_g1_msualg_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ( v1_msualg_1(g1_msualg_1(A,B,C,D)) & l1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ), file(msualg_1,g1_msualg_1), []). 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_k11_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k5_trees_3(A)) ) => m2_finseq_1(k11_trees_4(A,B),k2_trees_3) ) ), file(trees_4,k11_trees_4), []). 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_9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => m1_subset_1(k12_trees_9(A,B),k1_zfmisc_1(k9_trees_9(A))) ) ), file(trees_9,k12_trees_9), []). 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_k13_trees_9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ( v1_funct_1(k13_trees_9(A,B)) & v1_funct_2(k13_trees_9(A,B),k12_trees_9(A,B),k3_finseq_2(k9_trees_9(A))) & m2_relset_1(k13_trees_9(A,B),k12_trees_9(A,B),k3_finseq_2(k9_trees_9(A))) ) ) ), file(trees_9,k13_trees_9), []). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), []). fof(dt_k1_circtrm1,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)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( ~ v3_struct_0(k1_circtrm1(A,B,C)) & v1_msualg_1(k1_circtrm1(A,B,C)) & l1_msualg_1(k1_circtrm1(A,B,C)) ) ) ), file(circtrm1,k1_circtrm1), []). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), []). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), []). fof(dt_k1_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_pboole(B,u1_struct_0(A)) ) => m1_subset_1(k1_msaterm(A,B),k1_zfmisc_1(k5_trees_3(u1_struct_0(k5_msafree(A,B))))) ) ), file(msaterm,k1_msaterm), []). fof(dt_k1_msualg_1,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) ) => m2_finseq_2(k1_msualg_1(A,B),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) ), file(msualg_1,k1_msualg_1), []). fof(dt_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => ( v1_funct_1(k1_msualg_3(A,B,C,D,E)) & v1_funct_2(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m2_relset_1(k1_msualg_3(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ), file(msualg_3,k1_msualg_3), []). 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_3,axiom,( $true ), file(trees_3,k1_trees_3), []). 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_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), []). 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_msafree2,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k2_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) ), file(msafree2,k2_msafree2), []). fof(dt_k2_msaterm,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_struct_0(k2_msaterm(A,B,C),k5_msafree(A,B),k7_dtconstr(k5_msafree(A,B))) ) ), file(msaterm,k2_msaterm), []). 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_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => m1_pboole(k2_pboole(A,B,C),A) ) ), file(pboole,k2_pboole), []). 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_trees_3,axiom,( m1_subset_1(k2_trees_3,k1_zfmisc_1(k1_trees_3)) ), file(trees_3,k2_trees_3), []). 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_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_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k3_funct_6(A)) & v1_funct_1(k3_funct_6(A)) ) ) ), file(funct_6,k3_funct_6), []). fof(dt_k3_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k3_msualg_1(A,B,C),k2_relat_1(k6_pboole(u1_struct_0(A),u4_msualg_1(A,C)))) ) ), file(msualg_1,k3_msualg_1), []). fof(dt_k3_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)) ) ), file(trees_1,k3_trees_1), []). fof(dt_k4_card_3,axiom,( $true ), file(card_3,k4_card_3), []). fof(dt_k4_circtrm1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) & l3_msualg_1(D,A) ) => m1_pboole(k4_circtrm1(A,B,C,D),u1_struct_0(k1_circtrm1(A,B,C))) ) ), file(circtrm1,k4_circtrm1), []). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), []). fof(dt_k4_finseq_4,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & m1_relset_1(C,A,B) ) => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ), file(finseq_4,k4_finseq_4), []). fof(dt_k4_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => m1_subset_1(k4_msualg_1(A,B,C),k2_relat_1(u4_msualg_1(A,C))) ) ), file(msualg_1,k4_msualg_1), []). fof(dt_k4_tarski,axiom,( $true ), file(tarski,k4_tarski), []). fof(dt_k4_trees_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k5_numbers) ) => ( ~ v1_xboole_0(k4_trees_1(A,B)) & v1_trees_1(k4_trees_1(A,B)) ) ) ), file(trees_1,k4_trees_1), []). 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_circtrm1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) & v5_msualg_1(D,A) & l3_msualg_1(D,A) ) => m3_pboole(k5_circtrm1(A,B,C,D),u1_msualg_1(k1_circtrm1(A,B,C)),k8_pboole(u1_msualg_1(k1_circtrm1(A,B,C)),k3_finseq_2(u1_struct_0(k1_circtrm1(A,B,C))),u2_msualg_1(k1_circtrm1(A,B,C)),k6_pboole(u1_struct_0(k1_circtrm1(A,B,C)),k4_circtrm1(A,B,C,D))),k8_pboole(u1_msualg_1(k1_circtrm1(A,B,C)),u1_struct_0(k1_circtrm1(A,B,C)),u3_msualg_1(k1_circtrm1(A,B,C)),k4_circtrm1(A,B,C,D))) ) ), file(circtrm1,k5_circtrm1), []). fof(dt_k5_finseq_1,axiom,( $true ), file(finseq_1,k5_finseq_1), []). 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_msaterm,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & v2_relat_1(C) & m1_pboole(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,k1_funct_1(C,D)) ) => m1_dtconstr(k5_msaterm(A,B,C,D,E),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) ), file(msaterm,k5_msaterm), []). fof(dt_k5_msualg_1,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_msualg_1(A)) & l3_msualg_1(C,A) ) => ( v1_funct_1(k5_msualg_1(A,B,C)) & v1_funct_2(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) & m2_relset_1(k5_msualg_1(A,B,C),k3_msualg_1(A,B,C),k4_msualg_1(A,B,C)) ) ) ), file(msualg_1,k5_msualg_1), []). fof(dt_k5_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_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_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_circtrm1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) & v5_msualg_1(D,A) & l3_msualg_1(D,A) ) => ( v4_msualg_1(k6_circtrm1(A,B,C,D),k1_circtrm1(A,B,C)) & v5_msualg_1(k6_circtrm1(A,B,C,D),k1_circtrm1(A,B,C)) & l3_msualg_1(k6_circtrm1(A,B,C,D),k1_circtrm1(A,B,C)) ) ) ), file(circtrm1,k6_circtrm1), []). fof(dt_k6_circuit2,axiom,( ! [A,B,C] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) ) => m1_subset_1(k6_circuit2(A,B,C),k4_card_3(u4_msualg_1(A,B))) ) ), file(circuit2,k6_circuit2), []). 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_funct_3,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_funct_1(k6_funct_3(A,B)) & v1_funct_2(k6_funct_3(A,B),B,A) & m2_relset_1(k6_funct_3(A,B),B,A) ) ) ), file(funct_3,k6_funct_3), []). 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_msaterm,axiom,( ! [A,B,C,D] : ( ( ~ 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,k7_dtconstr(k5_msafree(A,B))) & m1_msaterm(D,A,B,C) ) => m1_dtconstr(k6_msaterm(A,B,C,D),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ), file(msaterm,k6_msaterm), []). fof(dt_k6_partfun1,axiom,( ! [A] : ( v1_partfun1(k6_partfun1(A),A,A) & m2_relset_1(k6_partfun1(A),A,A) ) ), file(partfun1,k6_partfun1), []). 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_relat_1,axiom,( ! [A] : v1_relat_1(k6_relat_1(A)) ), file(relat_1,k6_relat_1), []). fof(dt_k6_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => m2_subset_1(k6_trees_1(A),k1_numbers,k5_numbers) ) ), file(trees_1,k6_trees_1), []). fof(dt_k7_circtrm1,axiom,( $true ), file(circtrm1,k7_circtrm1), []). 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_msaterm,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,k1_msaterm(A,B)) ) => m1_subset_1(k7_msaterm(A,B,C),u1_struct_0(A)) ) ), file(msaterm,k7_msaterm), []). 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_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_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), []). fof(dt_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => ( v2_relat_1(k8_pboole(A,B,C,D)) & m1_pboole(k8_pboole(A,B,C,D),A) ) ) ), file(pboole,k8_pboole), []). fof(dt_k9_facirc_1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_msafree2(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k4_card_3(u4_msualg_1(A,B))) & m1_subset_1(D,k5_numbers) ) => m1_subset_1(k9_facirc_1(A,B,C,D),k4_card_3(u4_msualg_1(A,B))) ) ), file(facirc_1,k9_facirc_1), []). fof(dt_k9_msaterm,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & l3_msualg_1(B,A) & m4_msaterm(C,A,B) & m1_subset_1(D,k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) & m3_pboole(E,u1_struct_0(A),C,u4_msualg_1(A,B)) ) => m1_subset_1(k9_msaterm(A,B,C,D,E),k1_funct_1(u4_msualg_1(A,B),k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),D))) ) ), file(msaterm,k9_msaterm), []). fof(dt_k9_trees_9,axiom,( $true ), file(trees_9,k9_trees_9), []). 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_circtrm1,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m3_msaterm(C,A,B) & v5_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) & m1_subset_1(E,k4_card_3(u4_msualg_1(k1_circtrm1(A,B,C),k6_circtrm1(A,B,C,D)))) ) => ! [F] : ( m1_circtrm1(F,A,B,C,D,E) => m3_pboole(F,u1_struct_0(A),B,u4_msualg_1(A,D)) ) ) ), file(circtrm1,m1_circtrm1), []). 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_msaterm,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,k7_dtconstr(k5_msafree(A,B))) ) => ! [D] : ( m1_msaterm(D,A,B,C) => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ), file(msaterm,m1_msaterm), []). 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_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_msaterm,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)) ) => ! [C] : ( m2_msaterm(C,A,B) => m1_dtconstr(C,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ), file(msaterm,m2_msaterm), []). 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_msaterm,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)) ) => ! [C] : ( m3_msaterm(C,A,B) => ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) ) ) ), file(msaterm,m3_msaterm), []). 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_m3_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m3_trees_3(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) ) ) ), file(trees_3,m3_trees_3), []). fof(dt_m4_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ( v2_relat_1(C) & m1_pboole(C,u1_struct_0(A)) ) ) ) ), file(msaterm,m4_msaterm), []). 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_circtrm1,axiom,( ! [A,B,C,D,E] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m3_msaterm(C,A,B) & v5_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) & m1_subset_1(E,k4_card_3(u4_msualg_1(k1_circtrm1(A,B,C),k6_circtrm1(A,B,C,D)))) ) => ? [F] : m1_circtrm1(F,A,B,C,D,E) ) ), file(circtrm1,m1_circtrm1), []). 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_msaterm,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,k7_dtconstr(k5_msafree(A,B))) ) => ? [D] : m1_msaterm(D,A,B,C) ) ), file(msaterm,m1_msaterm), []). 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_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_msaterm,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)) ) => ? [C] : m2_msaterm(C,A,B) ) ), file(msaterm,m2_msaterm), []). 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_msaterm,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)) ) => ? [C] : m3_msaterm(C,A,B) ) ), file(msaterm,m3_msaterm), []). 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_m3_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ? [B] : m3_trees_3(B,A) ) ), file(trees_3,m3_trees_3), []). fof(existence_m4_msaterm,axiom,( ! [A,B] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : m4_msaterm(C,A,B) ) ), file(msaterm,m4_msaterm), []). 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_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(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_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(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_membered,axiom,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), []). 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_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_circtrm1,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)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( ~ v3_struct_0(k1_circtrm1(A,B,C)) & v1_msualg_1(k1_circtrm1(A,B,C)) & v2_msafree2(k1_circtrm1(A,B,C)) & v1_circcomb(k1_circtrm1(A,B,C)) & v1_instalg1(k1_circtrm1(A,B,C)) ) ) ), file(circtrm1,fc1_circtrm1), []). fof(fc1_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_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_instalg1,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(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ), file(instalg1,fc1_instalg1), []). fof(fc1_msaterm,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(msaterm,fc1_msaterm), []). 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_msualg_2,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & v2_relat_1(C) & m1_pboole(C,A) ) => ( v1_relat_1(k2_pboole(A,B,C)) & v2_relat_1(k2_pboole(A,B,C)) & v1_funct_1(k2_pboole(A,B,C)) ) ) ), file(msualg_2,fc1_msualg_2), []). fof(fc1_pboole,axiom,( ! [A,B] : ( ( v2_relat_1(B) & m1_pboole(B,A) ) => ( v1_relat_1(k6_pboole(A,B)) & v2_relat_1(k6_pboole(A,B)) & ~ v3_relat_1(k6_pboole(A,B)) & v1_funct_1(k6_pboole(A,B)) ) ) ), file(pboole,fc1_pboole), []). fof(fc1_struct_0,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) ), file(struct_0,fc1_struct_0), []). fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), []). fof(fc1_trees_3,axiom,( ~ v1_xboole_0(k1_trees_3) ), file(trees_3,fc1_trees_3), []). fof(fc1_trees_9,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)) & v1_trees_9(k1_trees_4(A)) ) ), file(trees_9,fc1_trees_9), []). fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), []). fof(fc21_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(k3_trees_1(A)) & v1_finset_1(k3_trees_1(A)) ) ) ), file(trees_3,fc21_trees_3), []). fof(fc23_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ( ~ v1_xboole_0(k13_trees_3(A)) & v1_finset_1(k13_trees_3(A)) & v1_trees_1(k13_trees_3(A)) ) ) ), file(trees_3,fc23_trees_3), []). fof(fc26_trees_3,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_trees_3(A)) ) => ( ~ v1_xboole_0(k1_relat_1(B)) & v1_finset_1(k1_relat_1(B)) & v1_trees_1(k1_relat_1(B)) ) ) ), file(trees_3,fc26_trees_3), []). fof(fc2_circtrm1,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)) & m3_msaterm(C,A,B) ) => ( ~ v3_struct_0(k1_circtrm1(A,B,C)) & v1_msualg_1(k1_circtrm1(A,B,C)) & ~ v2_msualg_1(k1_circtrm1(A,B,C)) & v2_msafree2(k1_circtrm1(A,B,C)) & v1_circcomb(k1_circtrm1(A,B,C)) & v1_instalg1(k1_circtrm1(A,B,C)) ) ) ), file(circtrm1,fc2_circtrm1), []). 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_funct_1,axiom,( ! [A] : ( v1_relat_1(k6_relat_1(A)) & v1_funct_1(k6_relat_1(A)) ) ), file(funct_1,fc2_funct_1), []). fof(fc2_membered,axiom, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), []). fof(fc2_msaterm,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_xboole_0(k1_msaterm(A,B)) & v3_trees_3(k1_msaterm(A,B)) ) ) ), file(msaterm,fc2_msaterm), []). fof(fc2_msualg_2,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & v2_relat_1(C) & m1_pboole(C,A) ) => ( v1_relat_1(k2_pboole(A,C,B)) & v2_relat_1(k2_pboole(A,C,B)) & v1_funct_1(k2_pboole(A,C,B)) ) ) ), file(msualg_2,fc2_msualg_2), []). fof(fc2_pboole,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & v2_relat_1(B) & m1_pboole(B,A) & m1_subset_1(C,A) ) => ~ v1_xboole_0(k1_funct_1(B,C)) ) ), file(pboole,fc2_pboole), []). fof(fc2_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) ), file(subset_1,fc2_subset_1), []). fof(fc2_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_trees_3,axiom,( ~ v1_xboole_0(k2_trees_3) ), file(trees_3,fc2_trees_3), []). fof(fc2_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) & v1_trees_2(k1_relat_1(A)) & v2_trees_9(k1_relat_1(A)) ) ) ), file(trees_9,fc2_trees_9), []). 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_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_fraenkel(k4_card_3(A)) ) ), file(card_3,fc3_card_3), []). fof(fc3_circtrm1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m3_msaterm(C,A,B) & m1_subset_1(D,u1_msualg_1(k1_circtrm1(A,B,C))) ) => ( v1_relat_1(k1_msualg_1(k1_circtrm1(A,B,C),D)) & v1_funct_1(k1_msualg_1(k1_circtrm1(A,B,C),D)) & v1_finset_1(k1_msualg_1(k1_circtrm1(A,B,C),D)) & v1_finseq_1(k1_msualg_1(k1_circtrm1(A,B,C),D)) & v6_trees_3(k1_msualg_1(k1_circtrm1(A,B,C),D)) ) ) ), file(circtrm1,fc3_circtrm1), []). 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_msualg_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ( ~ v3_struct_0(g1_msualg_1(A,B,C,D)) & v1_msualg_1(g1_msualg_1(A,B,C,D)) ) ) ), file(msualg_2,fc3_msualg_2), []). fof(fc3_subset_1,axiom,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), []). fof(fc3_trees_3,axiom, ( ~ v1_xboole_0(k1_trees_3) & v1_trees_3(k1_trees_3) ), file(trees_3,fc3_trees_3), []). fof(fc3_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v4_trees_9(A) ) => ( ~ v1_xboole_0(k1_relat_1(A)) & v1_trees_1(k1_relat_1(A)) & v2_trees_9(k1_relat_1(A)) ) ) ), file(trees_9,fc3_trees_9), []). 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_card_3,axiom,( ! [A,B,C] : ( ( v1_setfam_1(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( ~ v1_xboole_0(k4_card_3(C)) & v1_fraenkel(k4_card_3(C)) ) ) ), file(card_3,fc4_card_3), []). fof(fc4_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_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), []). fof(fc4_trees_3,axiom, ( ~ v1_xboole_0(k2_trees_3) & v1_trees_3(k2_trees_3) & v2_trees_3(k2_trees_3) ), file(trees_3,fc4_trees_3), []). fof(fc5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k4_card_3(A)) & v1_fraenkel(k4_card_3(A)) ) ) ), file(card_3,fc5_card_3), []). fof(fc5_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_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(fc5_trees_9,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)) & v3_trees_9(k5_trees_2(A,B)) & v4_trees_9(k5_trees_2(A,B)) ) ) ), file(trees_9,fc5_trees_9), []). fof(fc6_circtrm1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) & v5_msualg_1(D,A) & l3_msualg_1(D,A) ) => ( v1_relat_1(k4_circtrm1(A,B,C,D)) & v2_relat_1(k4_circtrm1(A,B,C,D)) & ~ v3_relat_1(k4_circtrm1(A,B,C,D)) & v1_funct_1(k4_circtrm1(A,B,C,D)) ) ) ), file(circtrm1,fc6_circtrm1), []). 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_msualg_2,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(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) & v5_msualg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ), file(msualg_2,fc6_msualg_2), []). 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_circtrm1,axiom,( ! [A,B,C,D] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v2_relat_1(B) & m1_pboole(B,u1_struct_0(A)) & m3_msaterm(C,A,B) & v5_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ( v4_msualg_1(k6_circtrm1(A,B,C,D),k1_circtrm1(A,B,C)) & v5_msualg_1(k6_circtrm1(A,B,C,D),k1_circtrm1(A,B,C)) & v4_msafree2(k6_circtrm1(A,B,C,D),k1_circtrm1(A,B,C)) ) ) ), file(circtrm1,fc7_circtrm1), []). fof(fc7_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ), file(funcop_1,fc7_funcop_1), []). fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) ), file(membered,fc7_membered), []). 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(fc8_circtrm1,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_finseq_1(D,k1_msaterm(B,C)) ) => ( v1_relat_1(k4_trees_4(A,D)) & v1_funct_1(k4_trees_4(A,D)) & v1_finset_1(k4_trees_4(A,D)) & v3_trees_2(k4_trees_4(A,D)) & v3_trees_9(k4_trees_4(A,D)) & v4_trees_9(k4_trees_4(A,D)) ) ) ), file(circtrm1,fc8_circtrm1), []). fof(fc8_funcop_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_funct_1(k5_relat_1(B,A)) & v1_funcop_1(k5_relat_1(B,A)) ) ) ), file(funcop_1,fc8_funcop_1), []). fof(fc8_membered,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_membered(k1_tarski(A)) & v2_membered(k1_tarski(A)) ) ) ), file(membered,fc8_membered), []). 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_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ( ~ v1_xboole_0(k9_trees_9(A)) & v3_trees_3(k9_trees_9(A)) ) ) ), file(trees_9,fc8_trees_9), []). fof(fc9_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) ), file(finseq_1,fc9_finseq_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_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v1_finset_1(k1_tarski(A)) & v3_trees_3(k1_tarski(A)) ) ) ), file(trees_9,fc9_trees_9), []). 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_g1_msualg_1,axiom,( ! [A,B,C,D] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k3_finseq_2(A)) & m1_relset_1(C,B,k3_finseq_2(A)) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_relset_1(D,B,A) ) => ! [E,F,G,H] : ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ), file(msualg_1,g1_msualg_1), []). 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_pboole,axiom,( ! [A,B,C] : ( ( m1_pboole(B,A) & m1_pboole(C,A) ) => k2_pboole(A,B,B) = B ) ), file(pboole,k2_pboole), []). fof(rc1_arytm_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), []). fof(rc1_circcomb,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(circcomb,rc1_circcomb), []). 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_fraenkel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_fraenkel(A) ) ), file(fraenkel,rc1_fraenkel), []). fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ), file(funcop_1,rc1_funcop_1), []). fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), []). fof(rc1_instalg1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v1_instalg1(A) ) ), file(instalg1,rc1_instalg1), []). 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_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & v1_msualg_1(A) ) ), file(msualg_1,rc1_msualg_1), []). fof(rc1_pboole,axiom,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), []). fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), []). fof(rc1_trees_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ), file(trees_2,rc1_trees_2), []). fof(rc1_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_3(A) & v2_trees_3(A) ) ), file(trees_3,rc1_trees_3), []). fof(rc1_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v1_trees_9(A) ) ), file(trees_9,rc1_trees_9), []). fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), []). fof(rc2_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & v1_msualg_1(A) & v2_msualg_1(A) ) ), file(msualg_1,rc2_msualg_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_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), []). fof(rc2_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) ), file(trees_3,rc2_trees_3), []). fof(rc2_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & ~ v1_trees_9(A) ) ), file(trees_9,rc2_trees_9), []). fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_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_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), []). fof(rc3_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v3_struct_0(A) & v1_msualg_1(A) & ~ v2_msualg_1(A) ) ), file(msualg_1,rc3_msualg_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_trees_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_trees_3)) & ~ v1_xboole_0(A) & v1_trees_3(A) & v2_trees_3(A) ) ), file(trees_3,rc3_trees_3), []). fof(rc3_trees_9,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & v1_trees_2(A) & v2_trees_9(A) ) ), file(trees_9,rc3_trees_9), []). 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_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_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v3_trees_9(A) & v4_trees_9(A) ) ), file(trees_9,rc4_trees_9), []). 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_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(rc5_trees_9,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(trees_9,rc5_trees_9), []). 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_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(rc6_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(trees_9,rc6_trees_9), []). 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_k11_trees_4,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k5_trees_3(A)) ) => k11_trees_4(A,B) = k2_funct_6(B) ) ), file(trees_4,k11_trees_4), []). 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_k1_msualg_3,axiom,( ! [A,B,C,D,E] : ( ( ~ v1_xboole_0(A) & m1_pboole(B,A) & m1_pboole(C,A) & m3_pboole(D,A,B,C) & m1_subset_1(E,A) ) => k1_msualg_3(A,B,C,D,E) = k1_funct_1(D,E) ) ), file(msualg_3,k1_msualg_3), []). 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_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), []). fof(redefinition_k2_msaterm,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)) ) => k2_msaterm(A,B,C) = k6_msafree(A,B,C) ) ), file(msaterm,k2_msaterm), []). 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_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_k5_numbers,axiom,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), []). fof(redefinition_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), []). fof(redefinition_k6_funct_3,axiom,( ! [A,B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k6_funct_3(A,B) = k6_relat_1(B) ) ), file(funct_3,k6_funct_3), []). fof(redefinition_k6_msaterm,axiom,( ! [A,B,C,D] : ( ( ~ 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,k7_dtconstr(k5_msafree(A,B))) & m1_msaterm(D,A,B,C) ) => k6_msaterm(A,B,C,D) = k4_trees_4(C,D) ) ), file(msaterm,k6_msaterm), []). fof(redefinition_k6_partfun1,axiom,( ! [A] : k6_partfun1(A) = k6_relat_1(A) ), file(partfun1,k6_partfun1), []). 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_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_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), []). fof(redefinition_k8_pboole,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & v2_relat_1(D) & m1_pboole(D,B) ) => k8_pboole(A,B,C,D) = k5_relat_1(C,D) ) ), file(pboole,k8_pboole), []). fof(redefinition_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_m3_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m3_trees_3(B,A) <=> m1_subset_1(B,A) ) ) ), file(trees_3,m3_trees_3), []). 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(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(s1_msaterm__e5_41__circtrm1,axiom,( ! [A,B,C,D,E,F] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m4_msaterm(C,A,B) & m3_msaterm(D,A,C) & m1_subset_1(E,k4_card_3(u4_msualg_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B)))) & m1_circtrm1(F,A,C,D,B,E) ) => ( ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_funct_1(C,G)) => ( r2_hidden(k1_trees_4(k4_tarski(H,G)),k9_trees_9(D)) => ( r1_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(k1_trees_4(k4_tarski(H,G))))),k1_trees_4(k4_tarski(H,G))) & k1_funct_1(k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(k1_trees_4(k4_tarski(H,G))))),k1_trees_4(k4_tarski(H,G))) = k7_circtrm1(A,B,C,k1_trees_4(k4_tarski(H,G)),F) ) ) ) ) & ! [G] : ( m1_subset_1(G,u1_msualg_1(A)) => ! [H] : ( m1_msaterm(H,A,C,k2_msaterm(A,C,G)) => ( ! [I] : ( m1_dtconstr(I,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => ( r2_hidden(I,k2_relat_1(H)) => ( r2_hidden(I,k9_trees_9(D)) => ( r1_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(I))),I) & k1_funct_1(k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(I))),I) = k7_circtrm1(A,B,C,I,F) ) ) ) ) => ( r2_hidden(k4_trees_4(k4_tarski(G,u1_struct_0(A)),H),k9_trees_9(D)) => ( r1_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(k4_trees_4(k4_tarski(G,u1_struct_0(A)),H)))),k4_trees_4(k4_tarski(G,u1_struct_0(A)),H)) & k1_funct_1(k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(k4_trees_4(k4_tarski(G,u1_struct_0(A)),H)))),k4_trees_4(k4_tarski(G,u1_struct_0(A)),H)) = k7_circtrm1(A,B,C,k4_trees_4(k4_tarski(G,u1_struct_0(A)),H),F) ) ) ) ) ) ) => ! [G] : ( m1_dtconstr(G,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => ( r2_hidden(G,k9_trees_9(D)) => ( r1_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(G))),G) & k1_funct_1(k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,k6_trees_1(k1_relat_1(G))),G) = k7_circtrm1(A,B,C,G,F) ) ) ) ) ) ), file(circtrm1,s1_msaterm__e5_41__circtrm1), []). fof(s2_finseq_1__e24_41_2__circtrm1,axiom,( ! [A,B,C,D,E,F,G,H] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) & v5_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) & m4_msaterm(C,A,B) & m3_msaterm(D,A,C) & m1_subset_1(E,k4_card_3(u4_msualg_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B)))) & m1_subset_1(F,u1_msualg_1(A)) & m1_msaterm(G,A,C,k2_msaterm(A,C,F)) & m2_subset_1(H,k1_numbers,k5_numbers) ) => ? [I] : ( v1_relat_1(I) & v1_funct_1(I) & v1_finseq_1(I) & k3_finseq_1(I) = k3_finseq_1(G) & ! [J] : ( m2_subset_1(J,k1_numbers,k5_numbers) => ( r2_hidden(J,k2_finseq_1(k3_finseq_1(G))) => k1_funct_1(I,J) = k1_funct_1(k9_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,H),k1_funct_1(G,J)) ) ) ) ) ), file(circtrm1,s2_finseq_1__e24_41_2__circtrm1), []). 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(t10_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => k1_funct_1(k6_circuit2(A,B,C),k2_msualg_1(A,D)) = k1_funct_1(k5_msualg_1(A,D,B),k5_relat_1(k1_msualg_1(A,D),C)) ) ) ) ) ), file(facirc_1,t10_facirc_1), []). fof(t10_trees_4,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => k1_relat_1(k4_trees_4(A,B)) = k13_trees_3(k2_funct_6(B)) ) ), file(trees_4,t10_trees_4), []). fof(t11_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => k9_facirc_1(A,B,C,0) = C ) ) ) ), file(facirc_1,t11_facirc_1), []). fof(t129_zfmisc_1,axiom,( ! [A,B,C,D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,k1_tarski(D))) <=> ( r2_hidden(A,C) & B = D ) ) ), file(zfmisc_1,t129_zfmisc_1), []). fof(t12_circtrm1,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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( r2_hidden(D,k2_msafree2(k1_circtrm1(A,B,C))) <=> ( r2_hidden(D,k9_trees_9(C)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,k1_funct_1(B,E)) & D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) ) ), file(circtrm1,t12_circtrm1), []). fof(t12_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => k9_facirc_1(A,B,C,k1_nat_1(D,1)) = k6_circuit2(A,B,k9_facirc_1(A,B,C,D)) ) ) ) ) ), file(facirc_1,t12_facirc_1), []). fof(t13_circtrm1,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] : ( m3_msaterm(C,A,B) => ! [D] : ( m1_subset_1(D,u1_msualg_1(k1_circtrm1(A,B,C))) => D = k4_trees_4(k1_funct_1(D,k1_xboole_0),k1_msualg_1(k1_circtrm1(A,B,C),D)) ) ) ) ) ), file(circtrm1,t13_circtrm1), []). fof(t13_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( m2_subset_1(D,k1_numbers,k5_numbers) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => k9_facirc_1(A,B,C,k1_nat_1(D,E)) = k9_facirc_1(A,B,k9_facirc_1(A,B,C,D),E) ) ) ) ) ) ), file(facirc_1,t13_facirc_1), []). 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_circtrm1,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] : ( ( v5_msualg_1(C,A) & v4_msafree2(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_msaterm(D,A,B) => ! [E] : ( m1_subset_1(E,u1_msualg_1(k1_circtrm1(A,B,D))) => ! [F] : ( m1_subset_1(F,u1_msualg_1(A)) => ( k1_funct_1(E,k1_xboole_0) = k4_tarski(F,u1_struct_0(A)) => k5_msualg_1(k1_circtrm1(A,B,D),E,k6_circtrm1(A,B,D,C)) = k5_msualg_1(A,F,C) ) ) ) ) ) ) ) ), file(circtrm1,t17_circtrm1), []). fof(t17_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( r1_facirc_1(A,B,C,D) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => r1_facirc_1(A,B,k9_facirc_1(A,B,C,E),D) ) ) ) ) ) ), file(facirc_1,t17_facirc_1), []). fof(t17_trees_4,axiom,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k1_trees_4(A) = k4_trees_4(B,C) & v6_trees_3(C) ) => ( A = B & C = k1_xboole_0 ) ) ) ), file(trees_4,t17_trees_4), []). fof(t18_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( r2_hidden(D,k2_msafree2(A)) => r1_facirc_1(A,B,C,D) ) ) ) ) ), file(facirc_1,t18_facirc_1), []). fof(t19_facirc_1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_msualg_1(A)) => ( ! [E] : ( r2_hidden(E,k2_relat_1(k1_msualg_1(A,D))) => r1_facirc_1(A,B,C,E) ) => r1_facirc_1(A,B,k6_circuit2(A,B,C),k2_msualg_1(A,D)) ) ) ) ) ) ), file(facirc_1,t19_facirc_1), []). fof(t1_circtrm1,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) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => ! [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) => ( E = D => k7_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E) = k7_msaterm(A,C,D) ) ) ) ) ) ) ), file(circtrm1,t1_circtrm1), []). fof(t1_numerals,axiom,( m1_subset_1(0,k5_numbers) ), file(numerals,t1_numerals), []). fof(t1_subset,axiom,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), []). fof(t20_trees_9,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r2_hidden(A,k9_trees_9(B)) <=> ? [C] : ( m3_trees_3(C,B) & ? [D] : ( m1_trees_1(D,k1_relat_1(C)) & A = k5_trees_2(C,D) ) ) ) ) ), file(trees_9,t20_trees_9), []). fof(t22_msaterm,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_msaterm(D,A,B,k2_msaterm(A,B,C)) => ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,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)) => m1_dtconstr(k1_funct_1(D,E),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ) ) ) ), file(msaterm,t22_msaterm), []). fof(t22_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ~ ( A != 0 & ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => A != k1_nat_1(B,1) ) ) ) ), file(nat_1,t22_nat_1), []). fof(t23_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), []). fof(t23_msaterm,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_msaterm(D,A,B,k2_msaterm(A,B,C)) => ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ( F = k1_funct_1(D,E) => ( F = k4_finseq_4(k5_numbers,k1_msaterm(A,B),D,E) & k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) & k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) ) ) ) ) ) ), file(msaterm,t23_msaterm), []). fof(t24_msaterm,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) ) => ~ ( ( k3_finseq_1(D) = k3_finseq_1(k1_msualg_1(A,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)) & ! [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ~ ( F = k1_funct_1(D,E) & k7_msaterm(A,B,F) = k1_funct_1(k1_msualg_1(A,C),E) ) ) ) ) | ! [E] : ( m2_subset_1(E,k1_numbers,k5_numbers) => ~ ( r2_hidden(E,k4_finseq_1(D)) & ! [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ~ ( F = k1_funct_1(D,E) & k7_msaterm(A,B,F) = k4_finseq_4(k5_numbers,u1_struct_0(A),k1_msualg_1(A,C),E) ) ) ) ) ) & ~ m1_msaterm(D,A,B,k2_msaterm(A,B,C)) ) ) ) ) ) ), file(msaterm,t24_msaterm), []). fof(t25_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) = 0 <=> A = k1_xboole_0 ) ) ), file(finseq_1,t25_finseq_1), []). fof(t25_trees_9,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(C) & v3_trees_3(C) ) => ( r2_hidden(A,k12_trees_9(C,B)) <=> ? [D] : ( m3_trees_3(D,C) & ? [E] : ( m1_trees_1(E,k1_relat_1(D)) & A = k5_trees_2(D,E) & ~ ( r2_hidden(E,k3_trees_1(k1_relat_1(D))) & ~ r2_hidden(k1_funct_1(D,E),B) ) ) ) ) ) ), file(trees_9,t25_trees_9), []). fof(t27_msaterm,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( v2_relat_1(C) & m1_pboole(C,u1_struct_0(A)) ) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,C)),k5_trees_3(u1_struct_0(k5_msafree(A,C))),k1_msaterm(A,C)) => m1_dtconstr(D,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) ) ) ) ) ), file(msaterm,t27_msaterm), []). fof(t28_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( r1_xreal_0(A,B) & ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => B != k2_xcmplx_0(A,C) ) ) ) ) ), file(nat_1,t28_nat_1), []). fof(t2_subset,axiom,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), []). fof(t31_funct_6,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k1_relat_1(B)) & C = k1_funct_1(B,A) ) => ( r2_hidden(A,k1_relat_1(k2_funct_6(B))) & k1_funct_1(k2_funct_6(B),A) = k1_relat_1(C) & r2_hidden(A,k1_relat_1(k3_funct_6(B))) & k1_funct_1(k3_funct_6(B),A) = k2_relat_1(C) ) ) ) ) ), file(funct_6,t31_funct_6), []). fof(t34_funct_1,axiom,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k6_relat_1(A) <=> ( k1_relat_1(B) = A & ! [C] : ( r2_hidden(C,A) => k1_funct_1(B,C) = C ) ) ) ) ), file(funct_1,t34_funct_1), []). fof(t38_nat_1,axiom,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A) <=> r1_xreal_0(A,B) ) ) ) ), file(nat_1,t38_nat_1), []). fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A ), file(boole,t3_boole), []). 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(t42_msaterm,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) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(C,E)) => k9_msaterm(A,B,C,k5_msaterm(A,B,C,E,F),D) = k8_funct_2(k1_funct_1(C,E),k1_funct_1(u4_msualg_1(A,B),E),k1_msualg_3(u1_struct_0(A),C,u4_msualg_1(A,B),D,E),F) ) ) ) ) ) ) ), file(msaterm,t42_msaterm), []). fof(t43_msaterm,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) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_pboole(D,u1_struct_0(A),C,u4_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u1_msualg_1(A)) => ! [F] : ( m1_msaterm(F,A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ( ( k3_finseq_1(G) = k3_finseq_1(F) & ! [H] : ( m2_subset_1(H,k1_numbers,k5_numbers) => ( r2_hidden(H,k4_finseq_1(F)) => ! [I] : ( m1_dtconstr(I,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C))) => ( I = k1_funct_1(F,H) => k1_funct_1(G,H) = k9_msaterm(A,B,C,I,D) ) ) ) ) ) => k9_msaterm(A,B,C,k6_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),k2_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,B),C),E),F),D) = k1_funct_1(k5_msualg_1(A,E,B),G) ) ) ) ) ) ) ) ) ), file(msaterm,t43_msaterm), []). fof(t46_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), []). fof(t47_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k7_finseq_1(A,k1_xboole_0) = A & k7_finseq_1(k1_xboole_0,A) = A ) ) ), file(finseq_1,t47_finseq_1), []). 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(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 ), file(boole,t4_boole), []). fof(t4_circtrm1,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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(k1_circtrm1(A,B,C))) => m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) & ! [D] : ( r2_hidden(D,u1_msualg_1(k1_circtrm1(A,B,C))) => m2_msaterm(D,A,B) ) ) ) ) ) ), file(circtrm1,t4_circtrm1), []). fof(t4_circuit1,axiom,( ! [A] : ( ( ~ v3_struct_0(A) & ~ v2_msualg_1(A) & v2_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,k4_card_3(u4_msualg_1(A,B))) => k1_relat_1(C) = u1_struct_0(A) ) ) ) ), file(circuit1,t4_circuit1), []). fof(t4_msaterm,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,k1_funct_1(B,C)) => m1_dtconstr(k1_trees_4(k4_tarski(D,C)),u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) ) ) ), file(msaterm,t4_msaterm), []). fof(t4_subset,axiom,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), []). fof(t5_subset,axiom,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), []). fof(t5_trees_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( k1_relat_1(A) = k2_trees_1(0) => A = k1_trees_4(k1_funct_1(A,k1_xboole_0)) ) ) ), file(trees_4,t5_trees_4), []). fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), []). fof(t79_trees_1,axiom,( k6_trees_1(k2_trees_1(0)) = 0 ), file(trees_1,t79_trees_1), []). fof(t7_boole,axiom,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), []). fof(t80_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( k6_trees_1(A) = 0 => A = k2_trees_1(0) ) ) ), file(trees_1,t80_trees_1), []). fof(t81_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ~ ( r2_hidden(B,k2_relat_1(A)) & r1_xreal_0(k6_trees_1(k13_trees_3(A)),k6_trees_1(B)) ) ) ) ), file(trees_3,t81_trees_3), []). fof(t8_boole,axiom,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), []). fof(t8_msaterm,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] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(B,D)) => m1_dtconstr(k1_trees_4(k4_tarski(E,D)),u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B)))),k1_msaterm(A,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),B))) ) ) ) ) ) ), file(msaterm,t8_msaterm), []). fof(t9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), []).